Based on a Brown University course in applied mathematics, this rigorous
and demanding treatment focuses on specific analytical methods. It
emphasizes nonlinear problems, acquainting readers with problems and
techniques in ordinary differential equations. The material is presented
in a manner that prepares students for informed research of differential
equations, teaching them how to be more effective in studies of the
current literature. In addressing the applied side of the subject, the
text devotes considerable attention to specific analytical methods
common to applications.
Introductory chapters offer necessary background material by reviewing
basic facts of analysis and covering the general properties of
differential equations. Topics include two-dimensional systems, linear
systems and linearization, perturbations of noncritical linear systems,
simple oscillatory phenomena and the method of averaging, and behavior
near a periodic orbit. Additional subjects include integral manifolds of
equations with a small parameter, periodic systems with a small
parameter, alternative problems for the solution of functional
equations, and the direct method of Liapunov. Exercises appear at the
end of each chapter, and the appendix contains a convenient reference
for almost every periodic functions.