Techniques of Mathematical Modelling (MAE646)

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Department of Mathematics
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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Undergraduate
Course Code	MAE646
Semester	6
Course Title	Techniques of Mathematical Modelling
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 6)
Course Type	Special Background
Prerequisite Courses	-
Language of Instruction and Examinations	Greek
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.

Learning Outcomes

Learning outcomes	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: Recognize the practical value of small or large parameters for calculating mathematical expressions. Understand the concept of (divergent) asymptotic series, and distinguish between regular and singular perturbations. Find dominant behaviors in algebraic and differential equations with small and large parameters. Calculate dominant behavior of integrals with a small parameter. Find a (in particular cases) the full asymptotic behavior of integrals. Identify the boundary layers in solutions of differential equations, and apply appropriate expansions to calculate the dominant solutions.
General Competences	Search for, analysis and synthesis of data and information, with the use of the necessary technology. Adapting to new situations. Decision-making.

Syllabus

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

Delivery

Face to face

Use of Information and Communications Technology

Yes

Teaching Methods

Activity	Semester Workload
Lectures	39
Self study	78
Exercises	33
Course total	150

Student Performance Evaluation

Weekly homework
Final project
Final exam

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

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.