Engelska Studiehandboken kurser
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/CREDITS
Laboratory work 0.7ECTS
Written exam 5.2ECTS
COURSE LITTERATURE
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 : 97-09-25
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