Cardiff University

Ordinary Differential Equations

MA 2005

Iowa State Course Substitution

Requires review after study abroad is complete

MATH

Course Info
International Credits:
10.0
Converted Credits:
3.0
Semester:
Spring
Country:
United Kingdom
Language:
English
Course Description:
Building upon a general understanding of the form and usefulness of ordinary differential equations and knowledge of elementary solution methods, this module explores the mathematical foundations of ordinary differential equation theory as well as methods for the asymptotic and qualitative study of their solutions. It is an intriguing observation that only a very small number of types of differential equation can be solved in terms of the well-known elementary functions. Differential equations are therefore a fruitful source of new functions and thus are of great practical value in applications and remain of continuing interest. However, this also means that mere knowledge of techniques for the explicit solution of differential equations will not reach very far. It is therefore essential to have a theoretical framework which ensures the existence of solutions of ordinary differential equations without the need to find them explicitly, and to study the uniqueness and continuous dependence of solutions on parameters of the equation. In the presence of singularities, the asymptotic behaviour of solutions is very valuable information. A further aspect of the qualitative study of ordinary differential equations is the question of stability: will nearby starting points lead to wildly different solutions (chaos), or will the solutions approach a fixed point or an attractive set of more complicated structure, e.g. a limit cycle? The module will provide an introduction to the existence theory of ordinary differential equations and to fundamental techniques of the asymptotic and qualitative study of their solutions.

Review

Evaluation Date:
March 6, 2014
Evaluated:
James Wilson
Comments: