Download PDF, EPUB, Kindle Solutions of Laplace
Download PDF, EPUB, Kindle Solutions of Laplace
Solutions of Laplace's Equation .D.R. Bland
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Author: D.R. Bland
Page Count: 106 pages
Published Date: 12 May 1961
Publisher: Kluwer Academic Publishers Group
Publication Country: Dordrecht, Netherlands
Language: English
ISBN: 9780710043535
File Name: Solutions.of.Laplace's.Equation.pdf
Download Link: Solutions of Laplace's Equation
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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.
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Solutions of Laplace's Equation .D.R. Bland
Author: D.R. Bland
Page Count: 106 pages
Published Date: 12 May 1961
Publisher: Kluwer Academic Publishers Group
Publication Country: Dordrecht, Netherlands
Language: English
ISBN: 9780710043535
File Name: Solutions.of.Laplace's.Equation.pdf
Download Link: Solutions of Laplace's Equation
---------------------------------------------------------------
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.
Read online Solutions of Laplace's Equation Buy and read online Solutions of Laplace's Equation Download and read Solutions of Laplace's Equation for pc, mac, kindle, readers Download to iPad/iPhone/iOS, B&N nook Solutions of Laplace's Equation
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