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

Prof. Dr. Barbara Wagner
3236 L 217
16.10.2014 to 12.02.2015 weekly:
Thu, 2 - 4 pm, room MA 742
The lecture can be hold in English or German.
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
  • 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.

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