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Introduction to Nonlinear Differential and Integral Equations by Harold T. Davis



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Introduction to Nonlinear Differential and Integral Equations written by Harold T. Davis .
This book covered include differential equations of the first order, the Riccati equation and existence theorems, second 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.
This book contains an introduction to various classical methods of numerical integration of nonlinear equations, those were abandoned in favor of a new tool designed as the method of continuous analytic continuation. There an interative process based upon Cauchy's method of limits.

Title: Introduction to Nonlinear Differential and Integral Equations
Author(s): Harold T. Davis
Publisher: Dover Publications
Series:
Year: 2010
Pages: 592
Type: PDF
Language: English
ISBN: 0486609715,9780486609713
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Introduction to Nonlinear Differential and Integral Equations written by Harold T. Davis cover the following topics.
1. Introduction
2. Differential Equation of First Order
3. The RICCATI Equation
4. Existence Theorems
5. An introduction to Second Order Equation- The problems of conflict and Pursuit
6. Elliptic Integral, Elliptic Functions and Theta Functions
7. Differential Equation of Second Order
8. Second Order Differential Equation of Polynomial Class
9. Continuous Analytic Continuation
10. The Phase Plane and Phenomena
11. Non Linear Mechanics
12. Some Particular Equations
13. Nonlinear Integral Equations
14. Problems From the Calculus of Variations
15. The Numerical Integration of Non Linear Equations

The author Harold Thayer Davis was a mathematician, statistician, and econometrician, known for the Davis distribution.
Davis received in 1915 his A.B. from Colorado College, in 1919 his A.M. from Harvard University, and in 1926 his PhD under Edward Burr Van Vleck from the University of Wisconsin, after working there as a mathematics instructor from 1920 to 1923. From 1923 to 1937 he taught mathematics at the Indiana University Bloomington, becoming a professor there. From February to August 1937 he was acting research director of the Cowles Commission. Davis became a professor in 1937 at Northwestern University in the mathematics department and the chair of the department in 1942. He was the author of many articles in refereed journals and numerous books and monographs.
Davis was an associate editor of Econometrica, Isis, and the Bulletin of the American Mathematical Society. He was elected a Fellow the Econometric Society.[4

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