Customer Reviews

Introduction to Nonlinear Differential and Integral Equations (Dover Books on Mathematics)

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This book contains a superb treatment of the classical theories of nonlinear equations including integral equations of the Volterra type. It was written in 1960, when the use of computers to solve differential equations and dynamical systems was in its infancy and the book is of course dated in this aspect. However, the book is a true treasure and is worth reading for its thorough and comprehensive treatment, including an introduction to the concept and usefulness of the phase space. It is bad that it is hard to get nowadays, but it is worth trying to get it used.

This book appeared a full generation before Gleick's classic popularization, "Chaos." It is easy to read, as math books go, and full of examples well worth studying for both practical and theoretical questions. Like many Dover reprints, it is a fantastic value. However, the only applications of CAC (continuous analytic continuation) you might find are some papers by D. Hartwell on orbits. An equally precise, but more versatile method is Picard-Chebyshev, but it has yet to develop a significant following. For references, see the New Preface in the Product Link. If amazon.com ever gets its "Shorts" program up and running again, I'll offer some of the examples from this classic work as Excel spreadsheets with VBA macros. Yes, you can do a lot of nonlinear dynamics with Excel because the secret is to use a small set of optimal variables rather than a large set of unstable ones. The Art of Modeling Dynamic Systems: Forecasting for Chaos, Randomness and Determinism (Dover Books on Mathematics)

Excellent coverage of the Painleve nonlinear differential equations.

Excellent presentation of the method of Continuous Analytic Continuation and its use to numerically advance the solution of nonlinear equations in the complex domain around poles that can occur in the real domain, such as those that arise with the Painleve equations.