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MAM150 Mathematics 9.0 ECTS credits | |
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TIMEPERIOD: LANGUAGE:English/Swedish EXAMINER Torbjörn Hedberg Prof PREREQUISITES The first year basic course in mathematics. COURSE AIM To make the student able to apply certain standard mathematical methods to problems in materials engineering and its scientific basis. CONTENTS Sequences and series: Positive series and convergence tests. Absolute and conditional convergence. Power series. Taylor and Maclaurin series.
Vector analysis: Curves and arc length. Vector fields, conservative fields, potentials, div, grad and rot. Line integrals and their independence of the path. Surface integrals and the theorems of Gauss, Green and Stokes.
Complex functions: Cauchy-Riemann equations. Integration, Cauchys theorem. Taylor and Laurent expansions. The residue theorem and conformal mappings.
The Laplace transform: Properties, convolution, inversion, application to ordinary differential equations.
Fourier analysis: Periodic functions, Fourier series.
Partial differential equations: The wave, heat and Laplace equations. Boundary and initial conditions. Separation of variables.
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| Written exam | 9.00ECTS |
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COURSE LITERATURE Kreyszig, Erwin: Advanced Engineering Mathematics. 8th Ed, Wiley. Course information from the department: http://www.sm.luth.se/math/education/ |
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