421-403 Mathematics for Engineers Unit 4.2

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Objectives:

On completion of this course students should have:

• an understanding of the variety of equation types that often occur in engineering when for instance the behaviour of the systems does not depend solely on the present state but upon the history of the state;

• an understanding of the techniques available to handle an equation which contains apparently negligible terms but where for various reasons the terms cannot be neglected.

Content:

Part 1 Advanced Equations: Delayed equations, difference equations, functional equations, integral equations of Fredholm and Volterra types, chaotic systems of equations.

Part 2 Perturbation Methods: Regular perturbations, the two types of singular perturbations, asymptotic behaviour for both boundary layers and long times.

Assessment: