The study of electrical and computer engineering (ECE) is introduced, both at the undergraduate and the graduate level, and the various applications of the subject are presented. Firms and institutes are visited and guest lecturers are invited to outline the diverse roles that electrical and computer engineers have in the job market. Professional societies in this field of engineering are presented, as well as the rules of ethics that they have adopted. Assignments are given to give further insight into the studies and the jobs that they lead to.

Concepts, units, scales and dimensions. Vectors. Kinematics of particles. Particle dynamics, inertia, forces and Newton's laws. Friction. Work and energy, conservation of energy. Momentum, collisions. Systems of particles, center of mass. Rotation of a rigid body. Angular momentum and moment of inertia. Statics. Gravity. Solids and fluids, Bernoulli's equation. Oscillations: Simple, damped and forced. Waves. Sound. Temperature. Ideal gas. Heat and the first law of thermodynamics. Kinetic theory of gases. Entropy and the second law of thermodynamics. Home problems: Once a week the students have to solve homeproblems on the website MasteringPhysics.

Laboratory work: Three exercises, mainly centered on mechanics, where students are trained in handling physical instruments, collecting and inspecting data. Students hand in their lab notebooks for a grade.

Note that the textbook is accessible to students via Canvas free of charge.

This is a foundational course in single variable calculus. The prerequisites are high school courses on algebra, trigonometry. derivatives, and integrals. The course aims to create a foundation for understanding of subjects such as natural and physical sciences, engineering, economics, and computer science. Topics of the course include the following:

• Real numbers.
• Limits and continuous functions.
• Differentiable functions, rules for derivatives, derivatives of higher order, applications of differential calculus (extremal value problems, linear approximation).
• Transcendental functions.
• Mean value theorem, theorems of l'Hôpital and Taylor.
• Integration, the definite integral and rules/techniques of integration, primitives, improper integrals.
• Fundamental theorem of calculus.
• Applications of integral calculus: Arc length, area, volume, centroids.
• Ordinary differential equations: First-order separable and homogeneous differential equations, first-order linear equations, second-order linear equations with constant coefficients.
• Sequences and series, convergence tests.
• Power series, Taylor series.

Basics of linear algebra over the reals.  

Subject matter: Systems of linear equations, matrices, Gauss-Jordan reduction.  Vector spaces and their subspaces.  Linearly independent sets, bases and dimension.  Linear maps, range space and nullk space.  The dot product, length and angle measures.  Volumes in higher dimension and the cross product in threedimensional space.  Flats, parametric descriptions and descriptions by equations.  Orthogonal projections and orthonormal bases.  Gram-Schmidt orthogonalization.  Determinants and inverses of matrices.  Eigenvalues, eigenvectors and diagonalization.

Note: Only one course of either TÖL101G Tölvunarfræði 1 or TÖL105G Tölvunarfræði 1a can count towards the BS degree.

The Java programming language is used to introduce basic concepts in computer programming: Expressions and statements, textual and numeric data types, conditions and loops, arrays, methods, classes and objects, input and output. Programming and debugging skills are practiced in quizzes and projects throughout the semester.

The programming language Java will be used in the course. Various data structures, algorithms and abstract data types will be covered. Among the data types and structures covered are lists, stacks, queues, priority queues, trees, binary trees, binary search trees and heaps along with related algorithms. Various search and sort algorithms will be covered. Algorithms will be analysed for their space and time complexity. There will be programming assignments in Java using the given data structures and algorithms. There will be many small assignments.

Teaching takes 12 weeks. Charge and electric field. Gauss' law. Electric potential. Capacitors and dielectrics. Electric currents and resistance. Circuits. Magnetic fields. The laws of Ampère and Faraday. Induction. Electric oscillation and alternating currents. Maxwell's equations. Electromagnetic waves. Reflection and refraction. Lenses and mirrors. Wave optics. Four laboratory exercises in optics and electromagnetism.

Definitions and basic concepts. Kirchoff's laws, mesh- and node-equations. Circuits with resistance, matrix representation. Dependent sources. Thevenin-Norton equivalent circuit theorems. Circuits with resistance, capacitance, inductance and mutual inductance. Time domain analysis. Initial conditions. Zero input solutions, zero state solutions, transients and steady state. Impulse response, convolution. Analysis of second order circuits. Systems with sinusoidal inputs. Computer exercises with PSpice and Matlab.

Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobi matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flow. Cylindrical and spherical coordinates. Taylor polynomials. Extreme values and the classification of stationary points. Extreme value problems with constraints. Implicit functions and local inverses. Line integrals, primitive functions and exact differential equations. Double integrals. Improper integrals. Green's theorem. Simply connected domains. Change of variables in double integrals. Multiple integrals. Change of variables in multiple integrals. Surface integrals. Integration of vector fields. The theorems of Stokes and Gauss.

Students will learn digital design principles and practice. Design is based on standard MSI and LSI devices or equivalent building blocks such as counters, shift registers, adders, and ROM. The design and analysis of combinatorial circuits for basic arithmetic is emphasized as well as the design an analysis of synchronous and asynchronous sequential circuits. Students will design circuits using basic building blocks such as flip flops and latches. Design and analysis of clocked sequential circuits based on Moore and Mealy FSM is emphasized. Introduction to Verilog HDL and FPGA in the design of as it applies to the previously described basic digital circuits. Students are required to complete 7 lab projects using FPGA. Students will also finish selected set of lab exercises using breadboards to contrast the state of the art design principles with classical principles. Students will work in teams to design and simulate digital circuits using a state-of-the-art CAD package. Both schematic and VHDL-based designs are emphasized.

Course Objective: Students will understand classical digital design principles and gain experience in using state of the art design tools.

Classes: Lectures 2 x 75 minutes, lab 1 x 120 minutes per week.

Co-requisites: Digital Circuits and Analysis lab

This is an introductory course on computer organization and architecture. The terminology and understanding of functional organizations and sequential operation of the HW/SW of modern digital computer is taught in this course. Topics include pipelining, microprocessor organization, microprogramming, cache memory, memory organization, addressing, stacks, argument passing, arithmetic operations, traps, and input/output.
Organization of RISC and CISC computers is discussed. Microcontrollers and embedded systems are discussed as well as Flynns's categories of large computer systems. Hands-on lab exercises make use of Motorolla 68k simulator for the illustration of addressing modes, and Xilinx Virtex Pro2 boards are used for exercises illustrating performance issues relating to different microprocessor organization.

Course Objective:
Main objective of the course is to understand main- and sub systems of modern digital computer and how these systems are interlinked. Among other objectives are: how performance issues are affected by different microprocessor organization, the implementation of soft-core processors in FPGA, and the understanding of how high-level programming languages and compilers take advantage of different computer hardware and organization.

Classes:
Lectures 2 x 75 minutes, lab and problem hours will be conducted as needed during the course. Students are expected to be proactive solving lab exercises and to seek assistance from the teacher as needed, 1 x 100 minutes per week.

Co-prerequisites: Hands-on lab exercises

Laboratory session in TÖV301G Computer Organization.

Basics of quantum mechanics and statistical physics. The atom. Crystal structure. The band theory of solids. Semiconductors. Transport properties of semiconductors and metals. The band theory of solids. Optical properties of semiconductors. P-n junctions. Diodes. Transistors. MOS devices. Lasers, diodes and semiconductor optics.

Discrete and continuous signals. Transfer functions and convolution. Difference equations and differential equations. Fourier series and Fourier transforms. Fourier analysis of discrete signals. The Laplace transform in analysis of continuous signals. The Z-transform in analysis of discrete signals. Homework and Matlab computer assignments.

Introduction to electrical signals, their properties and measurements
Treatment of measurement errors and their propagation in a measurement system
Power supplies and signal generators
Introduction to sensors and transducers that deliver an electrical signal
Introduction to measurement system components.
Electrical measurments with analogue and digital multimeters
Measurements using an oscilloscope
Measurements on resistance, inductance and capacitance with multimeters, oscilloscopes and bridges
Noise, interference and their consequennces
Resistors, capacitors, inductors and other components, their strcture, colour codes, treatment of semiconductors
Electrical network of houses and the laboratory, precautions in using electricity and equipment in a laboratory
Dangers and rules of conduct
Home problems and home projects
Laboratory exercises
Design project: Design of a specialised measurement system

Laboratory session in RAF301G Signals and Systems.

Functions of a complex variable. Analytic functions. The exponential function, logarithms and roots. Cauchy's Integral Theorem and Cauchy's Integral Formula. Uniform convergence. Power series. Laurent series. Residue integration method. Application of complex function theory to fluid flows. Ordinary differential equations and systems of ordinary differential equations. Linear differential equations with constant coefficients. Systems of linear differential equations. The matrix exponential function. Various methods for obtaining a particular solution. Green's functions for initial value problems. Flows and the phase plane. Nonlinear systems of ordinary differential equations in the plane, equilibrium points, stability and linear approximations. Series solutions and the method of Frobenius. Use of Laplace transforms in solving differential equations.

In this course, students learn to use the Laplace transform to analyze electrical circuits in the s-plane. Students are introduced to the properties of two-port circuits. Special emphasis is placed on second-order systems, and students learn to draw Bode plots, calculate transfer functions, and determine critical frequencies for such systems. The course covers approximation functions for analog filters and frequency transformations. It also includes synthesis of analog transfer functions, using LC and RC ladder circuits, as well as active components.

Electrostatics. Magnetostatics. The equations of Laplace and Poisson. Equation of continuity for time-varying fields. Maxwell's equations. Energy of the electromagnetic field. Electromagnetic waves. Plane waves in dielectric and conducting media. Elementary radiating systems. Reflection and refraction. Transmission lines. Wave guides. Electromagnetic radiation.

General characteristics of amplifiers, frequency response and Bode plots. Operational amplifiers and common circuits utilizing op amps, differential mode and common mode signals, offsets in operational amplifiers. Diodes and diode models, breakdown and zener operation, rectifiers, clipping and clamping circuits using diodes. Basic operation of bipolar junction transistors (BJT) and metal oxide field effect transistors (MOSFET), review of semiconductor physics, relationships between current and voltage, large signal models. Basic types of transistor amplifiers, small signal analysis, DC operating point regulation through feedback, common amplifier circuits.

An introductory treatment of probability theory including domains, dependent and independent events and probabilities. Random variables, one dimensional distributions, distribution functions, density functions, normal densities and the central limit theorem. Correlation and multidimensional distributions. Introduction to statistics. Random Processes. Autocorrelation and cross correlation. Power spectral density. Response of linear systems to random inputs.

Laboratory exercises for RAF401G Circuit Analysis and Synthesis.

This course consists of laboratory exercices related to the course RAF403G Electronics 1. This includes the construction of electronic circuits, measurements and tests following instructions. Students prepare lab reports of good quality where the laboratory work and main results are clearly summarized. The students learn about the equipment, components and tools used, and gain competence in their use. Instruments such as multimeters, oscilloscopes and signal generators are used and practiced in the lab exercises. Electronic circuits are analyzed with SPICE or similar simulation tools.

Exercices in RAF404G Probabilistic Methods.

Main features of integrated circuit amplifiers and comparison with circuits made from discrete components. Common circuits used in integrated circuit amplifiers such as current mirrors, differential pairs, cascode amplifiers, multistage amplifiers and output stages. High frequency characteristics of amplifiers, feedback and Miller effect. All of this is considered for both MOSFET and BJT circuits. Throughout the semester students work in groups on capstone projects where they apply theoretical knowledge and skills in the design and testing of electronic circuits.

Methods of classical automatic control systems. System models represented by transfer functions and state equations, simulation. System time and frequency responses. Properties of feedback control systems, stability, sensitivity, disturbance rejection, error coefficients. Stability analysis, Routh's stability criterion. Analysis and design using root-locus, lead, lag and PID controllers. Analysis and design in the frequency domain, lead, lag and PID compensators. Computer controlled systems, A/D and D/A converters, transformations of continuous controllers to discrete form. Analysis and design of digital control systems.

The objective is to provide the basic principles of digital filter design and signal processing. Strong emphasis is on individual projects and laboratory work. Syllabus: DTFT, DFT and FFT. Recursive filters (IIR), nonrecursive filters (FIR), effects of finite word length in digital filters. Filtering and analysis of random signals based on Fourier Analysis. Multirate digital signs processing.

Telecommunication systems are everywhere in modern societies, and great progress has been made in the field of telecommunications in recent years. The development is still going on and will be for coming years, both in terms of technology itself and its utilisation. It is therefore clear that there will be demand for knowledge on telecommunications in years to come.

In this course, basic understanding of telecommunications will be provided emphasising the system view. The course begins by a short review of the history of telecommunications.  Following is a discussion of major signal treatment methodologies before and after transmission over a communications channel, both for analogue and digital transmission. An introduction to telecommunications media will be given, wireless and wired telecommunications, amplitude and angle modulation, multiplexing and multiple access, random processes and noise in telecommunication systems. How to design a telecommunication system with respect to signal-noise ratio, digital modulation techniques, eye diagrams and Shannon’s law on channel capacity. Finally, data encoding and decoding will be introduced, how to detect and even correct errors.

The teaching will be in the form of lectures and discussions. Problems will be solved in class and home assignments given.

Databases and database management systems. Physical data organization. Data modelling using the Entity-Relationship model and the Relational model. Relational algebra and calculus.  The SQL query language. Design theory for relational data bases, functional dependencies, decomposition of relational schemes, normal forms. Query optimization. Concurrency control techniques and crash recovery. Database security and authorization. Data warehousing.

Survey of contemporary computer organisation covering performance measurement, design of instruction sets, instruction execution and recent techniques for exploiting instruction level paralellism. Design of caches, main memory. Virtual memory and storage systems. Design of multiprocessors.

This course is centered on the design, implementation, and testing of the electrical and electronic systems of the Formula Student project.
In addition students get training in working on a cross discipline design team with the main focus on the electrical system. This includes: power systems and wiring, charging system, propulsion system, micro controllers, sensors, real-time HW/SW development and communications.

Introduction to the instrumentation, physics and signal processing methods used in medical imaging systems from a signal processing perspective. The modalities covered include projection radiography, X-ray computed tomography, nuclear medicine (i.e. SPECT and PET), ultrasound, and magnetic resonance imaging.  The primary focus is on the methods required to reconstruct images within each modality, the kind of signals being measured and how these data culminate in an image.  Attention will also be given to image quality in each modality, including resolution, contrast, signal-to-noise ratio, and distortion of images.

The course introduces programming techniques for embedded systems. Emphasis is on concurrency, real-time systems and event driven programming. The course also addresses programming language support for the aforementioned issues. Unified Modeling Language (UML) for real-time systems is introduced along with the design and implementation of multitasking in embedded systems, and programming of threads that share memory and communicate. The course has lab sessions where development environment and boards from Xilinx are used.

This course is centered on the design, implementation, and testing of the electrical and electronic systems of the Formula Student project.
In addition students get training in working on a cross discipline design team with the main focus on the electrical system. This includes: power systems and wiring, charging system, propulsion system, micro controllers, sensors, real-time HW/SW development and communications.

Digital mobile telecommunication systems were first deployed in the early 1990s. This was the basis for a great societal change, people now being able to contact others where- and whenever needed. The emergence of the smartphone and high speed mobile infrastructure has furthermore revolutionised peoples’ possibilities to gain information in text-, sound-, and video formats almost irrespective of place and time. The development of Wi-Fi has also been fast in recent years causing people to enjoy more and more “wireless freedom” in their homes and workplaces. Wireless communications are important in many other areas including television, radio broadcast, marine and aeronautical communications, positioning and navigation systems. Internet of things or device-to-device communications are also wireless to a large extent.
In this course there will be treatment of the fundamentals of wireless, including antennas and wave propagation, transmission lines, high-frequency circuits and characteristics of different mobile phone generations, from the first to the fifth. This includes modulation and multiplexing/multiple access technologies such as QAM, FDMA, CDMA,TDMA, W-CDMA, OFDM(A) and MIMO antenna technology. The duplexing technologies FDD and TDD will be treated as well as mobile service concepts such as data connectivity and voice incl. VoLTE. Standards for Wi-Fi, Bluetooth, Zigbee and Z-wave will be covered along with a short handling of Wireless sensor networks.
Furthermore, short description will be given on digital broadcasting such as DVB-T and DVB-S, satellite communications and satellite positioning/navigation systems.
The form of the course will be lectures and discussions. Students will work on four projects and write reports, hold short presentations or present their results otherwise.

Machine learning is a field within artificial intelligence that focuses on methods enabling computers to learn patterns in data and use them to solve tasks, such as identifying objects in images. The applications of machine learning are extensive and include signal processing, control systems, computer vision, medical engineering, and much more. The purpose of this course is to introduce students to the main methods of machine learning along with its primary applications. The course will also cover key methods in deep learning, which underpins large language models. Emphasis will be placed on both theoretical foundations and practical training, with the aim of equipping students to use computers to solve practical problems. An important component of this course is the final project, where students will apply the methods learned in the course to solve interesting problems.

• Controllers for difficult systems
• Design of state feedback controllers
• Design of asymptotic observers
• Similarity transformations to canonical state space forms
• Controllability and observability
• Optimization (Linear Quadratic Regulator - LQR) - linear quadratic state feedback controllers
• Kalman filtering
• State feedback controllers and observers in transfer function form, reduced order observers
• Disturbance observers
• Feedforward (FF) controllers and Internal Model Controllers (IMC)
• Coefficient matching PID controllers
• Model Prediction Control (MPC)
• Systems Identification

This course covers concepts of operating systems. Besides foundations on computer hardware structures and general operating system architectures, this includes concepts of processes and threads and their management, principles of scheduling and scheduling algorithms, communication and synchronisation between processes and deadlock issues, principles of memory management including virtual memory and page replacement algorithms, file systems and their implementation as well as mass-storage management. If time allows, principles for achieving protection and security, and aspects of distribution (e.g. concepts of distributed systems and distributed file systems) are covered as well. This course does not deal with details of implementing operating systems, but introduces generic concepts that are used when implementing operating systems and that an application developer needs to know, when creating an application program. Where appropriate, current operating systems such as Microsoft Windows and POSIX-compliant UNIX-like systems (e.g. Linux) are used as case study for implementation and offered system calls. The usage of operating system services from within high-level programming languages (e.g. C, C++ or Java) is demonstrated based on Application Programming Interfaces (APIs) offered by prevailing system libraries.

Methodology for the design of algorithms and the analysis of their time conplexity. Analysis of algorithms for sorting, searching, graph theory and matrix computations. Intractable problems, heuristics, and randomized algorithms.

Aim: To introduce the student to Fourier analysis and partial differential equations and their applications.
Subject matter: Fourier series and orthonormal systems of functions, boundary-value problems for ordinary differential equations, the eigenvalue problem for Sturm-Liouville operators, Fourier transform. The wave equation, diffusion equation and Laplace's equation solved on various domains in one, two and three dimensions by methods based on the first part of the course, separation of variables, fundamental solution, Green's functions and the method of images.

Fundamental concepts on approximation and error estimates. Solutions of systems of linear and non-linear equations. PLU decomposition. Interpolating polynomials, spline interpolation and regression. Numerical differentiation and integration. Extrapolation. Numerical solutions of initial value problems of systems of ordinary differential equations. Multistep methods. Numerical solutions to boundary value problems for ordinary differential equations.

Grades are given for programning projects and in total they amount to 30% of the final grade. The student has to receive the minimum grade of 5 for both the projects and the final exam.

Comprehensive course on the Internet of Things and Sensors Networks covering all aspects relating to applications, architectures, and communication protocols in great detail. The course focuses on not only terrestrial networks, but also underwater, underground, and space networks.

Mathematical foundations of coordinate systems and transformations. Kinematics, direct and reverse solutions. Analysis and control of movements. Trajectories in three-dimensional space and interpolation between programmed trajectory points. Use of computer vision, sensors and end-effectors in robotics. Control and programming of robots. Exercises and simulations.

This course offers an advanced exploration of machine learning and high-performance computing (HPC) techniques tailored to satellite remote sensing and Earth observation (EO). Starting with the historical evolution of Earth observation—from early aerial photography to today’s high-throughput satellite constellations such as Sentinel and Landsat—the curriculum situates modern EO within the context of an unprecedented “big data” era, driven by terabytes of imagery captured daily.

Building on foundational concepts in traditional pixel-based analysis, students will progress to contemporary approaches that leverage the deep learning revolution and the emergence of AI foundation models. These models employ self-supervised learning and Transformer-based architectures to extract structure and meaning from vast amounts of unlabeled data at scale. The course emphasizes how these advanced machine learning paradigms are reshaping EO data analytics beyond classical handcrafted methods.

A core theme of the semester is the intersection of large-scale machine learning and HPC. Students will examine how modern supercomputers enable the training and deployment of Geospatial AI foundation models for Earth observation. This includes discussions on distributed training, parallel algorithm design, and performance optimization on HPC infrastructures. The course also covers benchmarking and performance evaluation, introducing students to standardized evaluation frameworks and metrics to assess model scalability, efficiency, and accuracy in real-world Earth observation applications.

To integrate theory and practice, students complete a semester-long capstone project. Through hands-on development with Python APIs and open models, students will design, implement, and evaluate machine learning solutions on real EO datasets. Projects reinforce the application of theoretical concepts to practical problems, preparing students for research or industry roles at the forefront of AI for EO.

Modern day telecommunications are characterised by the fact that communicated data is carried on fixed telecommunications infrastructure on a majority of the path between tranmitter and receiver. Wireless infrastructure often conveys the signals at the end of the path. This yields both high speed and the comfort of wireless communications. It is of utmost importance for engineers working in telecoms to have a fundamental knowledge of fixed networks and the range of technologies deployed.

In this course, the structure of fixed backbone and access networks will be described. Optical fibre and related technologies will be introduced, e.g. DWDM, SDH, Ethernet, ATM and MPLS-TP. Access network technologies on copper, coax and optical fibres will be treated, e.g. ADSL. VDSL, G.fast and  DOCSIS. Different FTTH (Fibre to the Home) technologies will be treated such as PON (Passive Optical Network), Active Ethernet and point-to-point Ethernet. 

IP (Internet Protocol) has become a fundamental technology for modern fixed networks. IP native technologies will be described from the physical to the application layer. On the link layer, Ethernet will be in the focus as well as MPLS. Circuit and packet switching will be treated as well as circuit and packet orientation of networks. Sevices such as PSTN, VoIP, OTT and P2P will be treated. Backhauling of wireless networks such as mobile networks and Wi-Fi will also be treated.
In introduction to network virtualisation and network function virtualisation (NFV) will be given as well as software defined networking (SDN). Legal and regulatory aspects will be introduced and aspects like network neutrality discfussed. Important players and stakeholders will be discussed, e.g. Google, Apple, Microsoft, Netflix and telecommunications service providers.
Finally, local area networks will be discussed, home networking, smart homes, set-top-boxes, NAS, PLC, plastic optical fibres, MOCA and Wi-Fi introduced.

The teaching form will be lectures and projects on IP communications will be worked. Students will write four papers on selected subjects and give presentations. 

Tutor classes for electrical and computer engineering students.

Tutor classes for electrical and computer engineering students.

The study of electrical and computer engineering (ECE) is introduced, both at the undergraduate and the graduate level, and the various applications of the subject are presented. Firms and institutes are visited and guest lecturers are invited to outline the diverse roles that electrical and computer engineers have in the job market. Professional societies in this field of engineering are presented, as well as the rules of ethics that they have adopted. Assignments are given to give further insight into the studies and the jobs that they lead to.

Concepts, units, scales and dimensions. Vectors. Kinematics of particles. Particle dynamics, inertia, forces and Newton's laws. Friction. Work and energy, conservation of energy. Momentum, collisions. Systems of particles, center of mass. Rotation of a rigid body. Angular momentum and moment of inertia. Statics. Gravity. Solids and fluids, Bernoulli's equation. Oscillations: Simple, damped and forced. Waves. Sound. Temperature. Ideal gas. Heat and the first law of thermodynamics. Kinetic theory of gases. Entropy and the second law of thermodynamics. Home problems: Once a week the students have to solve homeproblems on the website MasteringPhysics.

Laboratory work: Three exercises, mainly centered on mechanics, where students are trained in handling physical instruments, collecting and inspecting data. Students hand in their lab notebooks for a grade.

Note that the textbook is accessible to students via Canvas free of charge.

This is a foundational course in single variable calculus. The prerequisites are high school courses on algebra, trigonometry. derivatives, and integrals. The course aims to create a foundation for understanding of subjects such as natural and physical sciences, engineering, economics, and computer science. Topics of the course include the following:

• Real numbers.
• Limits and continuous functions.
• Differentiable functions, rules for derivatives, derivatives of higher order, applications of differential calculus (extremal value problems, linear approximation).
• Transcendental functions.
• Mean value theorem, theorems of l'Hôpital and Taylor.
• Integration, the definite integral and rules/techniques of integration, primitives, improper integrals.
• Fundamental theorem of calculus.
• Applications of integral calculus: Arc length, area, volume, centroids.
• Ordinary differential equations: First-order separable and homogeneous differential equations, first-order linear equations, second-order linear equations with constant coefficients.
• Sequences and series, convergence tests.
• Power series, Taylor series.

Basics of linear algebra over the reals.  

Subject matter: Systems of linear equations, matrices, Gauss-Jordan reduction.  Vector spaces and their subspaces.  Linearly independent sets, bases and dimension.  Linear maps, range space and nullk space.  The dot product, length and angle measures.  Volumes in higher dimension and the cross product in threedimensional space.  Flats, parametric descriptions and descriptions by equations.  Orthogonal projections and orthonormal bases.  Gram-Schmidt orthogonalization.  Determinants and inverses of matrices.  Eigenvalues, eigenvectors and diagonalization.

Note: Only one course of either TÖL101G Tölvunarfræði 1 or TÖL105G Tölvunarfræði 1a can count towards the BS degree.

The Java programming language is used to introduce basic concepts in computer programming: Expressions and statements, textual and numeric data types, conditions and loops, arrays, methods, classes and objects, input and output. Programming and debugging skills are practiced in quizzes and projects throughout the semester.

The programming language Java will be used in the course. Various data structures, algorithms and abstract data types will be covered. Among the data types and structures covered are lists, stacks, queues, priority queues, trees, binary trees, binary search trees and heaps along with related algorithms. Various search and sort algorithms will be covered. Algorithms will be analysed for their space and time complexity. There will be programming assignments in Java using the given data structures and algorithms. There will be many small assignments.

Teaching takes 12 weeks. Charge and electric field. Gauss' law. Electric potential. Capacitors and dielectrics. Electric currents and resistance. Circuits. Magnetic fields. The laws of Ampère and Faraday. Induction. Electric oscillation and alternating currents. Maxwell's equations. Electromagnetic waves. Reflection and refraction. Lenses and mirrors. Wave optics. Four laboratory exercises in optics and electromagnetism.

Definitions and basic concepts. Kirchoff's laws, mesh- and node-equations. Circuits with resistance, matrix representation. Dependent sources. Thevenin-Norton equivalent circuit theorems. Circuits with resistance, capacitance, inductance and mutual inductance. Time domain analysis. Initial conditions. Zero input solutions, zero state solutions, transients and steady state. Impulse response, convolution. Analysis of second order circuits. Systems with sinusoidal inputs. Computer exercises with PSpice and Matlab.

Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobi matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flow. Cylindrical and spherical coordinates. Taylor polynomials. Extreme values and the classification of stationary points. Extreme value problems with constraints. Implicit functions and local inverses. Line integrals, primitive functions and exact differential equations. Double integrals. Improper integrals. Green's theorem. Simply connected domains. Change of variables in double integrals. Multiple integrals. Change of variables in multiple integrals. Surface integrals. Integration of vector fields. The theorems of Stokes and Gauss.

Students will learn digital design principles and practice. Design is based on standard MSI and LSI devices or equivalent building blocks such as counters, shift registers, adders, and ROM. The design and analysis of combinatorial circuits for basic arithmetic is emphasized as well as the design an analysis of synchronous and asynchronous sequential circuits. Students will design circuits using basic building blocks such as flip flops and latches. Design and analysis of clocked sequential circuits based on Moore and Mealy FSM is emphasized. Introduction to Verilog HDL and FPGA in the design of as it applies to the previously described basic digital circuits. Students are required to complete 7 lab projects using FPGA. Students will also finish selected set of lab exercises using breadboards to contrast the state of the art design principles with classical principles. Students will work in teams to design and simulate digital circuits using a state-of-the-art CAD package. Both schematic and VHDL-based designs are emphasized.

Course Objective: Students will understand classical digital design principles and gain experience in using state of the art design tools.

Classes: Lectures 2 x 75 minutes, lab 1 x 120 minutes per week.

Co-requisites: Digital Circuits and Analysis lab

This is an introductory course on computer organization and architecture. The terminology and understanding of functional organizations and sequential operation of the HW/SW of modern digital computer is taught in this course. Topics include pipelining, microprocessor organization, microprogramming, cache memory, memory organization, addressing, stacks, argument passing, arithmetic operations, traps, and input/output.
Organization of RISC and CISC computers is discussed. Microcontrollers and embedded systems are discussed as well as Flynns's categories of large computer systems. Hands-on lab exercises make use of Motorolla 68k simulator for the illustration of addressing modes, and Xilinx Virtex Pro2 boards are used for exercises illustrating performance issues relating to different microprocessor organization.

Course Objective:
Main objective of the course is to understand main- and sub systems of modern digital computer and how these systems are interlinked. Among other objectives are: how performance issues are affected by different microprocessor organization, the implementation of soft-core processors in FPGA, and the understanding of how high-level programming languages and compilers take advantage of different computer hardware and organization.

Classes:
Lectures 2 x 75 minutes, lab and problem hours will be conducted as needed during the course. Students are expected to be proactive solving lab exercises and to seek assistance from the teacher as needed, 1 x 100 minutes per week.

Co-prerequisites: Hands-on lab exercises

Laboratory session in TÖV301G Computer Organization.

Basics of quantum mechanics and statistical physics. The atom. Crystal structure. The band theory of solids. Semiconductors. Transport properties of semiconductors and metals. The band theory of solids. Optical properties of semiconductors. P-n junctions. Diodes. Transistors. MOS devices. Lasers, diodes and semiconductor optics.

Discrete and continuous signals. Transfer functions and convolution. Difference equations and differential equations. Fourier series and Fourier transforms. Fourier analysis of discrete signals. The Laplace transform in analysis of continuous signals. The Z-transform in analysis of discrete signals. Homework and Matlab computer assignments.

Introduction to electrical signals, their properties and measurements
Treatment of measurement errors and their propagation in a measurement system
Power supplies and signal generators
Introduction to sensors and transducers that deliver an electrical signal
Introduction to measurement system components.
Electrical measurments with analogue and digital multimeters
Measurements using an oscilloscope
Measurements on resistance, inductance and capacitance with multimeters, oscilloscopes and bridges
Noise, interference and their consequennces
Resistors, capacitors, inductors and other components, their strcture, colour codes, treatment of semiconductors
Electrical network of houses and the laboratory, precautions in using electricity and equipment in a laboratory
Dangers and rules of conduct
Home problems and home projects
Laboratory exercises
Design project: Design of a specialised measurement system

Laboratory session in RAF301G Signals and Systems.

Functions of a complex variable. Analytic functions. The exponential function, logarithms and roots. Cauchy's Integral Theorem and Cauchy's Integral Formula. Uniform convergence. Power series. Laurent series. Residue integration method. Application of complex function theory to fluid flows. Ordinary differential equations and systems of ordinary differential equations. Linear differential equations with constant coefficients. Systems of linear differential equations. The matrix exponential function. Various methods for obtaining a particular solution. Green's functions for initial value problems. Flows and the phase plane. Nonlinear systems of ordinary differential equations in the plane, equilibrium points, stability and linear approximations. Series solutions and the method of Frobenius. Use of Laplace transforms in solving differential equations.

In this course, students learn to use the Laplace transform to analyze electrical circuits in the s-plane. Students are introduced to the properties of two-port circuits. Special emphasis is placed on second-order systems, and students learn to draw Bode plots, calculate transfer functions, and determine critical frequencies for such systems. The course covers approximation functions for analog filters and frequency transformations. It also includes synthesis of analog transfer functions, using LC and RC ladder circuits, as well as active components.

Electrostatics. Magnetostatics. The equations of Laplace and Poisson. Equation of continuity for time-varying fields. Maxwell's equations. Energy of the electromagnetic field. Electromagnetic waves. Plane waves in dielectric and conducting media. Elementary radiating systems. Reflection and refraction. Transmission lines. Wave guides. Electromagnetic radiation.

General characteristics of amplifiers, frequency response and Bode plots. Operational amplifiers and common circuits utilizing op amps, differential mode and common mode signals, offsets in operational amplifiers. Diodes and diode models, breakdown and zener operation, rectifiers, clipping and clamping circuits using diodes. Basic operation of bipolar junction transistors (BJT) and metal oxide field effect transistors (MOSFET), review of semiconductor physics, relationships between current and voltage, large signal models. Basic types of transistor amplifiers, small signal analysis, DC operating point regulation through feedback, common amplifier circuits.

An introductory treatment of probability theory including domains, dependent and independent events and probabilities. Random variables, one dimensional distributions, distribution functions, density functions, normal densities and the central limit theorem. Correlation and multidimensional distributions. Introduction to statistics. Random Processes. Autocorrelation and cross correlation. Power spectral density. Response of linear systems to random inputs.

Laboratory exercises for RAF401G Circuit Analysis and Synthesis.

This course consists of laboratory exercices related to the course RAF403G Electronics 1. This includes the construction of electronic circuits, measurements and tests following instructions. Students prepare lab reports of good quality where the laboratory work and main results are clearly summarized. The students learn about the equipment, components and tools used, and gain competence in their use. Instruments such as multimeters, oscilloscopes and signal generators are used and practiced in the lab exercises. Electronic circuits are analyzed with SPICE or similar simulation tools.

Exercices in RAF404G Probabilistic Methods.

Main features of integrated circuit amplifiers and comparison with circuits made from discrete components. Common circuits used in integrated circuit amplifiers such as current mirrors, differential pairs, cascode amplifiers, multistage amplifiers and output stages. High frequency characteristics of amplifiers, feedback and Miller effect. All of this is considered for both MOSFET and BJT circuits. Throughout the semester students work in groups on capstone projects where they apply theoretical knowledge and skills in the design and testing of electronic circuits.

Methods of classical automatic control systems. System models represented by transfer functions and state equations, simulation. System time and frequency responses. Properties of feedback control systems, stability, sensitivity, disturbance rejection, error coefficients. Stability analysis, Routh's stability criterion. Analysis and design using root-locus, lead, lag and PID controllers. Analysis and design in the frequency domain, lead, lag and PID compensators. Computer controlled systems, A/D and D/A converters, transformations of continuous controllers to discrete form. Analysis and design of digital control systems.

The objective is to provide the basic principles of digital filter design and signal processing. Strong emphasis is on individual projects and laboratory work. Syllabus: DTFT, DFT and FFT. Recursive filters (IIR), nonrecursive filters (FIR), effects of finite word length in digital filters. Filtering and analysis of random signals based on Fourier Analysis. Multirate digital signs processing.

Telecommunication systems are everywhere in modern societies, and great progress has been made in the field of telecommunications in recent years. The development is still going on and will be for coming years, both in terms of technology itself and its utilisation. It is therefore clear that there will be demand for knowledge on telecommunications in years to come.

In this course, basic understanding of telecommunications will be provided emphasising the system view. The course begins by a short review of the history of telecommunications.  Following is a discussion of major signal treatment methodologies before and after transmission over a communications channel, both for analogue and digital transmission. An introduction to telecommunications media will be given, wireless and wired telecommunications, amplitude and angle modulation, multiplexing and multiple access, random processes and noise in telecommunication systems. How to design a telecommunication system with respect to signal-noise ratio, digital modulation techniques, eye diagrams and Shannon’s law on channel capacity. Finally, data encoding and decoding will be introduced, how to detect and even correct errors.

The teaching will be in the form of lectures and discussions. Problems will be solved in class and home assignments given.

Databases and database management systems. Physical data organization. Data modelling using the Entity-Relationship model and the Relational model. Relational algebra and calculus.  The SQL query language. Design theory for relational data bases, functional dependencies, decomposition of relational schemes, normal forms. Query optimization. Concurrency control techniques and crash recovery. Database security and authorization. Data warehousing.

Survey of contemporary computer organisation covering performance measurement, design of instruction sets, instruction execution and recent techniques for exploiting instruction level paralellism. Design of caches, main memory. Virtual memory and storage systems. Design of multiprocessors.

This course is centered on the design, implementation, and testing of the electrical and electronic systems of the Formula Student project.
In addition students get training in working on a cross discipline design team with the main focus on the electrical system. This includes: power systems and wiring, charging system, propulsion system, micro controllers, sensors, real-time HW/SW development and communications.

Introduction to the instrumentation, physics and signal processing methods used in medical imaging systems from a signal processing perspective. The modalities covered include projection radiography, X-ray computed tomography, nuclear medicine (i.e. SPECT and PET), ultrasound, and magnetic resonance imaging.  The primary focus is on the methods required to reconstruct images within each modality, the kind of signals being measured and how these data culminate in an image.  Attention will also be given to image quality in each modality, including resolution, contrast, signal-to-noise ratio, and distortion of images.

The course introduces programming techniques for embedded systems. Emphasis is on concurrency, real-time systems and event driven programming. The course also addresses programming language support for the aforementioned issues. Unified Modeling Language (UML) for real-time systems is introduced along with the design and implementation of multitasking in embedded systems, and programming of threads that share memory and communicate. The course has lab sessions where development environment and boards from Xilinx are used.

This course is centered on the design, implementation, and testing of the electrical and electronic systems of the Formula Student project.
In addition students get training in working on a cross discipline design team with the main focus on the electrical system. This includes: power systems and wiring, charging system, propulsion system, micro controllers, sensors, real-time HW/SW development and communications.

Digital mobile telecommunication systems were first deployed in the early 1990s. This was the basis for a great societal change, people now being able to contact others where- and whenever needed. The emergence of the smartphone and high speed mobile infrastructure has furthermore revolutionised peoples’ possibilities to gain information in text-, sound-, and video formats almost irrespective of place and time. The development of Wi-Fi has also been fast in recent years causing people to enjoy more and more “wireless freedom” in their homes and workplaces. Wireless communications are important in many other areas including television, radio broadcast, marine and aeronautical communications, positioning and navigation systems. Internet of things or device-to-device communications are also wireless to a large extent.
In this course there will be treatment of the fundamentals of wireless, including antennas and wave propagation, transmission lines, high-frequency circuits and characteristics of different mobile phone generations, from the first to the fifth. This includes modulation and multiplexing/multiple access technologies such as QAM, FDMA, CDMA,TDMA, W-CDMA, OFDM(A) and MIMO antenna technology. The duplexing technologies FDD and TDD will be treated as well as mobile service concepts such as data connectivity and voice incl. VoLTE. Standards for Wi-Fi, Bluetooth, Zigbee and Z-wave will be covered along with a short handling of Wireless sensor networks.
Furthermore, short description will be given on digital broadcasting such as DVB-T and DVB-S, satellite communications and satellite positioning/navigation systems.
The form of the course will be lectures and discussions. Students will work on four projects and write reports, hold short presentations or present their results otherwise.

Machine learning is a field within artificial intelligence that focuses on methods enabling computers to learn patterns in data and use them to solve tasks, such as identifying objects in images. The applications of machine learning are extensive and include signal processing, control systems, computer vision, medical engineering, and much more. The purpose of this course is to introduce students to the main methods of machine learning along with its primary applications. The course will also cover key methods in deep learning, which underpins large language models. Emphasis will be placed on both theoretical foundations and practical training, with the aim of equipping students to use computers to solve practical problems. An important component of this course is the final project, where students will apply the methods learned in the course to solve interesting problems.

• Controllers for difficult systems
• Design of state feedback controllers
• Design of asymptotic observers
• Similarity transformations to canonical state space forms
• Controllability and observability
• Optimization (Linear Quadratic Regulator - LQR) - linear quadratic state feedback controllers
• Kalman filtering
• State feedback controllers and observers in transfer function form, reduced order observers
• Disturbance observers
• Feedforward (FF) controllers and Internal Model Controllers (IMC)
• Coefficient matching PID controllers
• Model Prediction Control (MPC)
• Systems Identification

This course covers concepts of operating systems. Besides foundations on computer hardware structures and general operating system architectures, this includes concepts of processes and threads and their management, principles of scheduling and scheduling algorithms, communication and synchronisation between processes and deadlock issues, principles of memory management including virtual memory and page replacement algorithms, file systems and their implementation as well as mass-storage management. If time allows, principles for achieving protection and security, and aspects of distribution (e.g. concepts of distributed systems and distributed file systems) are covered as well. This course does not deal with details of implementing operating systems, but introduces generic concepts that are used when implementing operating systems and that an application developer needs to know, when creating an application program. Where appropriate, current operating systems such as Microsoft Windows and POSIX-compliant UNIX-like systems (e.g. Linux) are used as case study for implementation and offered system calls. The usage of operating system services from within high-level programming languages (e.g. C, C++ or Java) is demonstrated based on Application Programming Interfaces (APIs) offered by prevailing system libraries.

Methodology for the design of algorithms and the analysis of their time conplexity. Analysis of algorithms for sorting, searching, graph theory and matrix computations. Intractable problems, heuristics, and randomized algorithms.

Aim: To introduce the student to Fourier analysis and partial differential equations and their applications.
Subject matter: Fourier series and orthonormal systems of functions, boundary-value problems for ordinary differential equations, the eigenvalue problem for Sturm-Liouville operators, Fourier transform. The wave equation, diffusion equation and Laplace's equation solved on various domains in one, two and three dimensions by methods based on the first part of the course, separation of variables, fundamental solution, Green's functions and the method of images.

Fundamental concepts on approximation and error estimates. Solutions of systems of linear and non-linear equations. PLU decomposition. Interpolating polynomials, spline interpolation and regression. Numerical differentiation and integration. Extrapolation. Numerical solutions of initial value problems of systems of ordinary differential equations. Multistep methods. Numerical solutions to boundary value problems for ordinary differential equations.

Grades are given for programning projects and in total they amount to 30% of the final grade. The student has to receive the minimum grade of 5 for both the projects and the final exam.

Comprehensive course on the Internet of Things and Sensors Networks covering all aspects relating to applications, architectures, and communication protocols in great detail. The course focuses on not only terrestrial networks, but also underwater, underground, and space networks.

Mathematical foundations of coordinate systems and transformations. Kinematics, direct and reverse solutions. Analysis and control of movements. Trajectories in three-dimensional space and interpolation between programmed trajectory points. Use of computer vision, sensors and end-effectors in robotics. Control and programming of robots. Exercises and simulations.

This course offers an advanced exploration of machine learning and high-performance computing (HPC) techniques tailored to satellite remote sensing and Earth observation (EO). Starting with the historical evolution of Earth observation—from early aerial photography to today’s high-throughput satellite constellations such as Sentinel and Landsat—the curriculum situates modern EO within the context of an unprecedented “big data” era, driven by terabytes of imagery captured daily.

Building on foundational concepts in traditional pixel-based analysis, students will progress to contemporary approaches that leverage the deep learning revolution and the emergence of AI foundation models. These models employ self-supervised learning and Transformer-based architectures to extract structure and meaning from vast amounts of unlabeled data at scale. The course emphasizes how these advanced machine learning paradigms are reshaping EO data analytics beyond classical handcrafted methods.

A core theme of the semester is the intersection of large-scale machine learning and HPC. Students will examine how modern supercomputers enable the training and deployment of Geospatial AI foundation models for Earth observation. This includes discussions on distributed training, parallel algorithm design, and performance optimization on HPC infrastructures. The course also covers benchmarking and performance evaluation, introducing students to standardized evaluation frameworks and metrics to assess model scalability, efficiency, and accuracy in real-world Earth observation applications.

To integrate theory and practice, students complete a semester-long capstone project. Through hands-on development with Python APIs and open models, students will design, implement, and evaluate machine learning solutions on real EO datasets. Projects reinforce the application of theoretical concepts to practical problems, preparing students for research or industry roles at the forefront of AI for EO.

Modern day telecommunications are characterised by the fact that communicated data is carried on fixed telecommunications infrastructure on a majority of the path between tranmitter and receiver. Wireless infrastructure often conveys the signals at the end of the path. This yields both high speed and the comfort of wireless communications. It is of utmost importance for engineers working in telecoms to have a fundamental knowledge of fixed networks and the range of technologies deployed.

In this course, the structure of fixed backbone and access networks will be described. Optical fibre and related technologies will be introduced, e.g. DWDM, SDH, Ethernet, ATM and MPLS-TP. Access network technologies on copper, coax and optical fibres will be treated, e.g. ADSL. VDSL, G.fast and  DOCSIS. Different FTTH (Fibre to the Home) technologies will be treated such as PON (Passive Optical Network), Active Ethernet and point-to-point Ethernet. 

IP (Internet Protocol) has become a fundamental technology for modern fixed networks. IP native technologies will be described from the physical to the application layer. On the link layer, Ethernet will be in the focus as well as MPLS. Circuit and packet switching will be treated as well as circuit and packet orientation of networks. Sevices such as PSTN, VoIP, OTT and P2P will be treated. Backhauling of wireless networks such as mobile networks and Wi-Fi will also be treated.
In introduction to network virtualisation and network function virtualisation (NFV) will be given as well as software defined networking (SDN). Legal and regulatory aspects will be introduced and aspects like network neutrality discfussed. Important players and stakeholders will be discussed, e.g. Google, Apple, Microsoft, Netflix and telecommunications service providers.
Finally, local area networks will be discussed, home networking, smart homes, set-top-boxes, NAS, PLC, plastic optical fibres, MOCA and Wi-Fi introduced.

The teaching form will be lectures and projects on IP communications will be worked. Students will write four papers on selected subjects and give presentations. 

Tutor classes for electrical and computer engineering students.

Tutor classes for electrical and computer engineering students.

The study of electrical and computer engineering (ECE) is introduced, both at the undergraduate and the graduate level, and the various applications of the subject are presented. Firms and institutes are visited and guest lecturers are invited to outline the diverse roles that electrical and computer engineers have in the job market. Professional societies in this field of engineering are presented, as well as the rules of ethics that they have adopted. Assignments are given to give further insight into the studies and the jobs that they lead to.

Concepts, units, scales and dimensions. Vectors. Kinematics of particles. Particle dynamics, inertia, forces and Newton's laws. Friction. Work and energy, conservation of energy. Momentum, collisions. Systems of particles, center of mass. Rotation of a rigid body. Angular momentum and moment of inertia. Statics. Gravity. Solids and fluids, Bernoulli's equation. Oscillations: Simple, damped and forced. Waves. Sound. Temperature. Ideal gas. Heat and the first law of thermodynamics. Kinetic theory of gases. Entropy and the second law of thermodynamics. Home problems: Once a week the students have to solve homeproblems on the website MasteringPhysics.

Laboratory work: Three exercises, mainly centered on mechanics, where students are trained in handling physical instruments, collecting and inspecting data. Students hand in their lab notebooks for a grade.

Note that the textbook is accessible to students via Canvas free of charge.

This is a foundational course in single variable calculus. The prerequisites are high school courses on algebra, trigonometry. derivatives, and integrals. The course aims to create a foundation for understanding of subjects such as natural and physical sciences, engineering, economics, and computer science. Topics of the course include the following:

• Real numbers.
• Limits and continuous functions.
• Differentiable functions, rules for derivatives, derivatives of higher order, applications of differential calculus (extremal value problems, linear approximation).
• Transcendental functions.
• Mean value theorem, theorems of l'Hôpital and Taylor.
• Integration, the definite integral and rules/techniques of integration, primitives, improper integrals.
• Fundamental theorem of calculus.
• Applications of integral calculus: Arc length, area, volume, centroids.
• Ordinary differential equations: First-order separable and homogeneous differential equations, first-order linear equations, second-order linear equations with constant coefficients.
• Sequences and series, convergence tests.
• Power series, Taylor series.

Basics of linear algebra over the reals.  

Subject matter: Systems of linear equations, matrices, Gauss-Jordan reduction.  Vector spaces and their subspaces.  Linearly independent sets, bases and dimension.  Linear maps, range space and nullk space.  The dot product, length and angle measures.  Volumes in higher dimension and the cross product in threedimensional space.  Flats, parametric descriptions and descriptions by equations.  Orthogonal projections and orthonormal bases.  Gram-Schmidt orthogonalization.  Determinants and inverses of matrices.  Eigenvalues, eigenvectors and diagonalization.

Note: Only one course of either TÖL101G Tölvunarfræði 1 or TÖL105G Tölvunarfræði 1a can count towards the BS degree.

The Java programming language is used to introduce basic concepts in computer programming: Expressions and statements, textual and numeric data types, conditions and loops, arrays, methods, classes and objects, input and output. Programming and debugging skills are practiced in quizzes and projects throughout the semester.

The programming language Java will be used in the course. Various data structures, algorithms and abstract data types will be covered. Among the data types and structures covered are lists, stacks, queues, priority queues, trees, binary trees, binary search trees and heaps along with related algorithms. Various search and sort algorithms will be covered. Algorithms will be analysed for their space and time complexity. There will be programming assignments in Java using the given data structures and algorithms. There will be many small assignments.

Teaching takes 12 weeks. Charge and electric field. Gauss' law. Electric potential. Capacitors and dielectrics. Electric currents and resistance. Circuits. Magnetic fields. The laws of Ampère and Faraday. Induction. Electric oscillation and alternating currents. Maxwell's equations. Electromagnetic waves. Reflection and refraction. Lenses and mirrors. Wave optics. Four laboratory exercises in optics and electromagnetism.

Definitions and basic concepts. Kirchoff's laws, mesh- and node-equations. Circuits with resistance, matrix representation. Dependent sources. Thevenin-Norton equivalent circuit theorems. Circuits with resistance, capacitance, inductance and mutual inductance. Time domain analysis. Initial conditions. Zero input solutions, zero state solutions, transients and steady state. Impulse response, convolution. Analysis of second order circuits. Systems with sinusoidal inputs. Computer exercises with PSpice and Matlab.

Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobi matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flow. Cylindrical and spherical coordinates. Taylor polynomials. Extreme values and the classification of stationary points. Extreme value problems with constraints. Implicit functions and local inverses. Line integrals, primitive functions and exact differential equations. Double integrals. Improper integrals. Green's theorem. Simply connected domains. Change of variables in double integrals. Multiple integrals. Change of variables in multiple integrals. Surface integrals. Integration of vector fields. The theorems of Stokes and Gauss.

Students will learn digital design principles and practice. Design is based on standard MSI and LSI devices or equivalent building blocks such as counters, shift registers, adders, and ROM. The design and analysis of combinatorial circuits for basic arithmetic is emphasized as well as the design an analysis of synchronous and asynchronous sequential circuits. Students will design circuits using basic building blocks such as flip flops and latches. Design and analysis of clocked sequential circuits based on Moore and Mealy FSM is emphasized. Introduction to Verilog HDL and FPGA in the design of as it applies to the previously described basic digital circuits. Students are required to complete 7 lab projects using FPGA. Students will also finish selected set of lab exercises using breadboards to contrast the state of the art design principles with classical principles. Students will work in teams to design and simulate digital circuits using a state-of-the-art CAD package. Both schematic and VHDL-based designs are emphasized.

Course Objective: Students will understand classical digital design principles and gain experience in using state of the art design tools.

Classes: Lectures 2 x 75 minutes, lab 1 x 120 minutes per week.

Co-requisites: Digital Circuits and Analysis lab

This is an introductory course on computer organization and architecture. The terminology and understanding of functional organizations and sequential operation of the HW/SW of modern digital computer is taught in this course. Topics include pipelining, microprocessor organization, microprogramming, cache memory, memory organization, addressing, stacks, argument passing, arithmetic operations, traps, and input/output.
Organization of RISC and CISC computers is discussed. Microcontrollers and embedded systems are discussed as well as Flynns's categories of large computer systems. Hands-on lab exercises make use of Motorolla 68k simulator for the illustration of addressing modes, and Xilinx Virtex Pro2 boards are used for exercises illustrating performance issues relating to different microprocessor organization.

Course Objective:
Main objective of the course is to understand main- and sub systems of modern digital computer and how these systems are interlinked. Among other objectives are: how performance issues are affected by different microprocessor organization, the implementation of soft-core processors in FPGA, and the understanding of how high-level programming languages and compilers take advantage of different computer hardware and organization.

Classes:
Lectures 2 x 75 minutes, lab and problem hours will be conducted as needed during the course. Students are expected to be proactive solving lab exercises and to seek assistance from the teacher as needed, 1 x 100 minutes per week.

Co-prerequisites: Hands-on lab exercises

Laboratory session in TÖV301G Computer Organization.

Basics of quantum mechanics and statistical physics. The atom. Crystal structure. The band theory of solids. Semiconductors. Transport properties of semiconductors and metals. The band theory of solids. Optical properties of semiconductors. P-n junctions. Diodes. Transistors. MOS devices. Lasers, diodes and semiconductor optics.

Discrete and continuous signals. Transfer functions and convolution. Difference equations and differential equations. Fourier series and Fourier transforms. Fourier analysis of discrete signals. The Laplace transform in analysis of continuous signals. The Z-transform in analysis of discrete signals. Homework and Matlab computer assignments.

Introduction to electrical signals, their properties and measurements
Treatment of measurement errors and their propagation in a measurement system
Power supplies and signal generators
Introduction to sensors and transducers that deliver an electrical signal
Introduction to measurement system components.
Electrical measurments with analogue and digital multimeters
Measurements using an oscilloscope
Measurements on resistance, inductance and capacitance with multimeters, oscilloscopes and bridges
Noise, interference and their consequennces
Resistors, capacitors, inductors and other components, their strcture, colour codes, treatment of semiconductors
Electrical network of houses and the laboratory, precautions in using electricity and equipment in a laboratory
Dangers and rules of conduct
Home problems and home projects
Laboratory exercises
Design project: Design of a specialised measurement system

Laboratory session in RAF301G Signals and Systems.

Functions of a complex variable. Analytic functions. The exponential function, logarithms and roots. Cauchy's Integral Theorem and Cauchy's Integral Formula. Uniform convergence. Power series. Laurent series. Residue integration method. Application of complex function theory to fluid flows. Ordinary differential equations and systems of ordinary differential equations. Linear differential equations with constant coefficients. Systems of linear differential equations. The matrix exponential function. Various methods for obtaining a particular solution. Green's functions for initial value problems. Flows and the phase plane. Nonlinear systems of ordinary differential equations in the plane, equilibrium points, stability and linear approximations. Series solutions and the method of Frobenius. Use of Laplace transforms in solving differential equations.

In this course, students learn to use the Laplace transform to analyze electrical circuits in the s-plane. Students are introduced to the properties of two-port circuits. Special emphasis is placed on second-order systems, and students learn to draw Bode plots, calculate transfer functions, and determine critical frequencies for such systems. The course covers approximation functions for analog filters and frequency transformations. It also includes synthesis of analog transfer functions, using LC and RC ladder circuits, as well as active components.

Electrostatics. Magnetostatics. The equations of Laplace and Poisson. Equation of continuity for time-varying fields. Maxwell's equations. Energy of the electromagnetic field. Electromagnetic waves. Plane waves in dielectric and conducting media. Elementary radiating systems. Reflection and refraction. Transmission lines. Wave guides. Electromagnetic radiation.

General characteristics of amplifiers, frequency response and Bode plots. Operational amplifiers and common circuits utilizing op amps, differential mode and common mode signals, offsets in operational amplifiers. Diodes and diode models, breakdown and zener operation, rectifiers, clipping and clamping circuits using diodes. Basic operation of bipolar junction transistors (BJT) and metal oxide field effect transistors (MOSFET), review of semiconductor physics, relationships between current and voltage, large signal models. Basic types of transistor amplifiers, small signal analysis, DC operating point regulation through feedback, common amplifier circuits.

An introductory treatment of probability theory including domains, dependent and independent events and probabilities. Random variables, one dimensional distributions, distribution functions, density functions, normal densities and the central limit theorem. Correlation and multidimensional distributions. Introduction to statistics. Random Processes. Autocorrelation and cross correlation. Power spectral density. Response of linear systems to random inputs.

Laboratory exercises for RAF401G Circuit Analysis and Synthesis.

This course consists of laboratory exercices related to the course RAF403G Electronics 1. This includes the construction of electronic circuits, measurements and tests following instructions. Students prepare lab reports of good quality where the laboratory work and main results are clearly summarized. The students learn about the equipment, components and tools used, and gain competence in their use. Instruments such as multimeters, oscilloscopes and signal generators are used and practiced in the lab exercises. Electronic circuits are analyzed with SPICE or similar simulation tools.

Exercices in RAF404G Probabilistic Methods.

Main features of integrated circuit amplifiers and comparison with circuits made from discrete components. Common circuits used in integrated circuit amplifiers such as current mirrors, differential pairs, cascode amplifiers, multistage amplifiers and output stages. High frequency characteristics of amplifiers, feedback and Miller effect. All of this is considered for both MOSFET and BJT circuits. Throughout the semester students work in groups on capstone projects where they apply theoretical knowledge and skills in the design and testing of electronic circuits.

Methods of classical automatic control systems. System models represented by transfer functions and state equations, simulation. System time and frequency responses. Properties of feedback control systems, stability, sensitivity, disturbance rejection, error coefficients. Stability analysis, Routh's stability criterion. Analysis and design using root-locus, lead, lag and PID controllers. Analysis and design in the frequency domain, lead, lag and PID compensators. Computer controlled systems, A/D and D/A converters, transformations of continuous controllers to discrete form. Analysis and design of digital control systems.

The objective is to provide the basic principles of digital filter design and signal processing. Strong emphasis is on individual projects and laboratory work. Syllabus: DTFT, DFT and FFT. Recursive filters (IIR), nonrecursive filters (FIR), effects of finite word length in digital filters. Filtering and analysis of random signals based on Fourier Analysis. Multirate digital signs processing.

Telecommunication systems are everywhere in modern societies, and great progress has been made in the field of telecommunications in recent years. The development is still going on and will be for coming years, both in terms of technology itself and its utilisation. It is therefore clear that there will be demand for knowledge on telecommunications in years to come.

In this course, basic understanding of telecommunications will be provided emphasising the system view. The course begins by a short review of the history of telecommunications.  Following is a discussion of major signal treatment methodologies before and after transmission over a communications channel, both for analogue and digital transmission. An introduction to telecommunications media will be given, wireless and wired telecommunications, amplitude and angle modulation, multiplexing and multiple access, random processes and noise in telecommunication systems. How to design a telecommunication system with respect to signal-noise ratio, digital modulation techniques, eye diagrams and Shannon’s law on channel capacity. Finally, data encoding and decoding will be introduced, how to detect and even correct errors.

The teaching will be in the form of lectures and discussions. Problems will be solved in class and home assignments given.

Databases and database management systems. Physical data organization. Data modelling using the Entity-Relationship model and the Relational model. Relational algebra and calculus.  The SQL query language. Design theory for relational data bases, functional dependencies, decomposition of relational schemes, normal forms. Query optimization. Concurrency control techniques and crash recovery. Database security and authorization. Data warehousing.

Survey of contemporary computer organisation covering performance measurement, design of instruction sets, instruction execution and recent techniques for exploiting instruction level paralellism. Design of caches, main memory. Virtual memory and storage systems. Design of multiprocessors.

This course is centered on the design, implementation, and testing of the electrical and electronic systems of the Formula Student project.
In addition students get training in working on a cross discipline design team with the main focus on the electrical system. This includes: power systems and wiring, charging system, propulsion system, micro controllers, sensors, real-time HW/SW development and communications.

Introduction to the instrumentation, physics and signal processing methods used in medical imaging systems from a signal processing perspective. The modalities covered include projection radiography, X-ray computed tomography, nuclear medicine (i.e. SPECT and PET), ultrasound, and magnetic resonance imaging.  The primary focus is on the methods required to reconstruct images within each modality, the kind of signals being measured and how these data culminate in an image.  Attention will also be given to image quality in each modality, including resolution, contrast, signal-to-noise ratio, and distortion of images.

The course introduces programming techniques for embedded systems. Emphasis is on concurrency, real-time systems and event driven programming. The course also addresses programming language support for the aforementioned issues. Unified Modeling Language (UML) for real-time systems is introduced along with the design and implementation of multitasking in embedded systems, and programming of threads that share memory and communicate. The course has lab sessions where development environment and boards from Xilinx are used.

This course is centered on the design, implementation, and testing of the electrical and electronic systems of the Formula Student project.
In addition students get training in working on a cross discipline design team with the main focus on the electrical system. This includes: power systems and wiring, charging system, propulsion system, micro controllers, sensors, real-time HW/SW development and communications.

Digital mobile telecommunication systems were first deployed in the early 1990s. This was the basis for a great societal change, people now being able to contact others where- and whenever needed. The emergence of the smartphone and high speed mobile infrastructure has furthermore revolutionised peoples’ possibilities to gain information in text-, sound-, and video formats almost irrespective of place and time. The development of Wi-Fi has also been fast in recent years causing people to enjoy more and more “wireless freedom” in their homes and workplaces. Wireless communications are important in many other areas including television, radio broadcast, marine and aeronautical communications, positioning and navigation systems. Internet of things or device-to-device communications are also wireless to a large extent.
In this course there will be treatment of the fundamentals of wireless, including antennas and wave propagation, transmission lines, high-frequency circuits and characteristics of different mobile phone generations, from the first to the fifth. This includes modulation and multiplexing/multiple access technologies such as QAM, FDMA, CDMA,TDMA, W-CDMA, OFDM(A) and MIMO antenna technology. The duplexing technologies FDD and TDD will be treated as well as mobile service concepts such as data connectivity and voice incl. VoLTE. Standards for Wi-Fi, Bluetooth, Zigbee and Z-wave will be covered along with a short handling of Wireless sensor networks.
Furthermore, short description will be given on digital broadcasting such as DVB-T and DVB-S, satellite communications and satellite positioning/navigation systems.
The form of the course will be lectures and discussions. Students will work on four projects and write reports, hold short presentations or present their results otherwise.

Machine learning is a field within artificial intelligence that focuses on methods enabling computers to learn patterns in data and use them to solve tasks, such as identifying objects in images. The applications of machine learning are extensive and include signal processing, control systems, computer vision, medical engineering, and much more. The purpose of this course is to introduce students to the main methods of machine learning along with its primary applications. The course will also cover key methods in deep learning, which underpins large language models. Emphasis will be placed on both theoretical foundations and practical training, with the aim of equipping students to use computers to solve practical problems. An important component of this course is the final project, where students will apply the methods learned in the course to solve interesting problems.

• Controllers for difficult systems
• Design of state feedback controllers
• Design of asymptotic observers
• Similarity transformations to canonical state space forms
• Controllability and observability
• Optimization (Linear Quadratic Regulator - LQR) - linear quadratic state feedback controllers
• Kalman filtering
• State feedback controllers and observers in transfer function form, reduced order observers
• Disturbance observers
• Feedforward (FF) controllers and Internal Model Controllers (IMC)
• Coefficient matching PID controllers
• Model Prediction Control (MPC)
• Systems Identification

This course covers concepts of operating systems. Besides foundations on computer hardware structures and general operating system architectures, this includes concepts of processes and threads and their management, principles of scheduling and scheduling algorithms, communication and synchronisation between processes and deadlock issues, principles of memory management including virtual memory and page replacement algorithms, file systems and their implementation as well as mass-storage management. If time allows, principles for achieving protection and security, and aspects of distribution (e.g. concepts of distributed systems and distributed file systems) are covered as well. This course does not deal with details of implementing operating systems, but introduces generic concepts that are used when implementing operating systems and that an application developer needs to know, when creating an application program. Where appropriate, current operating systems such as Microsoft Windows and POSIX-compliant UNIX-like systems (e.g. Linux) are used as case study for implementation and offered system calls. The usage of operating system services from within high-level programming languages (e.g. C, C++ or Java) is demonstrated based on Application Programming Interfaces (APIs) offered by prevailing system libraries.

Methodology for the design of algorithms and the analysis of their time conplexity. Analysis of algorithms for sorting, searching, graph theory and matrix computations. Intractable problems, heuristics, and randomized algorithms.

Aim: To introduce the student to Fourier analysis and partial differential equations and their applications.
Subject matter: Fourier series and orthonormal systems of functions, boundary-value problems for ordinary differential equations, the eigenvalue problem for Sturm-Liouville operators, Fourier transform. The wave equation, diffusion equation and Laplace's equation solved on various domains in one, two and three dimensions by methods based on the first part of the course, separation of variables, fundamental solution, Green's functions and the method of images.

Fundamental concepts on approximation and error estimates. Solutions of systems of linear and non-linear equations. PLU decomposition. Interpolating polynomials, spline interpolation and regression. Numerical differentiation and integration. Extrapolation. Numerical solutions of initial value problems of systems of ordinary differential equations. Multistep methods. Numerical solutions to boundary value problems for ordinary differential equations.

Grades are given for programning projects and in total they amount to 30% of the final grade. The student has to receive the minimum grade of 5 for both the projects and the final exam.

Comprehensive course on the Internet of Things and Sensors Networks covering all aspects relating to applications, architectures, and communication protocols in great detail. The course focuses on not only terrestrial networks, but also underwater, underground, and space networks.

Mathematical foundations of coordinate systems and transformations. Kinematics, direct and reverse solutions. Analysis and control of movements. Trajectories in three-dimensional space and interpolation between programmed trajectory points. Use of computer vision, sensors and end-effectors in robotics. Control and programming of robots. Exercises and simulations.

This course offers an advanced exploration of machine learning and high-performance computing (HPC) techniques tailored to satellite remote sensing and Earth observation (EO). Starting with the historical evolution of Earth observation—from early aerial photography to today’s high-throughput satellite constellations such as Sentinel and Landsat—the curriculum situates modern EO within the context of an unprecedented “big data” era, driven by terabytes of imagery captured daily.

Building on foundational concepts in traditional pixel-based analysis, students will progress to contemporary approaches that leverage the deep learning revolution and the emergence of AI foundation models. These models employ self-supervised learning and Transformer-based architectures to extract structure and meaning from vast amounts of unlabeled data at scale. The course emphasizes how these advanced machine learning paradigms are reshaping EO data analytics beyond classical handcrafted methods.

A core theme of the semester is the intersection of large-scale machine learning and HPC. Students will examine how modern supercomputers enable the training and deployment of Geospatial AI foundation models for Earth observation. This includes discussions on distributed training, parallel algorithm design, and performance optimization on HPC infrastructures. The course also covers benchmarking and performance evaluation, introducing students to standardized evaluation frameworks and metrics to assess model scalability, efficiency, and accuracy in real-world Earth observation applications.

To integrate theory and practice, students complete a semester-long capstone project. Through hands-on development with Python APIs and open models, students will design, implement, and evaluate machine learning solutions on real EO datasets. Projects reinforce the application of theoretical concepts to practical problems, preparing students for research or industry roles at the forefront of AI for EO.

Modern day telecommunications are characterised by the fact that communicated data is carried on fixed telecommunications infrastructure on a majority of the path between tranmitter and receiver. Wireless infrastructure often conveys the signals at the end of the path. This yields both high speed and the comfort of wireless communications. It is of utmost importance for engineers working in telecoms to have a fundamental knowledge of fixed networks and the range of technologies deployed.

In this course, the structure of fixed backbone and access networks will be described. Optical fibre and related technologies will be introduced, e.g. DWDM, SDH, Ethernet, ATM and MPLS-TP. Access network technologies on copper, coax and optical fibres will be treated, e.g. ADSL. VDSL, G.fast and  DOCSIS. Different FTTH (Fibre to the Home) technologies will be treated such as PON (Passive Optical Network), Active Ethernet and point-to-point Ethernet. 

IP (Internet Protocol) has become a fundamental technology for modern fixed networks. IP native technologies will be described from the physical to the application layer. On the link layer, Ethernet will be in the focus as well as MPLS. Circuit and packet switching will be treated as well as circuit and packet orientation of networks. Sevices such as PSTN, VoIP, OTT and P2P will be treated. Backhauling of wireless networks such as mobile networks and Wi-Fi will also be treated.
In introduction to network virtualisation and network function virtualisation (NFV) will be given as well as software defined networking (SDN). Legal and regulatory aspects will be introduced and aspects like network neutrality discfussed. Important players and stakeholders will be discussed, e.g. Google, Apple, Microsoft, Netflix and telecommunications service providers.
Finally, local area networks will be discussed, home networking, smart homes, set-top-boxes, NAS, PLC, plastic optical fibres, MOCA and Wi-Fi introduced.

The teaching form will be lectures and projects on IP communications will be worked. Students will write four papers on selected subjects and give presentations. 

Tutor classes for electrical and computer engineering students.

Tutor classes for electrical and computer engineering students.

The study of electrical and computer engineering (ECE) is introduced, both at the undergraduate and the graduate level, and the various applications of the subject are presented. Firms and institutes are visited and guest lecturers are invited to outline the diverse roles that electrical and computer engineers have in the job market. Professional societies in this field of engineering are presented, as well as the rules of ethics that they have adopted. Assignments are given to give further insight into the studies and the jobs that they lead to.

Concepts, units, scales and dimensions. Vectors. Kinematics of particles. Particle dynamics, inertia, forces and Newton's laws. Friction. Work and energy, conservation of energy. Momentum, collisions. Systems of particles, center of mass. Rotation of a rigid body. Angular momentum and moment of inertia. Statics. Gravity. Solids and fluids, Bernoulli's equation. Oscillations: Simple, damped and forced. Waves. Sound. Temperature. Ideal gas. Heat and the first law of thermodynamics. Kinetic theory of gases. Entropy and the second law of thermodynamics. Home problems: Once a week the students have to solve homeproblems on the website MasteringPhysics.

Laboratory work: Three exercises, mainly centered on mechanics, where students are trained in handling physical instruments, collecting and inspecting data. Students hand in their lab notebooks for a grade.

Note that the textbook is accessible to students via Canvas free of charge.

This is a foundational course in single variable calculus. The prerequisites are high school courses on algebra, trigonometry. derivatives, and integrals. The course aims to create a foundation for understanding of subjects such as natural and physical sciences, engineering, economics, and computer science. Topics of the course include the following:

• Real numbers.
• Limits and continuous functions.
• Differentiable functions, rules for derivatives, derivatives of higher order, applications of differential calculus (extremal value problems, linear approximation).
• Transcendental functions.
• Mean value theorem, theorems of l'Hôpital and Taylor.
• Integration, the definite integral and rules/techniques of integration, primitives, improper integrals.
• Fundamental theorem of calculus.
• Applications of integral calculus: Arc length, area, volume, centroids.
• Ordinary differential equations: First-order separable and homogeneous differential equations, first-order linear equations, second-order linear equations with constant coefficients.
• Sequences and series, convergence tests.
• Power series, Taylor series.

Basics of linear algebra over the reals.  

Subject matter: Systems of linear equations, matrices, Gauss-Jordan reduction.  Vector spaces and their subspaces.  Linearly independent sets, bases and dimension.  Linear maps, range space and nullk space.  The dot product, length and angle measures.  Volumes in higher dimension and the cross product in threedimensional space.  Flats, parametric descriptions and descriptions by equations.  Orthogonal projections and orthonormal bases.  Gram-Schmidt orthogonalization.  Determinants and inverses of matrices.  Eigenvalues, eigenvectors and diagonalization.

Note: Only one course of either TÖL101G Tölvunarfræði 1 or TÖL105G Tölvunarfræði 1a can count towards the BS degree.

The Java programming language is used to introduce basic concepts in computer programming: Expressions and statements, textual and numeric data types, conditions and loops, arrays, methods, classes and objects, input and output. Programming and debugging skills are practiced in quizzes and projects throughout the semester.

The programming language Java will be used in the course. Various data structures, algorithms and abstract data types will be covered. Among the data types and structures covered are lists, stacks, queues, priority queues, trees, binary trees, binary search trees and heaps along with related algorithms. Various search and sort algorithms will be covered. Algorithms will be analysed for their space and time complexity. There will be programming assignments in Java using the given data structures and algorithms. There will be many small assignments.

Teaching takes 12 weeks. Charge and electric field. Gauss' law. Electric potential. Capacitors and dielectrics. Electric currents and resistance. Circuits. Magnetic fields. The laws of Ampère and Faraday. Induction. Electric oscillation and alternating currents. Maxwell's equations. Electromagnetic waves. Reflection and refraction. Lenses and mirrors. Wave optics. Four laboratory exercises in optics and electromagnetism.

Definitions and basic concepts. Kirchoff's laws, mesh- and node-equations. Circuits with resistance, matrix representation. Dependent sources. Thevenin-Norton equivalent circuit theorems. Circuits with resistance, capacitance, inductance and mutual inductance. Time domain analysis. Initial conditions. Zero input solutions, zero state solutions, transients and steady state. Impulse response, convolution. Analysis of second order circuits. Systems with sinusoidal inputs. Computer exercises with PSpice and Matlab.

Open and closed sets. Mappings, limits and continuity. Differentiable mappings, partial derivatives and the chain rule. Jacobi matrices. Gradients and directional derivatives. Mixed partial derivatives. Curves. Vector fields and flow. Cylindrical and spherical coordinates. Taylor polynomials. Extreme values and the classification of stationary points. Extreme value problems with constraints. Implicit functions and local inverses. Line integrals, primitive functions and exact differential equations. Double integrals. Improper integrals. Green's theorem. Simply connected domains. Change of variables in double integrals. Multiple integrals. Change of variables in multiple integrals. Surface integrals. Integration of vector fields. The theorems of Stokes and Gauss.

Students will learn digital design principles and practice. Design is based on standard MSI and LSI devices or equivalent building blocks such as counters, shift registers, adders, and ROM. The design and analysis of combinatorial circuits for basic arithmetic is emphasized as well as the design an analysis of synchronous and asynchronous sequential circuits. Students will design circuits using basic building blocks such as flip flops and latches. Design and analysis of clocked sequential circuits based on Moore and Mealy FSM is emphasized. Introduction to Verilog HDL and FPGA in the design of as it applies to the previously described basic digital circuits. Students are required to complete 7 lab projects using FPGA. Students will also finish selected set of lab exercises using breadboards to contrast the state of the art design principles with classical principles. Students will work in teams to design and simulate digital circuits using a state-of-the-art CAD package. Both schematic and VHDL-based designs are emphasized.

Course Objective: Students will understand classical digital design principles and gain experience in using state of the art design tools.

Classes: Lectures 2 x 75 minutes, lab 1 x 120 minutes per week.

Co-requisites: Digital Circuits and Analysis lab

This is an introductory course on computer organization and architecture. The terminology and understanding of functional organizations and sequential operation of the HW/SW of modern digital computer is taught in this course. Topics include pipelining, microprocessor organization, microprogramming, cache memory, memory organization, addressing, stacks, argument passing, arithmetic operations, traps, and input/output.
Organization of RISC and CISC computers is discussed. Microcontrollers and embedded systems are discussed as well as Flynns's categories of large computer systems. Hands-on lab exercises make use of Motorolla 68k simulator for the illustration of addressing modes, and Xilinx Virtex Pro2 boards are used for exercises illustrating performance issues relating to different microprocessor organization.

Course Objective:
Main objective of the course is to understand main- and sub systems of modern digital computer and how these systems are interlinked. Among other objectives are: how performance issues are affected by different microprocessor organization, the implementation of soft-core processors in FPGA, and the understanding of how high-level programming languages and compilers take advantage of different computer hardware and organization.

Classes:
Lectures 2 x 75 minutes, lab and problem hours will be conducted as needed during the course. Students are expected to be proactive solving lab exercises and to seek assistance from the teacher as needed, 1 x 100 minutes per week.

Co-prerequisites: Hands-on lab exercises

Laboratory session in TÖV301G Computer Organization.

Basics of quantum mechanics and statistical physics. The atom. Crystal structure. The band theory of solids. Semiconductors. Transport properties of semiconductors and metals. The band theory of solids. Optical properties of semiconductors. P-n junctions. Diodes. Transistors. MOS devices. Lasers, diodes and semiconductor optics.

Discrete and continuous signals. Transfer functions and convolution. Difference equations and differential equations. Fourier series and Fourier transforms. Fourier analysis of discrete signals. The Laplace transform in analysis of continuous signals. The Z-transform in analysis of discrete signals. Homework and Matlab computer assignments.

Introduction to electrical signals, their properties and measurements
Treatment of measurement errors and their propagation in a measurement system
Power supplies and signal generators
Introduction to sensors and transducers that deliver an electrical signal
Introduction to measurement system components.
Electrical measurments with analogue and digital multimeters
Measurements using an oscilloscope
Measurements on resistance, inductance and capacitance with multimeters, oscilloscopes and bridges
Noise, interference and their consequennces
Resistors, capacitors, inductors and other components, their strcture, colour codes, treatment of semiconductors
Electrical network of houses and the laboratory, precautions in using electricity and equipment in a laboratory
Dangers and rules of conduct
Home problems and home projects
Laboratory exercises
Design project: Design of a specialised measurement system

Laboratory session in RAF301G Signals and Systems.

Functions of a complex variable. Analytic functions. The exponential function, logarithms and roots. Cauchy's Integral Theorem and Cauchy's Integral Formula. Uniform convergence. Power series. Laurent series. Residue integration method. Application of complex function theory to fluid flows. Ordinary differential equations and systems of ordinary differential equations. Linear differential equations with constant coefficients. Systems of linear differential equations. The matrix exponential function. Various methods for obtaining a particular solution. Green's functions for initial value problems. Flows and the phase plane. Nonlinear systems of ordinary differential equations in the plane, equilibrium points, stability and linear approximations. Series solutions and the method of Frobenius. Use of Laplace transforms in solving differential equations.

In this course, students learn to use the Laplace transform to analyze electrical circuits in the s-plane. Students are introduced to the properties of two-port circuits. Special emphasis is placed on second-order systems, and students learn to draw Bode plots, calculate transfer functions, and determine critical frequencies for such systems. The course covers approximation functions for analog filters and frequency transformations. It also includes synthesis of analog transfer functions, using LC and RC ladder circuits, as well as active components.

Electrostatics. Magnetostatics. The equations of Laplace and Poisson. Equation of continuity for time-varying fields. Maxwell's equations. Energy of the electromagnetic field. Electromagnetic waves. Plane waves in dielectric and conducting media. Elementary radiating systems. Reflection and refraction. Transmission lines. Wave guides. Electromagnetic radiation.

General characteristics of amplifiers, frequency response and Bode plots. Operational amplifiers and common circuits utilizing op amps, differential mode and common mode signals, offsets in operational amplifiers. Diodes and diode models, breakdown and zener operation, rectifiers, clipping and clamping circuits using diodes. Basic operation of bipolar junction transistors (BJT) and metal oxide field effect transistors (MOSFET), review of semiconductor physics, relationships between current and voltage, large signal models. Basic types of transistor amplifiers, small signal analysis, DC operating point regulation through feedback, common amplifier circuits.

An introductory treatment of probability theory including domains, dependent and independent events and probabilities. Random variables, one dimensional distributions, distribution functions, density functions, normal densities and the central limit theorem. Correlation and multidimensional distributions. Introduction to statistics. Random Processes. Autocorrelation and cross correlation. Power spectral density. Response of linear systems to random inputs.

Laboratory exercises for RAF401G Circuit Analysis and Synthesis.

This course consists of laboratory exercices related to the course RAF403G Electronics 1. This includes the construction of electronic circuits, measurements and tests following instructions. Students prepare lab reports of good quality where the laboratory work and main results are clearly summarized. The students learn about the equipment, components and tools used, and gain competence in their use. Instruments such as multimeters, oscilloscopes and signal generators are used and practiced in the lab exercises. Electronic circuits are analyzed with SPICE or similar simulation tools.

Exercices in RAF404G Probabilistic Methods.

Main features of integrated circuit amplifiers and comparison with circuits made from discrete components. Common circuits used in integrated circuit amplifiers such as current mirrors, differential pairs, cascode amplifiers, multistage amplifiers and output stages. High frequency characteristics of amplifiers, feedback and Miller effect. All of this is considered for both MOSFET and BJT circuits. Throughout the semester students work in groups on capstone projects where they apply theoretical knowledge and skills in the design and testing of electronic circuits.

Methods of classical automatic control systems. System models represented by transfer functions and state equations, simulation. System time and frequency responses. Properties of feedback control systems, stability, sensitivity, disturbance rejection, error coefficients. Stability analysis, Routh's stability criterion. Analysis and design using root-locus, lead, lag and PID controllers. Analysis and design in the frequency domain, lead, lag and PID compensators. Computer controlled systems, A/D and D/A converters, transformations of continuous controllers to discrete form. Analysis and design of digital control systems.

The objective is to provide the basic principles of digital filter design and signal processing. Strong emphasis is on individual projects and laboratory work. Syllabus: DTFT, DFT and FFT. Recursive filters (IIR), nonrecursive filters (FIR), effects of finite word length in digital filters. Filtering and analysis of random signals based on Fourier Analysis. Multirate digital signs processing.

Telecommunication systems are everywhere in modern societies, and great progress has been made in the field of telecommunications in recent years. The development is still going on and will be for coming years, both in terms of technology itself and its utilisation. It is therefore clear that there will be demand for knowledge on telecommunications in years to come.

In this course, basic understanding of telecommunications will be provided emphasising the system view. The course begins by a short review of the history of telecommunications.  Following is a discussion of major signal treatment methodologies before and after transmission over a communications channel, both for analogue and digital transmission. An introduction to telecommunications media will be given, wireless and wired telecommunications, amplitude and angle modulation, multiplexing and multiple access, random processes and noise in telecommunication systems. How to design a telecommunication system with respect to signal-noise ratio, digital modulation techniques, eye diagrams and Shannon’s law on channel capacity. Finally, data encoding and decoding will be introduced, how to detect and even correct errors.

The teaching will be in the form of lectures and discussions. Problems will be solved in class and home assignments given.

Databases and database management systems. Physical data organization. Data modelling using the Entity-Relationship model and the Relational model. Relational algebra and calculus.  The SQL query language. Design theory for relational data bases, functional dependencies, decomposition of relational schemes, normal forms. Query optimization. Concurrency control techniques and crash recovery. Database security and authorization. Data warehousing.

Survey of contemporary computer organisation covering performance measurement, design of instruction sets, instruction execution and recent techniques for exploiting instruction level paralellism. Design of caches, main memory. Virtual memory and storage systems. Design of multiprocessors.

This course is centered on the design, implementation, and testing of the electrical and electronic systems of the Formula Student project.
In addition students get training in working on a cross discipline design team with the main focus on the electrical system. This includes: power systems and wiring, charging system, propulsion system, micro controllers, sensors, real-time HW/SW development and communications.

Introduction to the instrumentation, physics and signal processing methods used in medical imaging systems from a signal processing perspective. The modalities covered include projection radiography, X-ray computed tomography, nuclear medicine (i.e. SPECT and PET), ultrasound, and magnetic resonance imaging.  The primary focus is on the methods required to reconstruct images within each modality, the kind of signals being measured and how these data culminate in an image.  Attention will also be given to image quality in each modality, including resolution, contrast, signal-to-noise ratio, and distortion of images.

The course introduces programming techniques for embedded systems. Emphasis is on concurrency, real-time systems and event driven programming. The course also addresses programming language support for the aforementioned issues. Unified Modeling Language (UML) for real-time systems is introduced along with the design and implementation of multitasking in embedded systems, and programming of threads that share memory and communicate. The course has lab sessions where development environment and boards from Xilinx are used.

This course is centered on the design, implementation, and testing of the electrical and electronic systems of the Formula Student project.
In addition students get training in working on a cross discipline design team with the main focus on the electrical system. This includes: power systems and wiring, charging system, propulsion system, micro controllers, sensors, real-time HW/SW development and communications.

Digital mobile telecommunication systems were first deployed in the early 1990s. This was the basis for a great societal change, people now being able to contact others where- and whenever needed. The emergence of the smartphone and high speed mobile infrastructure has furthermore revolutionised peoples’ possibilities to gain information in text-, sound-, and video formats almost irrespective of place and time. The development of Wi-Fi has also been fast in recent years causing people to enjoy more and more “wireless freedom” in their homes and workplaces. Wireless communications are important in many other areas including television, radio broadcast, marine and aeronautical communications, positioning and navigation systems. Internet of things or device-to-device communications are also wireless to a large extent.
In this course there will be treatment of the fundamentals of wireless, including antennas and wave propagation, transmission lines, high-frequency circuits and characteristics of different mobile phone generations, from the first to the fifth. This includes modulation and multiplexing/multiple access technologies such as QAM, FDMA, CDMA,TDMA, W-CDMA, OFDM(A) and MIMO antenna technology. The duplexing technologies FDD and TDD will be treated as well as mobile service concepts such as data connectivity and voice incl. VoLTE. Standards for Wi-Fi, Bluetooth, Zigbee and Z-wave will be covered along with a short handling of Wireless sensor networks.
Furthermore, short description will be given on digital broadcasting such as DVB-T and DVB-S, satellite communications and satellite positioning/navigation systems.
The form of the course will be lectures and discussions. Students will work on four projects and write reports, hold short presentations or present their results otherwise.

Machine learning is a field within artificial intelligence that focuses on methods enabling computers to learn patterns in data and use them to solve tasks, such as identifying objects in images. The applications of machine learning are extensive and include signal processing, control systems, computer vision, medical engineering, and much more. The purpose of this course is to introduce students to the main methods of machine learning along with its primary applications. The course will also cover key methods in deep learning, which underpins large language models. Emphasis will be placed on both theoretical foundations and practical training, with the aim of equipping students to use computers to solve practical problems. An important component of this course is the final project, where students will apply the methods learned in the course to solve interesting problems.

• Controllers for difficult systems
• Design of state feedback controllers
• Design of asymptotic observers
• Similarity transformations to canonical state space forms
• Controllability and observability
• Optimization (Linear Quadratic Regulator - LQR) - linear quadratic state feedback controllers
• Kalman filtering
• State feedback controllers and observers in transfer function form, reduced order observers
• Disturbance observers
• Feedforward (FF) controllers and Internal Model Controllers (IMC)
• Coefficient matching PID controllers
• Model Prediction Control (MPC)
• Systems Identification

This course covers concepts of operating systems. Besides foundations on computer hardware structures and general operating system architectures, this includes concepts of processes and threads and their management, principles of scheduling and scheduling algorithms, communication and synchronisation between processes and deadlock issues, principles of memory management including virtual memory and page replacement algorithms, file systems and their implementation as well as mass-storage management. If time allows, principles for achieving protection and security, and aspects of distribution (e.g. concepts of distributed systems and distributed file systems) are covered as well. This course does not deal with details of implementing operating systems, but introduces generic concepts that are used when implementing operating systems and that an application developer needs to know, when creating an application program. Where appropriate, current operating systems such as Microsoft Windows and POSIX-compliant UNIX-like systems (e.g. Linux) are used as case study for implementation and offered system calls. The usage of operating system services from within high-level programming languages (e.g. C, C++ or Java) is demonstrated based on Application Programming Interfaces (APIs) offered by prevailing system libraries.

Methodology for the design of algorithms and the analysis of their time conplexity. Analysis of algorithms for sorting, searching, graph theory and matrix computations. Intractable problems, heuristics, and randomized algorithms.

Aim: To introduce the student to Fourier analysis and partial differential equations and their applications.
Subject matter: Fourier series and orthonormal systems of functions, boundary-value problems for ordinary differential equations, the eigenvalue problem for Sturm-Liouville operators, Fourier transform. The wave equation, diffusion equation and Laplace's equation solved on various domains in one, two and three dimensions by methods based on the first part of the course, separation of variables, fundamental solution, Green's functions and the method of images.

Fundamental concepts on approximation and error estimates. Solutions of systems of linear and non-linear equations. PLU decomposition. Interpolating polynomials, spline interpolation and regression. Numerical differentiation and integration. Extrapolation. Numerical solutions of initial value problems of systems of ordinary differential equations. Multistep methods. Numerical solutions to boundary value problems for ordinary differential equations.

Grades are given for programning projects and in total they amount to 30% of the final grade. The student has to receive the minimum grade of 5 for both the projects and the final exam.

Comprehensive course on the Internet of Things and Sensors Networks covering all aspects relating to applications, architectures, and communication protocols in great detail. The course focuses on not only terrestrial networks, but also underwater, underground, and space networks.

Mathematical foundations of coordinate systems and transformations. Kinematics, direct and reverse solutions. Analysis and control of movements. Trajectories in three-dimensional space and interpolation between programmed trajectory points. Use of computer vision, sensors and end-effectors in robotics. Control and programming of robots. Exercises and simulations.

This course offers an advanced exploration of machine learning and high-performance computing (HPC) techniques tailored to satellite remote sensing and Earth observation (EO). Starting with the historical evolution of Earth observation—from early aerial photography to today’s high-throughput satellite constellations such as Sentinel and Landsat—the curriculum situates modern EO within the context of an unprecedented “big data” era, driven by terabytes of imagery captured daily.

Building on foundational concepts in traditional pixel-based analysis, students will progress to contemporary approaches that leverage the deep learning revolution and the emergence of AI foundation models. These models employ self-supervised learning and Transformer-based architectures to extract structure and meaning from vast amounts of unlabeled data at scale. The course emphasizes how these advanced machine learning paradigms are reshaping EO data analytics beyond classical handcrafted methods.

A core theme of the semester is the intersection of large-scale machine learning and HPC. Students will examine how modern supercomputers enable the training and deployment of Geospatial AI foundation models for Earth observation. This includes discussions on distributed training, parallel algorithm design, and performance optimization on HPC infrastructures. The course also covers benchmarking and performance evaluation, introducing students to standardized evaluation frameworks and metrics to assess model scalability, efficiency, and accuracy in real-world Earth observation applications.

To integrate theory and practice, students complete a semester-long capstone project. Through hands-on development with Python APIs and open models, students will design, implement, and evaluate machine learning solutions on real EO datasets. Projects reinforce the application of theoretical concepts to practical problems, preparing students for research or industry roles at the forefront of AI for EO.

Modern day telecommunications are characterised by the fact that communicated data is carried on fixed telecommunications infrastructure on a majority of the path between tranmitter and receiver. Wireless infrastructure often conveys the signals at the end of the path. This yields both high speed and the comfort of wireless communications. It is of utmost importance for engineers working in telecoms to have a fundamental knowledge of fixed networks and the range of technologies deployed.

In this course, the structure of fixed backbone and access networks will be described. Optical fibre and related technologies will be introduced, e.g. DWDM, SDH, Ethernet, ATM and MPLS-TP. Access network technologies on copper, coax and optical fibres will be treated, e.g. ADSL. VDSL, G.fast and  DOCSIS. Different FTTH (Fibre to the Home) technologies will be treated such as PON (Passive Optical Network), Active Ethernet and point-to-point Ethernet. 

IP (Internet Protocol) has become a fundamental technology for modern fixed networks. IP native technologies will be described from the physical to the application layer. On the link layer, Ethernet will be in the focus as well as MPLS. Circuit and packet switching will be treated as well as circuit and packet orientation of networks. Sevices such as PSTN, VoIP, OTT and P2P will be treated. Backhauling of wireless networks such as mobile networks and Wi-Fi will also be treated.
In introduction to network virtualisation and network function virtualisation (NFV) will be given as well as software defined networking (SDN). Legal and regulatory aspects will be introduced and aspects like network neutrality discfussed. Important players and stakeholders will be discussed, e.g. Google, Apple, Microsoft, Netflix and telecommunications service providers.
Finally, local area networks will be discussed, home networking, smart homes, set-top-boxes, NAS, PLC, plastic optical fibres, MOCA and Wi-Fi introduced.

The teaching form will be lectures and projects on IP communications will be worked. Students will write four papers on selected subjects and give presentations. 

Tutor classes for electrical and computer engineering students.

Tutor classes for electrical and computer engineering students.