Differential Equations, Mechanics, and Computation (First Edition) Richard S. Palais

Differential Equations, Mechanics, and Computation (First Edition) Richard S. Palais 2012; 313 pp; Paperback; 180 × 240 mm; 978-0-8218-8735-6 For sale only in India,Pakistan,Nepal,Bhutan,Bangladesh,Sri Lanka,Maldives 720.00 This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject. Table of Contents * Introduction  * Differential equations and their solutions  * Linear differential equations  * Second-order ODE and the calculus of variations  * Newtonian mechanics  * Numerical methods * Linear algebra and analysis  * The magic of iteration Vector fields as differential operators  * Coordinate systems and canonical forms  * Parametrized curves and arclength  * Smoothness with respect to initial conditions  * Canonical form for linear operators  * Runge-Kutta Methods  * Multistep methods  * Iterative interpolation and its error  * Bibliography  * Index About the Author Richard S. Palais, University of California, Irvine, CA, and Robert A. Palais, University of Utah, Salt Lake City, UT.