By
Ted Burton, Ph.D., Professor Emeritus of Southern Illinois University, Carbondale, Illinois 62901, Northwest Research Institute
Description
Most mathematicians, engineers, and many other scientists are well-acquainted with theory and application of ordinary differential equations.
This book seeks to present Volterra integral and functional differential equations in that same framwork, allowing the readers to parlay
their knowledge of ordinary differential equations into theory and application of the more general problems. Thus, the presentation
starts slowly with very familiar concepts and shows how these are generalized in a natural way to problems involving a memory. Liapunov's
direct method is gently introduced and applied to many particular examples in ordinary differential equations, Volterra integro-differential
equations, and functional differential equations.
By Chapter 7 the momentum has built until we are looking at problems on the frontier.
Chapter 7 is entirely new, dealing with fundamental problems of the resolvent, Floquet theory, and total stability. Chapter 8 presents
a solid foundation for the theory of functional differential equations. Many recent results on stability and periodic solutions of functional
differential equations are given and unsolved problems are stated.
Key Features:
- Smooth transition from ordinary differential
equations to integral and functional differential equations.
- Unification of the theories, methods, and applications of ordinary
and functional differential equations.
- Large collection of examples of Liapunov functions.
- Description of the history of
stability theory leading up to unsolved problems.
- Applications of the resolvent to stability and periodic problems.
Included in series
Mathematics in Science and Engineering
Audience:
University libraries. Mathematics, Physics and Engineering Faculties within Universities.Industrial Mathematics, Science and Engineering departments in aerospace companies.
