Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).
Overview
- Swedish nameKomplex matematisk analys
- CodeMVE025
- Credits6 Credits
- OwnerTKTFY
- 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 57136
- Maximum participants130
- 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 |
|---|---|---|---|---|---|---|---|
| 0105 Examination 6 c Grading: TH | 6 c |
|
In programmes
Examiner
David Witt Nyström- Full 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
Basic courses in mathematics.
Aim
To treat the fundamental theory for complex functions and to demonstrate important areas of application.
Learning outcomes (after completion of the course the student should be able to)
After completion of the course the student should be able to:
- define basic concepts and prove basic theorems in complex analysis,
- construct and analyse Möbius transformations and other conformal mappings,
- find Taylor and Laurent series of holomorphic functions,
- compute residues,
- calculate certain real integrals as well as contour integrals using residue calculus,
- use the Laplace transform and the z-transform to solve certain equations.
Content
Analytic and harmonic functions. Elementary functions and mappings. Multivalued functions, branch points. Complex integration. Cauchy's theorem. Cauchy's integral formula. Taylor and Laurent series. Isolated singularities. Residues. Calculation of Fourier transforms using residues. Conformal mappings. Linear fractional mappings. Applications to the Laplace equation in the plane. The argument pronciple. Laplace and z-transforms and applications. Nyquist diagrams.
Organisation
Lectures and practical exercises.
Literature
Beck, Marchesi, Pixton and Sabalka: A First Course of Complex AnalysisSee the course homepage for further information
Examination including compulsory elements
A written paper. Hand-ins can occur.
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.