421-205 Mathematics for Engineers Unit 2.2

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Objectives:

On completion of this course students should have:

• a firm grasp of the important concept of a vector with particular emphasis on its manipulation and use in conjunction with calculus;

• a knowledge of Fourier and Laplace Transforms which are essential to the understanding of the response of systems to both forcing and initial conditions. These transformations are used widely in vibrational problems and in the study of electrical networks.

Content:

Part 1 Vector Analysis: Gradient, divergence, and curl of a vector. Line, surface, and volume integral theorems of Green, Gauss, and Stokes. Irrotational and solenoidal fields.

Part 2 Transform Methods: Fourier series and transform. Simple expansions: sine, cosine and exponential series, least square errors. Introduction to Fourier transforms, Laplace transforms, operational calculus and applications including the solution of linear differential equations.

Assessment: