Dept of Mathematics

MAM058 Complex functions and theory of transforms 6.0 ECTS credits

DENNA SIDA FINNS OCKSÅ PÅ SVENSKA

General information about studying at Luleå University
TIMEPERIOD:

LANGUAGE: Swedish

EXAMINER
G Brandell Univ lekt

PREREQUISITES


COURSE AIM
The course is designed to give the student understanding and basic knowledge of - the theory of analytic functions and their applications in different areas such as electrotechnics, fluid dynamics and control theory - the theory of the most commonly used integral transforms, the Fourier transform, the Laplace transform and the Z-transform and their applications

CONTENTS
Complex functions: Basic concepts, the equations of Cauchy-Riemann, elementary complex functions. Complex integration, Cauchy's theorem, the residue theorem, residue integrals. Laurent series, poles and zeroes. Conformal mapping, bilinear transformations. Harmonic functions. Applications. Theory of transforms: The concept of an integral transform. The Fourier transform, the Laplace transform and the Z-transform. Parseval's relation. Solving differential equations and difference equations with the transform method. Applications.

TEACHING
Instruction consists of lectures and laboratory lessons.

EXAMINATION
Examination is written. Correction of examination according to alternative A in "Regler för tentamen".
COURSE GRADE SCALE:

ITEMS AND CREDITS 
Laboratory work                                             	0.7 ECTS
Written exam                                                	5.2 ECTS

COURSE LITERATURE
Fisher, Stephen D.: Complex Variables, Wadsworth & Brooks/Cole, second edition, 1990 Råde L., Westergren B.: BETA, Mathematics Handbook, Studentlitteratur, second edition, 1990 or later.

REMARKS
Last modified 97-03-05
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