Course syllabus adopted 2022-05-02 by Head of Programme (or corresponding).
Overview
- Swedish nameFouriermetoder
- CodeMVE290
- Credits7.5 Credits
- OwnerTKKEF
- Education cycleFirst-cycle
- Main field of studyChemical Engineering with Engineering Physics, Mathematics, Engineering Physics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language Swedish
- Application code 54119
- Maximum participants45
- Open for exchange studentsNo
- Only students with the course round in the programme overview.
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0109 Examination 6 c Grading: TH | 0 c | 0 c | 6 c | 0 c | 0 c | 0 c |
|
| 0209 Written and oral assignments 1.5 c Grading: UG | 0 c | 0 c | 1.5 c | 0 c | 0 c | 0 c |
In programmes
- TKAUT - AUTOMATION AND MECHATRONICS ENGINEERING, Year 3 (elective)
- TKKEF - CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 2 (compulsory)
Examiner
Julie Rowlett- Professor, Analysis and Probability Theory, Mathematical Sciences
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)
After completing the course, the student will be able to solve
partial differential equations using separation of variables,
eigenfunction and Fourier series expansions, eigenfunction expansions
using Sturm-Liouville problems, as well as Fourier and Laplace
transforms. In addition, the student will be able to apply the
theoretical concepts of Hilbert spaces to solving physical problems. In
this regard, the student will be able to determine, based on the
geometry of the physical domain and the character of the equation, which
orthogonal system, such as trigonometric functions, Bessel functions,
or orthogonal polynomials, is best suited to solve the physical
problem. The student will also be able to use Fourier series to compute
sums, like the sum of 1/n^2. The student will learn how to use Fourier
transforms to compute tricky integrals.
Content
The method of separation of variables. Trigonometric Fourier series and their convergence. Examples of initial and boundary value problems for partial differential equations: the heat equation, the wave equation, Laplace/Poisson's equation. Orthogonal systems of functions, completeness, Sturm-Liouville eigenvalue problems. Various solution techniques like homogenization, superposition and eigenfunction expansion. Bessel functions and orthogonal polynomials (Legendre, Hermite and Laguerre polynomials). Solution methods in spherical or cylindrical coordinates. Fourier transforms and their applications to partial differential equations. Signal analysis, discrete Fourier transforms and Fast Fourier Transforms. Laplace transforms with applications.
Organisation
The course is organized in lectures and exercises (about 5h/week of each). It includes a hand-in assignment, and computer laborations may occur.
Literature
Custom course book plus some additional material.
Examination including compulsory elements
A written exam with about 6 problems and 2 theory questions, in 5 hours.
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.
The course syllabus contains changes
- Changes to module:
- 2022-05-02: Digital exam Changed to digital exam by Emilio
[0109 Examination 6,0 credit] Changed to digital examination - 2022-03-03: Digital exam Changed to digital exam by vana
[0109 Examination 6,0 credit] Changed to digital examination
- 2022-05-02: Digital exam Changed to digital exam by Emilio
- Changes to examination:
- 2022-05-02: Digital exam Changed to digital exam by Emilio
[0109 Exam 6,0 hp] Changed to digital examination - 2022-05-02: Digital exam Changed to digital exam by Emilio
[0109 Exam 6,0 hp] Changed to digital examination - 2022-03-03: Digital exam Changed to digital exam by vana
[0109 Exam 6,0 hp] Changed to digital examination
- 2022-05-02: Digital exam Changed to digital exam by Emilio