Wiki Τμήματος Μαθηματικών
Methods of Applied Mathematics ΙI (EM2)

Methods of Applied Mathematics ΙI (EM2)

Από Wiki Τμήματος Μαθηματικών

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.
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