Introduction to Nonlinear Differential and Integral Equations (Dover Books on Mathematics) by Harold T. Davis (PDF)

Description

Within recent years interest in nonlinear equations has grown enormously. They are extremely important as basic equations in many areas of mathematical physics, and they have received renewed attention because of progress in their solution by machines.This volume undertakes a definition of the field, indicating advances that have been made up through 1960. The author’s position is that while the advent of machines has resulted in much new knowledge, one should not disregard analytical methods, since the solution of nonlinear equations possesses singularities which only the analytical method (as based upon the work of Poincare, Liapounoff, Painleve and Goursatl can discover.After a general survey of the problem presented by nonlinear equations, the author discusses the differential equation of the first order, following this by chapters on the Riccati equation (as a bridge between linear and nonlinear equations) and existence theorems, with special reference to Cauchy’s method. Second order equations are introduced via Volterra’s problem and the problem of pursuit, and succeeding chapters cover elliptic integrals and functions and theta functions; differential equations of the second order; and second order differential equations of the polynomial class, with special reference to Painleve transcendents. The technique of continuous analytical continuation is shown, while phenomena of the phase plane are studied as an introduction to nonlinear mechanics. Nonlinear 111echanics is then discussed, with various classical equations like Van der Pol’s equations, Emden’s equation, and the Duffing problem. The remaining chapters are concerned with nonlinear integral equations, problems from the calculus of variations, and numerical integration of nonlinear equations. Throughout the book the results of distinguished analysis of the past and modern machine computations are both taken into account. Despite the thoroughness of its coverage this is a very fine introduction to this important area of mathematics, and it can easily be followed by the mathematically sophisticated reader who knows very little about nonlinear equations.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book arrives promptly and is in very good condition.

⭐Beautifully written book. The first chapter gives a taste of some of the solution techniques of some ODE’s, and the rest is working on those techniques. The entire book is devoted to a motivating writing style in the sense that you are introduced to a concept or an idea in a very general sense, you get some background, a little history, names of the mathematicians that worked on it, and then the following sections show how the solutions came to be. I could not ask for more.

⭐Comprehensive and thorough.

⭐Dover does it again! I would recommend just about any Dover book on physics or mathematics and this one is high on my list!

⭐Excellent tools for working first and second order NL systems

⭐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.

⭐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.

⭐The contents of the book makes a good impression. Of course I couldn’t work it through in the short time. But the first steps are promising. However there are two things that bother me greatly: First the text on the pages is badly positioned which means the upper margin on the pages is too small, the lower too large. Or, the text was properly placed but when cutting the etches of the paperback the book was unprecisely positioned. This is more probable because I have to separate many pages at the lower edge manually with a thin knive. Secondly the book was badly packed which resulted in a buckled corner (book flew around in a too big package. Sending the book back is out of question because the postage to here and back costs more than the book.

Keywords

Free Download Introduction to Nonlinear Differential and Integral Equations (Dover Books on Mathematics) in PDF format
Introduction to Nonlinear Differential and Integral Equations (Dover Books on Mathematics) PDF Free Download
Download Introduction to Nonlinear Differential and Integral Equations (Dover Books on Mathematics) 2010 PDF Free
Introduction to Nonlinear Differential and Integral Equations (Dover Books on Mathematics) 2010 PDF Free Download
Download Introduction to Nonlinear Differential and Integral Equations (Dover Books on Mathematics) PDF
Free Download Ebook Introduction to Nonlinear Differential and Integral Equations (Dover Books on Mathematics)