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

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



Source work progress
* : Chapter $1$ Basic Concepts: $1.1$ Introduction