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Syllabus for

Academic year
TMA362 - Fourier analysis
 
Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: B
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0101 Examination 5,0 c Grading: TH   5,0 c   28 Oct 2006 am V,  24 Aug 2007 am V

In programs

EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)
TM Teknisk matematik, Year 1 (compulsory)
CEMAS MSc PROGRAMME IN COMPUTATIONAL AND EXPERIMENTAL TURBULENCE, Year 1 (elective)

Examiner:

Professor  Peter Sjögren



Eligibility:

For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

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

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, periodic and general Fourier series and their convergence theorems, linear spaces, scalar product and norms, orthogo-nal sets, Bessel's inequality, Parseval's formula, completeness, Sturm-Liouville problems, eigenfun-ction expansions, method of separation of variables for solving PDEs, techniques of solving inhomo-geneous problems, some examples of physics, Bessel functions, Solving problems in cylindrical coordinates, orthogonal polynomials (Legendre, Hermite, Laguerre polynomials), Solving problems in spherical coordinates, Fourier Transform and Laplace transform (calculi, applications to, both ordinary and partial, differential equations), and an introduction to generalized functions and their applications to differential equations.

Content

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.

Organisation

Lectures and problem sessions

Literature

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

Examination

Written exam.


Page manager Published: Thu 03 Nov 2022.