Synopses & Reviews
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.
Synopsis
Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. "Highly recommended"
Electronics Industries.Synopsis
Explains and analyzes theory of ordinary differential equations in real and complex domains. "Highly recommended,"--"Electronics Industries."
Synopsis
Among the topics covered in this classic treatment are linear differential equations; solution in an infinite form; solution by definite integrals; algebraic theory; Sturmian theory and its later developments; much more. "Highly recommended"
Electronics Industries.
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