Synopses & Reviews
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.
Scientists and engineers who need to model problems must often use mathematical concepts, such as Laplace transforms and Fourier series. This introduction is intended for self-study, and contains many problems and fully worked-out solutions.
Includes bibliographical references (p. 245-246) and index.
This book is a self-contained introduction to Laplace Transforms and Fourier Series; emphasising the applications of Laplace transforms throughout, the book also provides coverage of the underlying pure mathematical structures. Alongside the Laplace transform, the notion of Fourier series is developed from first principles. Exercises are provided to consolidate understanding of the concepts and techniques, and only a knowledge of elementary calculus and trigonometry is assumed. For second and third year students looking for a rigorous and practical introduction to the subject, this book will be an invaluable source.
Table of Contents
The Laplace Transform.- Further Properties.- Convolution and the Solutions.- Fourier Series.- Partial Differential Equations.- Fourier Transforms.- Complex Variables and Laplace Transforms.- Appendices: A: Answers to Exercises.- B: Table of Laplace Transforms.- C: Linear Spaces.