Theo Bühler: Catalogue data in Spring Semester 2016 |
Name | Dr. Theo Bühler |
Department | Mathematics |
Relationship | Lecturer |
Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|
401-0272-00L | Mathematical Foundations I: Analysis B | 3 credits | 2V + 1U | T. Bühler | |
Abstract | Ordinary differential equations as mathematical models to describe processes. Numerical, analytical and geometrical aspects of differential equations. More on multidimensional calculus: vector analysis. | ||||
Objective | Introduction to calculus in one and several dimensions. Building simple models and analysing them mathematically. | ||||
Content | Ordinary differential equations as mathematical models to describe processes. Numerical, analytical and geometrical aspects of differential equations. More on multidimensional calculus: vector analysis. | ||||
Literature | - D. W. Jordan, P. Smith: Mathematische Methoden für die Praxis, Spektrum Akademischer Verlag - M. Akveld/R. Sperb: Analysis I, Analysis II (vdf) - L. Papula: Mathematik für Ingenieure und Naturwissenschaftler Bde 1,2,3. (Vieweg) | ||||
401-0302-10L | Complex Analysis | 4 credits | 3V + 1U | T. Bühler | |
Abstract | Basics of complex analysis in theory and applications, in particular the global properties of analytic functions. Introduction to the integral transforms and description of some applications | ||||
Objective | Erwerb von einigen grundlegenden Werkzeuge der komplexen Analysis. | ||||
Content | Examples of analytic functions, Cauchy‘s theorem, Taylor and Laurent series, singularities of analytic functions, residues. Fourier series and Fourier integral, Laplace transform. | ||||
Literature | M. Ablowitz, A. Fokas: "Complex variables: introduction and applications", Cambridge Text in Applied Mathematics, Cambridge University Press 1997 E. Kreyszig: "Advanced Engineering Analysis", Wiley 1999 J. Brown, R. Churchill: "Complex Analysis and Applications", McGraw-Hill 1995 J. Marsden, M. Hoffman: "Basic complex analysis", W. H. Freeman 1999 P. P. G. Dyke: "An Introduction to Laplace Transforms and Fourier Series", Springer 2004 Ch. Blatter: "Komplexe Analysis, Fourier- und Laplace-Transformation", Autographie A. Oppenheim, A. Willsky: "Signals & Systems", Prentice Hall 1997 M. Spiegel: "Laplace Transforms", Schaum's Outlines, Mc Graw Hill | ||||
Prerequisites / Notice | Prerequisites: Analysis I and II |