Search programme

​Use the search function to search amongst programmes at Chalmers. The study programme and the study programme syllabus relating to your studies are generally from the academic year you began your studies.

Syllabus for

Academic year
TMA362 - Fourier analysis
 
Syllabus is not yet adopted
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: X

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0101 Examination 7,5c Grading: TH   7,5c   26 Oct 2013 am V,  11 Jan 2014 am V,  18 Aug 2014 am V

In programs

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

Examiner:

Bitr professor  Hjalmar Rosengren



  Go to Course Homepage

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

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, 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.

Organisation

Lectures and problem sessions

Literature

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

Examination

Written exam.


Published: Mon 28 Nov 2016.