An Introduction to Laplace Transforms and Fourier Series / Edition 1

An Introduction to Laplace Transforms and Fourier Series / Edition 1

by Phil Dyke
     
 

ISBN-10: 1852330155

ISBN-13: 9781852330156

Pub. Date: 10/15/1999

Publisher: Springer London

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

Overview

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.

Product Details

ISBN-13:
9781852330156
Publisher:
Springer London
Publication date:
10/15/1999
Series:
Springer Undergraduate Mathematics Series
Edition description:
1st Corrected ed. 2001. Corr. 2nd printing 2000
Pages:
250
Sales rank:
936,552
Product dimensions:
7.01(w) x 9.25(h) x 0.36(d)

Table of Contents

1. The Laplace Transform.- 1.1 Introduction.- 1.2 The Laplace Transform.- 1.3 Elementary Properties.- 1.4 Exercises.- 2. Further Properties of the Laplace Transform.- 2.1 Real Functions.- 2.2 Derivative Property of the Laplace Transform.- 2.3 Heaviside’s Unit Step Function.- 2.4 Inverse Laplace Transform.- 2.5 Limiting Theorems.- 2.6 The Impulse Function.- 2.7 Periodic Functions.- 2.8 Exercises.- 3. Convolution and the Solution of Ordinary Differential Equations.- 3.1 Introduction.- 3.2 Convolution.- 3.3 Ordinary Differential Equations.- 3.3.1 Second Order Differential Equations.- 3.3.2 Simultaneous Differential Equations.- 3.4 Using Step and Impulse Functions.- 3.5 Integral Equations.- 3.6 Exercises.- 4. Fourier Series.- 4.1 Introduction.- 4.2 Definition of a Fourier Series.- 4.3 Odd and Even Functions.- 4.4 Complex Fourier Series.- 4.5 Half Range Series.- 4.6 Properties of Fourier Series.- 4.7 Exercises.- 5. Partial Differential Equations.- 5.1 Introduction.- 5.2 Classification of Partial Differential Equations.- 5.3 Separation of Variables.- 5.4 Using Laplace Transforms to Solve PDEs.- 5.5 Boundary Conditions and Asymptotics.- 5.6 Exercises.- 6. Fourier Transforms.- 6.1 Introduction.- 6.2 Deriving the Fourier Transform.- 6.3 Basic Properties of the Fourier Transform.- 6.4 Fourier Transforms and PDEs.- 6.5 Signal Processing.- 6.6 Exercises.- 7. Complex Variables and Laplace Transforms.- 7.1 Introduction.- 7.2 Rudiments of Complex Analysis.- 7.3 Complex Integration.- 7.4 Branch Points.- 7.5 The Inverse Laplace Transform.- 7.6 Using the Inversion Formula in Asymptotics.- 7.7 Exercises.- A. Solutions to Exercises.- B. Table of Laplace Transforms.- C. Linear Spaces.- C.1 Linear Algebra.- C.2 Gramm-Schmidt Orthonormalisation Process.

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