Ordinary Differential Equations

Front Cover
Courier Corporation, Apr 27, 2012 - Mathematics - 576 pages

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.

 

Contents

CHAPTER PAGE
3
ELEMENTARY METHODS OF INTECRATION
16
THE EXISTENCE AND NATURE OF SOLUTIONS OF ORDINARY DIFFERENTIAL
62
CONTINUOUS TRANSFORMATIONGROUPS
93
LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS
133
THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS IN AN INFINITE
158
ExISTENCE THEOREMS IN THE COMPLEX DOMAIN
281
EQUATIONS OF THE FIRST ORDER BUT NOT OF THE FIRST DECREE
304
LINEAR EQUATIONS IN THE COMPLEX DOMAIN
356
THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS IN SERIES
396
EQUATIONS WITH IRREGULAR SINCULAR POINTS
417
THE SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS BY METHODS
438
SYSTEMS OF LINEAR EQUATIONS OF THE FIRST ORDER
469
CLASSIFICATION OF LINEAR DIFFERENTIAL EQUATIONS OF THE SECOND
494
OSCILLATION THEOREMS IN THE COMPLEX DOMAIN
508
INDEXOFAUTHORS
551

NONLINEAR EQUATIONS OF HIGHER ORDER
317

Other editions - View all

Common terms and phrases

Bibliographic information