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## Syllabus for

MVE295 - Complex analysis

Owner: TKTEM
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: First-cycle
Major subject: Chemical Engineering with Engineering Physics, Mathematics, Engineering Physics
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: Swedish

 Course module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0109 Examination 6,0c Grading: TH 6,0c 27 Oct 2016 am M, 22 Dec 2016 am SB, 25 Aug 2017 pm SB 0209 Written and oral assignments 1,5c Grading: UG 1,5c

#### In programs

TKKEF CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 2 (compulsory)
TKTEM ENGINEERING MATHEMATICS, Year 2 (compulsory)

#### Examiner:

Universitetslektor  David Witt Nyström

#### Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

#### 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)

The course aims at providing knowledge of analytical functions, Laplace and z-transforms and some applications to PDE.

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

A written paper and hand-in problems (vector fields).

Page manager Published: Thu 04 Feb 2021.