Course syllabus for Complex analysis

Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameKomplex analys
  • CodeMVE295
  • Credits7.5 Credits
  • OwnerTKTEM
  • 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 59113
  • Maximum participants90
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0109 Examination 6 c
Grading: TH		6 c
  • 27 Okt 2022 am J
  • 05 Jan 2023 pm J
  • 25 Aug 2023 pm J
0209 Written and oral assignments1 1.5 c
Grading: UG		1.5 c
1 The course module is provided by the department PHYSICS

In programmes

Examiner

Go to coursepage (Opens in new tab)

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

Linear algebra, analysis in several variables.

Aim

To treat the fundamental theory for complex functions and to demonstrate important areas of application.

Aim for the 1,5 c moment: To give a basic knowledge of scalar och vector fields with applications to e.g. electrodynamics.

Learning outcomes (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.
The course also gives some basic knowledge of scalar and vector fields with applications to e.g. electrodynamics. Learning outcome: After completion of this course, the student should be able to independently solve simple problems in the field. For the students of Engineering Mathematics this knowledge is a prerequisite for the course in Electromagnetic fields.

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.

Scalar and vector fields, curvilinear coordinate systems, differential operators, Maxwell's equations.

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 and hand-in problems (vector fields).

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.