Periodic Differential Equations: An Introduction to Mathieu, Lamé, and Allied Functions covers the fundamental problems and techniques of solution of periodic differential equations. This book is composed of 10 chapters that present important equations and the special functions they generate, ranging from Mathieu's equation to the intractable ellipsoidal wave equation.

This book starts with a survey of the main problems related to the formation of periodic differential equations. The subsequent chapters deal with the general theory of Mathieu's equation, Mathieu functions of integral order, and the principles of asymptotic expansions. These topics are followed by discussions of the stable and unstable solutions of Mathieu's general equation; general properties and characteristic exponent of Hill's equation; and the general nature and solutions of the spheroidal wave equation. The concluding chapters explore the polynomials, orthogonality properties, and integral relations of Lamé's equation. These chapters also describe the wave functions and solutions of the ellipsoidal wave equation.

This book will prove useful to pure and applied mathematicians and functional analysis.

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Yes, you can access Periodic Differential Equations by F. M. Arscott, I. N. Sneddon,M. Stark,S. Ulam in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.

Information

Publisher

Pergamon

Year

2014

ISBN

9781483164885

Topic

Mathematics

Subtopic

Differential Equations

Index

Mathematics

Front Cover
Periodic Differential Equations: An Introduction to Mathieu, Lamé, and Allied Functions
Copyright Page
Table of Contents
PREFACE
CHAPTER 1. FORMATION OF THE EQUATIONS: THE MAIN PROBLEMS
CHAPTER 2. MATHIEU'S EQUATION — GENERAL THEORY
CHAPTER 3. MATHIEU FUNCTIONS OF INTEGRAL ORDER
CHAPTER 4. MATHIEU FUNCTIONS OF INTEGRAL ORDER — FURTHER PROPERTIES
CHAPTER 5. ASYMPTOTIC EXPANSIONS
CHAPTER 6. MATHIEU'S GENERAL EQUATION
CHAPTER 7. HILL'S EQUATION
CHAPTER 8. THE SPHEROIDAL WAVE EQUATION
CHAPTER 9. LAMÉ'S EQUATION
CHAPTER 10. THE ELLIPSOIDAL WAVE EQUATION
APPENDIX A — BESSEL FUNCTIONS
APPENDIX B — LEGENDRE, GEGENBAUER AND TCHEBYCHEFF FUNCTIONS
APPENDIX C — ELLIPTIC FUNCTIONS
REFERENCES
ADDITIONAL NOTES
INDEX
OTHER VOLUMES IN THE SERIES IN PURE AND APPLIED MATHEMATICS