Methods of Applied Mathematics ΙI (EM2)

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General

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	EM2
Semester	2
Course Title	Methods of Applied Mathematics ΙI
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
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. 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

Adapting to new situations Decision-making Working independently Team work

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	In class
Use of Information and Communications Technology	Use of computer (Mechanics) lab
Teaching Methods	Activity Semester Workload Lectures 39 Self study 78 Homework - Projects 70.50 Course total 187.5
Student Performance Evaluation	Weekly assignments Final project

Attached Bibliography

• Εφαρμοσμένα Μαθηματικά, Logan D.J. Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, 1η έκδοση, 2010.
• Perturbation Methods, A.H. Nayfeh, 1η έκδοση, Willey-VCH, 2000.