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Graduate courses

Departments' graduate courses for PhD-students.

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Course syllabus for

Academic year
MVE025 - Complex mathematical analysis
Komplex matematisk analys
 
Course syllabus adopted 2021-02-26 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: 57141
Open for exchange students: No
Maximum participants: 130
Only students with the course round in the programme overview

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0105 Examination 6,0 c Grading: TH   6,0 c   27 Oct 2022 am J,  05 Jan 2023 pm J,  25 Aug 2023 pm J

In programs

TKTFY ENGINEERING PHYSICS, Year 2 (compulsory)

Examiner:

David Witt Nyström

  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

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 Analysis

See 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.


Page manager Published: Thu 04 Feb 2021.