Course syllabus adopted 2021-03-30 by Head of Programme (or corresponding).
Overview
- Swedish nameTransformer- och differentialekvationer
- CodeMVE101
- Credits7.5 Credits
- OwnerTKMAS
- Education cycleFirst-cycle
- Main field of studyMathematics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language Swedish
- Application code 55119
- Block schedule
- 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 |
|---|---|---|---|---|---|---|---|
| 0121 Written and oral assignments 2.5 c Grading: UG | 2.5 c | ||||||
| 0221 Examination 5 c Grading: TH | 5 c |
In programmes
Examiner
Stefan Lemurell- Associate Professor, Algebra and Geometry, 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
Calculus, linear algebra and mathematical software comparable to TMV225, TMV 151, TMV166, TMV255 and TME135.Aim
The aim of the course is to give basic knowledge of transform methods (Fourier transform, Laplace transform, discrete Fourier transform and Fourier series), which are important tools for solving differential equations, as well as for system analysis and signal processing. Moreover, the course treats eigenvalue and boundary value problems for differential operators. The course gives a theoretical foundation for various mathematical methods, and ability to apply them to concrete situations in physics and engineering, such as coupled oscillations, oscillating beams and analogue filters.Learning outcomes (after completion of the course the student should be able to)
- Expand functions as Fourier series. - Compute Laplace and Fourier transforms, as well as the inverse transforms, of certain functions. - Solve differential equations using the Laplace transform. - Determine normal modes and eigenfrequencies of linear dynamical systems. - Determine the motion of such systems under external forces. - Determine eigenvalues and eigenfunctions to boundary value problems. - Determine the transfer function, frequency response and impulse response to a dynamical system. - Solve partial differential equations using separation of variables. - Describe and motivate methods of solutions and conditions for their applicability.Content
The course treats step and impulse functions, Laplace and Fourier transform, Fourier series, discrete Fourier transform, and eigenvalue problems and boundary value problems for differential operators. These mathematical tools are used to analyze various problems in physics and engineering leading to differential equations. Examples include oscillating strings and beams, loaded beams and coupled oscillating systems. Dynamical systems are also studied from the viewpoint of control engineering, leading to concepts such as transfer functions, frequency response and impulse response. Examples include analogue filters. There is a possibility for adapting the course according to the interests and needs of the students. An important part of the course is to use mathematical software for solving and visualizing problems mentioned above.Organisation
The teaching consists of lectures and tutoring in connection with hand-in problems. Detailed information will be given at the course homepage before the start of the course.Literature
Glyn James: Advanced modern engineering mathematics, (Pearson) Chapters 2, 4 and 5. These chapters are also included in: Series and Transforms, Compiled by B Behrens, J Madjarova (Pearson). F Eriksson, C-H Fant and K Holmåker: Differentialekvationer och egenvärdesproblem (Department of Mathematical Sciences, Chalmers University and University of Gothenburg).Examination including compulsory elements
Examination is based on compulsory hand-in problems and a written 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.