Book:G. Stephenson/An Introduction to Partial Differential Equations for Science Students

G. Stephenson: An Introduction to Partial Differential Equations for Science Students

Published $\text {1968}$, Longmans

Subject Matter

• Partial Differential Equations

Contents

Preface

1. Basic Concepts

1.1 Introduction

1.2 The wave equation

1.3 Some important equations

Problems 1

2. Classification of Equations and Boundary Conditions

2.1 Types of equation

2.2 Euler's equation

2.3 Boundary conditions

2.4 Laplace's equation and the Dirichlet problem

2.5 D'Alembert's solution of the wave equation

Problems 2

3. Orthonormal Functions

3.1 Superposition of solutions

3.2 Orthonormal functions

3.3 Expansion of a function in a series of orthonormal functions

3.4 The Sturm-Lioouville equation

Problems 3

4. Applications of Fourier's Method

4.1 Coordinate systems and separability

4.2 Homogeneous equations

4.3 Non-homogeneous boundary conditions

4.4 Inhomogeneous equations

Problems 4

5. Problems involving Cylindrical and Spherical Symmetry

5.1 Simple solutions of Laplace's equation

5.2 The Dirichlet problem for a circle

5.3 Special functions

5.4 Boundary value problems involving special functions

Problems 5

6. Continuous Eigenvalues and Fourier Integrals

6.1 Introduction

6.2 The Fourier integral

6.3 Application of Fourier integrals to boundary-value problems

Problems 6

7. The Laplace Transform

7.1 Integral transforms

7.2 The Laplace transform

7.3 Inverse Laplace transforms

7.4 The error function

7.5 The Heaviside unit step function

7.6 Laplace transforms of derivatives

7.7 Solution of ordinary differential equations

8. Transform Methods for Boundary Value Problems

8.1 Introduction

8.2 Applications of the Laplace transform

8.3 Applications of the Fourier sine and cosine transformations

8.4 Inhomogeneous equations

Problems 8

9. Related Topics

9.1 Introduction

9.2 Conformal transformations

9.3 Perturbation theory

9.4 Variational methods

9.5 Green's functions

Further Reading

Answers to Problems

Index

Next

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