Periodic Differential Equations
eBook - PDF

Periodic Differential Equations

An Introduction to Mathieu, Lamé, and Allied Functions

  1. 294 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Periodic Differential Equations

An Introduction to Mathieu, Lamé, and Allied Functions

About this book

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
Print ISBN
9780080099842
eBook ISBN
9781483164885
Topic
Mathematics
Subtopic
Differential Equations
Index
Mathematics

Table of contents

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