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## Syllabus for

TMA362 - Fourier analysis

Syllabus adopted 2015-02-11 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: First-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: English
Open for exchange students
Block schedule:

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0101 Examination 7,5 c Grading: TH 7,5 c 24 Oct 2015 am V, 04 Jan 2016 am H 15 Aug 2016 am SB

#### In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)

#### Examiner:

Professor  Genkai Zhang

#### Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

#### Course specific prerequisites

The participant is presumed to have
(i) a solid background in calculus of one and several variables and linear algebra
(ii) knowledge of the elementary theory of linear ordinary differential equations
(iii) an acquantaince with the complex number system and the complex exponential function.

#### Aim

To give a solid background for the students to solve, e.g., partial differential equations using the ideas from modern analysis without getting bogged down in the technicalities of rigorous proofs.

#### Learning outcomes (after completion of the course the student should be able to)

compute Fourier series and transforms for functions and use the transforms to find solutions on partial differential equations

#### Content

This course presents the theory and applications of Fourier series and integrals. It covers the following topics: Examples of initial-boundary value problems for partial differential equations (PDEs), the method of separation of variables, trigonometric Fourier series and their convergence, linear spaces, scalar product and norms, orthogonal functions, Bessel's inequality, Parseval's formula, completeness, Sturm-Liouville problems, method of separation of variables for solving PDEs, techniques of solving inhomogeneous problems, some examples from physics, Fourier transform and Laplace transform with applications to ordinary and partial differential equations.

#### Organisation

Lectures and problem sessions

#### Literature

Fourier Analysis and Its Applications, G. B. Folland, Wadsworth & Brooks/Cole, 1992

#### Examination

Written exam.

Page manager Published: Mon 28 Nov 2016.