An introduction to Laplace transforms and Fourier series

Description

This introduction to Laplace transforms and Fourier series is aimed at second year students in applied mathematics. It is unusual in treating Laplace transforms at a relatively simple level with many examples. Mathematics students do not usually meet this material until later in their degree course but applied mathematicians and engineers need an early introduction. Suitable as a course text, it will also be of interest to physicists and engineers as supplementary material. Cover......Page 1 Title ......Page 4 Preface ......Page 8 Contents ......Page 12 I. The Laplace Transform ......Page 14 II. Further Properties of the Laplace Transform ......Page 26 III. Convolution and the Solution of Ordinary Differential Equations ......Page 50 IV. Fourier Series ......Page 92 V. Partial Differential Equations ......Page 124 VI. Fourier Transforms ......Page 142 VII. Complex Variables and Laplace Transforms......Page 170 A. Solutions to Exercises ......Page 198 B. Table of Laplace Transforms ......Page 240 C. Linear Spaces ......Page 244 Bibliography ......Page 258 Index ......Page 260