421-303 Mathematics for Engineers Unit 3.1

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Objectives:

On completion of this course students should have:

• an advanced understanding of systems of ordinary differential equations which govern for instance the time evolution of many discrete systems and provide the background the numerical solution of many high order ordinary differential equations;

• a knowledge of solution methods for solving partial differential equations which are the fundamental equations governing most phenomena of a continuous nature in more than one dimension, ranging from settlement of foundations to traffic flow on a highway.

Content:

Part 1 Systems of Differential Equations: Sets of differential equations. Elementary approach for linear differential equations with constant coefficients, solution of homogeneous systems, normal modes, stability, classification of the critical point for linear systems, solutions of forced systems by fundamental matrices, linear differential equations with variable coefficients, independent solutions, Wronskians, numerical methods.

Part 2 Partial Differential Equations: Partial differential equations of first and second order including Laplace's equation, the wave equation and the diffusion equation in various geometries. Separation of variables, methods of characteristics, numerical methods.

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