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MAM058 Complex functions and theory of transforms 6.0 ECTS credits | |
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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 | 0.75ECTS |
| Written exam | 5.25ECTS |
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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 |
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