Ordinary Differential Equations

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The theory of ordinary differential equations in real and complex domains is here clearly explained and analyzed. Not only classical theory, but also the main developments of modern times are covered. Exhaustive sections on the existence and nature of solutions, continuous transformation groups, the algebraic theory of linear differential systems, and the solution of differential equations by contour integration are as valuable to the pure mathematician as the fine treatment of the equations of Legendre, Bessel, and Mathieu, the conditions for the oscillatory character of solutions of a differential equation, and the relation between a linear differential system and an integral equation are to the engineer and the physicist.
Partial contents: real domain (elementary methods of integration, the existence and nature of solutions, continuous transformation-groups, linear differential equations-the general theory, with constant coefficients, solutions, algebraic theory, Sturmian theory, and later developments); complex domain (existence theorems, equations of first order, non-linear equations of higher order, solutions, systems, classifications of linear equations, oscillation theorems).
"Highly recommended." — Electronics Industries.
"Deserves the highest praise." — Bulletin, American Mathematical Society.

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Product Details

  • ISBN-13: 9780486603490
  • Publisher: Dover Publications
  • Publication date: 6/1/1956
  • Series: Dover Books on Mathematics Series
  • Edition description: DOVER EDITION
  • Pages: 558
  • Sales rank: 549,258
  • Product dimensions: 5.41 (w) x 8.36 (h) x 1.05 (d)

Table of Contents

Part I. Differential Equations in the Real Domain
  I. Introduction
  II. Elementary Methods of Integration
  III. The Existence and Nature of Solutions of Ordinary Differential Equations
  IV. Continuous Transformation-Groups
  V. The General Theory of Linear Differential Equations
  VI. Linear Equations with Constant Coefficients
  VII. The Solution of Linear Differential Equations in an Infinite Form
  VIII. The Solution of Linear Differential Equations by Definite Integrals
  IX. The Algebraic Theory of Linear Differential Systems
  X. The Sturmian Theory and its Later Developments
  XI. Further Developments in the Theory of Boundary Problems
Part II. Differential Equations in the Complex Domain
  XII. Existence Theorems in the Complex Domain
  XIII. Equations of the First Order But Not of the First Degree
  XIV. Non-Linear Equations of Higher Order
  XV. Linear Equations in the Complex Domain
  XVI. The Solution of Linear Differential Equations in Series
  XVII. Equations with Irregular Singular Points
  XVIII. The Solution of Linear Differential Equations by Methods of Contour Integration
  XIX. Systems of Linear Equations of the First Order
  XX. Classification of Linear Differential Equations of the Second Order with Rational Coefficients
  XXI. Oscillation Theorems in the Complex Domain
Appendix A. Historical Note on Formal Methods of Integration
Appendix B. Numerical Integration of Ordinary Differential Equations
Appendix C. List of Journals Quoted in Footnotes to the Text
Appendix D. Bibliography
  Index of Authors; General index
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