Solutions of Laplace’s Equation

  • Authors
  • D. R. Bland

Part of the Library of Mathematics book series (LIMA)

Table of contents

  1. Front Matter
    Pages N2-viii
  2. D. R. Bland
    Pages 15-28
  3. D. R. Bland
    Pages 29-47
  4. D. R. Bland
    Pages 61-77
  5. Back Matter
    Pages 97-98

About this book

Introduction

THIS book is an introduction both to Laplace's equation and its solutions and to a general method of treating partial differential equations. Chapter 1 discusses vector fields and shows how Laplace's equation arises for steady fields which are irrotational and solenoidal. In the second chapter the method of separation of variables is introduced and used to reduce each partial differential equation, Laplace's equa­ tion in different co-ordinate systems, to three ordinary differential equations. Chapters 3 and 5 are concerned with the solutions of two of these ordinary differential equations, which lead to treatments of Bessel functions and Legendre polynomials. Chapters 4 and 6 show how such solutions are combined to solve particular problems. This general method of approach has been adopted because it can be applied to other scalar and vector fields arising in the physi­ cal sciences; special techniques applicable only to the solu­ tions of Laplace's equation have been omitted. In particular generating functions have been relegated to exercises. After mastering the content of this book, the reader will have methods at his disposal to enable him to look for solutions of other partial differential equations. The author would like to thank Dr. W. Ledermann for his criticism of the first draft of this book. D. R. BLAND The University, Sussex. v Contents Preface page v 1. Occurrence and Derivation of Laplace's Equation 1. Situations in which Laplace's equation arises 1 2. Laplace's equation in orthogonal curvilinear co-ordinates 8 3.

Keywords

Finite behavior derivation derivative distribution equation evolution field form function functions variable

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-011-7694-1
  • Copyright Information Springer Science+Business Media B.V. 1961
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-7100-4353-5
  • Online ISBN 978-94-011-7694-1
  • About this book