Ordinary Differential Equations: Methods and Applications

General data

Course ID:	1000-1M11ODE
Erasmus code / ISCED:	11.134 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Ordinary Differential Equations: Methods and Applications
Name in Polish:	Równania różniczkowe zwyczajne: metody i zastosowania
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective monographs
Prerequisites (description):	diff equations, analysis
Mode:	Self-reading
Short description:	In this course we shall introduce methods to solve or analyze solutions of ordinary differential equations used in modern mathematics and mathematical physics. We shall mainly concentrate on second order linear and nonlinear differential equations. Some special functions, like the hypergeometric, Bessel and Airy functions and orthogonal polynomials will be studied in more detail.
Full description:	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.
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
Learning outcomes:	Knowledge of new methods to analyze diff equations
Assessment methods and assessment criteria:	written exam (several topics from the lectures) or the reports on some topics at problem classes

This course is not currently offered.

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Copyright by University of Warsaw.