Ordinary Differential EquationsThe 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. |
Contents
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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 |