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

Davis, Harold T.

ISBN 10: 0486609715 / ISBN 13: 9780486609713

Edité par Dover Publications, New York, 1962

A propos de cet article

Softcover. Condition: Very Good. Signs of wear on cover and pencil marks on pages. No creases or tears.
This edition is an unabridged and unaltered version of the work first published in 1960 by the United States Atomic Energy Commission.
Contents include:
1. Introduction;
2. The Differential Equations of First Order;
3. The Riccati Equation;
4. Existence Theorems;
5. An Introduction to Second Order Equations ? The Problems of Conflict and Pursuit;
6. Elliptic Integrals, Elliptic Functions, and Theta Functions;
7. Differential Equations of Second Order;
8. Second Order Differential Equations of Polynomial Class;
9. Continuous Analytic Continuation;
10. The Phase Plane and its Phenomena;
11. Nonlinear Mechanics;
12. Some Particular Equations;
13. Nonlinear Integral Equations;
14. Problems from the Calculus of Variations; and
15. The Numerical Integration of Nonlinear Equations
Includes bookmark from store (Books, Inc. in San Jose) where the book may have been previously purchased. This bookstore was in the historic Town & Country Village in San Jose that was demolished and replaced by the prominent Santana Row shopping center.

N° de réf. du vendeur ABE-1768520514308

Détails bibliographiques

• Titre: Introduction to Nonlinear Differential and Integral Equations (Dover Books on Mathematics)
• Éditeur: Dover Publications, New York
• Date de parution: 1962
• Langue: anglais
• ISBN à 10 chiffres: 0486609715
• ISBN à 13 chiffres: 9780486609713
• Reliure: Couverture souple
• Édition: Edition originale
• État de l'article: Assez bon
• Dimensions: 1,25 L x 5,75 H x 8,75 P (en pouces) 1,25 pouces de largeur par 5,75 pouces de hauteur par 8,75 pouces de profondeur
• Poids: 294 grammes
• Catalogues du vendeur:
  • Education
  • Mathematics

A propos de ce titre

Synopsis

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.

Présentation de l'éditeur

Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, the technique of continuous analysical continuation, the phenomena of the phase plane, nonlinear mechanics, nonlinear integral equations, problems from the calculus of variations and more. 1960 edition. Includes 137 problems.