Search course

Use the search function to find more information about the study programmes and courses available at Chalmers. When there is a course homepage, a house symbol is shown that leads to this page.

Graduate courses

Departments' graduate courses for PhD-students.

​​​​
​​

Course syllabus for

Academic year
MVE030 - Fourier analysis  
Fourieranalys
 
Course syllabus adopted 2022-05-03 by Head of Programme (or corresponding)
Owner: TKTFY
6,0 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: First-cycle
Main field of study: Chemical Engineering with Engineering Physics, Mathematics, Engineering Physics
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: Swedish
Application code: 57115
Open for exchange students: No
Maximum participants: 180
Only students with the course round in the programme overview
Status, available places (updated regularly): Yes

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0105 Examination 6,0 c Grading: TH   6,0 c    

In programs

TKTFY ENGINEERING PHYSICS, Year 2 (compulsory)

Examiner:

Julie Rowlett

  Go to Course Homepage


Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Real analysis, Multivariable analysis, Linear algebra, Complex mathematical analysis.

Aim

The course introduces Fourier methods in the program. These methods are powerful mathematical tools in technology and science.

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

 1. Solve partial differential equations using variable separation as well as Fourier and Laplace transformers.

2. Constructively apply a selection of the methods: hilbert spaces, orthogonal systems, eigenfunctions and Fourier series expansions, eigenfunction expansions with Sturm-Liouville problems, Bessel functions or orthogonal polynomials to solve partial differential equations, calculate sums and integrals, and approximate functions.
3. Decide which method is best suited to solve a problem, based on the physical and geometric properties and nature of the problem.

Content

Introduction to the variable separation method. Trigonometric Fourier series and their
convergence. Examples of boundary value and initial value problems for
partial differential equations. The wave equation,
the heat conduction equation and the Laplace and Poisson equations.
Orthogonal function systems and general Fourier series. Bessels inequality, Parseval's formula, completeness, Sturm-Liouville  eigenvalue problems.
The variable separation method for solving partial
differential equations. Different methods to solve inhomogeneous problems.
Physical examples. Bessel functions. Solving problems in cylinder coordinates.
Orthogonal Polynomials: Legendre- Hermite and Laguerre Polynomials. Solving problems in spherical coordinates.
Fourier transforms: properties, convolution, Plancherel's formula,
applications to signal processing, the sampling theorem. Application of
Fourier and Laplace transforms to solving partial differential equations.
Discrete Fourier transform, FFT algorithm.

Organisation

The teaching consists of scheduled lectures and exercises, 6 hours of lectures per week, 2 hours of large group exercises, and 2 hours of small group exercises.

Literature

Custom course book plus some additional material.

Examination including compulsory elements

A written or digital 5 hour exam. 



The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.


Page manager Published: Thu 04 Feb 2021.