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Lecture: "Asymptotic Analysis: Theory and Methods", winter term 2014/15

Oragnisation
Coordinator	Prof. Dr. Barbara Wagner
Lecture-number	3236 L 217
Dates	16.10.2014 to 12.02.2015 weekly: Thu, 2 - 4 pm, room MA 742
Language	The lecture can be hold in English or German.
Content	Problems in the natural sciences and technology typically act on different (large and small) time- and spatial scales. In the corresponding mathematical model equations this is reflected by the appearance of small parameters in the model. In this course we develop theory and methods that enable reduction and asymptotic solution of these multiple-scale problems. We cover the method of "matched asymptotics", the method of multiple scales, WKBJ method and apply them for the analysis of partial differential equations. Apart from these methods we also introduce the method of homogenisation, linear and nonlinear wave motion, weakly nonlinear stability analysis, asymptotic derivation of sharp-interface models.
Target group	Mathematik MSc Scientific Computing MSc Technomathematik MSc Physik MSc Elektrotechnik MSc Informatik MSc
Literature	Kevorkian/Cole, "Multiple Scales and Singular Perturbation Methods", Springer 1996. J.A. Murdock, "Perturbations: Theory and Methods", SIAM 1999. Lin/Segel/Handelman, "Deterministic Problems in the Nartural Sciences", Macmillan Publishing Co., Inc. J.D. Murray, Asymptotic Analysis, Applied Mathematical Sciences Vo. 48. Springer, 1992.