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School of Science
Department of Mathematics
|Level of Studies||
Techniques of Mathematical Modelling
|Independent Teaching Activities||
Lectures (Weekly Teaching Hours: 3, Credits: 6)
|Language of Instruction and Examinations||
|Is the Course Offered to Erasmus Students||
Yes (in English)
|Course Website (URL)||See eCourse, the Learning Management System maintained by the University of Ioannina.|
The course is a first introduction to the basic methods of applied mathematics and particularly in perturbation theory. There are many situations in mathematics where one finds expressions that cannot be calculated with absolute precision, or where exact answers are too complicated to provide useful information. In many of these cases, it is possible to find a relatively simple expression which, in practice, is just as good as the complete, exact solution. The asymptotic analysis deals with methods for finding such approximations and has a wide range of applications, both in the fields of pure mathematics such as combinatorics, probability, number theory and applied mathematics and computer science, for example, the analysis of runtime algorithms. The goal of this course is to introduce some of the basic techniques and to apply these methods to a variety of problems. Upon completion of this course students will be able to:
Introduction and notation of perturbation theory. Regular and singular perturbations. Asymptotic expansions of integrals. Asymptotic solutions of linear and nonlinear differential equations. Laplace and Fourier transforms (if time permits).
Teaching and Learning Methods - Evaluation
Face to face
|Use of Information and Communications Technology||Yes|
|Student Performance Evaluation||
- C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory, Springer, 1999.
- E. J. Hinch, Perturbation Methods, Cambridge University Press, 1991.
- A. H. Nayfeh, Perturbation Methods, Wiley-Interscience, 1973.