Ordinary Differential Equations: Methods and Applications 1000-1M11ODE
Various methods of asymptotic theory, including contour integration, asymptotic evaluation of integrals (Laplace and Fourier type integrals), Watson lemma, stationary phase method, steepest descent, Stokes phenomenon, WKB method. Introduction to special functions and elliptic functions. If time permits, we shall also discuss the basics of Nevanlinna theory and its application to ODEs.
Type of course
Mode
Prerequisites (description)
Learning outcomes
Knowledge of new methods to analyze diff equations
Assessment criteria
written exam (several topics from the lectures) or the reports on some topics at problem classes
Bibliography
M. Fedoryuk Asymptotic analysis.
F. Olver Introduction to asymptotic methods and special functions.
W. Wasow Asymptotic expansions of solutions of ODEs; Linear turning point theory.
Whittaker and Watson, A course of modern analysis.
I. Laine, Nevenlinna theory and complex differential equations
R. Wong
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
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