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## Numerical Methods in Electrical Engineering

Lecturer (assistant) Helmut Gräb 0000004382 4 SWS Wintersemester 2022/23 German See TUMonline

See TUMonline
Note: The registration is done in TUMonline.

### Objectives

After passing this course the student is able to use basic numerical methods in fundamental tasks of electrical engineering, e.g. numerical simulation processes.

### Description

- methods for solving linear equation systems, e.g. Gaussian elimination, cholesky decomposition, SVD, conjugated gradients method, relaxation - methods for model order reduction (Krylov subspace transformation), e.g. Arnoldi-iteration, Lanczos method - methods for finding the root of a real-valued function, e.g. Newton-Raphson method, interval section - numerical methods for integration of differential equation systems, e.g. explicit and implicit Euler method, trapezoidal method, Gear method The named methods are developed in context of their application area in electrical engineering. One famous example is electronic circuit simulation - a time-saving key technique that allows to design large circuits and systems without loss of material. Numerical methods and algorithm are the main part of modern simulation processes. The following simulation types are used to explain the named numerical methods: - linear small-signal frequency domain analysis (AC analysis) - nonlinear quiescent point calculation (DC analysis) - transient analysis - nonlinear frequency analysis (Harmonic Balance, shooting methods)

### Prerequisites

Good knowledge in higher mathematics are needed (offered in B.Sc. program).

### Teaching and learning methods

In addition to individual learning methods of the student the knowledge is transfered by solving exercises. The preferred teaching method in the lecture is teacher-centered learning. In the Exercise course the students solve problems on their own. Furthermore home exercises in Matlab help to understand how the numerical methods are realized in practice.

### Examination

There is a final exam in written form (120 min., open book policy).

### Recommended literature

Strang - "Computational Science and Engineering"

## All courses

Bachelorbereich: BSc-EI, MSE, BSEDE

 WS SS Diskrete Mathematik für Ingenieure (BSEI, EI00460) Discrete Mathematics for Engineers (BSEDE ) (Schlichtmann) (Januar) WS SS Entwurf digitaler Systeme mit VHDL u. System C (BSEI, EI0690) (Ecker) SS Entwurfsverfahren für integrierte Schaltungen (MSE, EI43811) (Schlichtmann) WS Methoden der Unternehmensführung (BSEI, EI0481) (Weigel) WS Praktikum System- und Schaltungstechnik (BSEI, EI0664) (Schlichtmann et al.) SS Schaltungssimulation (BSEI, EI06691) (Gräb/Schlichtmann)

Masterbereich: MSc-EI, MSCE, ICD

 SS Advanced Topics in Communication Electronics (MSCE, MSEI, EI79002) WS Electronic Design Automation (MSCE, MSEI, EI70610) (B. Li, Tseng) WS Design Methodology and Automation (ICD) (Schlichtmann) (Nov) WS SS Machine Learning: Methods and Tools (MSCE, MSEI, EI71040) (Ecker) WS SS SS Mathematical Methods of Circuit Design (MSCE, MSEI, EI74042) (Gräb) Simulation and Optimization of Analog Circuits (ICD) (Gräb) (Mai) WS Mixed Integer Programming and Graph Algorithms in Engineering Problems (MSCE, MSEI, EI71059) (Tseng) WS SS Numerische Methoden der Elektrotechnik (MSEI, EI70440) (Schlichtmann oder Gräb) WS WS SS Seminar VLSI-Entwurfsverfahren (MSEI, EI7750) (Schlichtmann/Müller-Gritschneder) Seminar on Topics in Electronic Design Automation (MSCE, EI77502) (Schlichtmann/Müller-Gritschneder) WS SS Synthesis of Digital Systems (MSCE, MSEI, EI70640) (Müller-Gritschneder) WS Testing Digital Circuits (MSCE, MSEI, EI50141) (Otterstedt) WS Timing of Digital Circuits (MSCE, MSEI, EI70550) (B. Li, Zhang) WS SS VHDL System Design Laboratory (MSCE, MSEI, EI7403) (Schlichtmann)

`MSE: Munich School of Engineering (TUM)`

BSEDE`: Bachelor of Science in Electronics and Data Engineering`` (TUM-Asia)`

`ICD: Master of Science in Integrated Circuit Design (TUM-Asia)`

`MSCE: Master of Science in Communications Engineering (TUM)`

`MSEI: Master of Science in Elektrotechnik und Informationstechnik`

`BSEI: Bachelor of Science in Elektrotechnik und Informationstechnik`

Aktuelle Infos zur Lehre/Current information on teaching: https://www.tum.de/die-tum/aktuelles/coronavirus/studium/, www.ei.tum.de