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:


General Competences 

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 
 
Student Performance Evaluation 

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, WileyInterscience, 1973.