Differential equations, mechanics, and computation

by Palais, Richard S.

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Title Statements

Full title :Differential equations, mechanics, and computation / Richard S. Palais, Robert A. Palais.

Summary

"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. This book is published in cooperation with IAS/Park City Mathematics Institute."--Provided by publisher.

Edition Statements

Publication Date:©2009.

Publication Statements

Publisher(s):American mathematical Society, Institute for Advanced Study
Place of Publication:Providence, R.I
Language:eng
Publication Date:©2009.

The Physical Object

Description:xiii, 313 pages : : illustrations ; : 22 cm

Edition Identifiers

ISBN:9780821821381, 0821821385
oclc:ocn144529436
LC Classification:QA371
Dewey Decimal:518/.6

Differential equations and their solutions -- Linear differential equations -- Second-order ODE and calculus of variations -- Newtonian mechanics -- Numerical methods -- Appendix A: Linear algebra and analysis -- Appendix B: The magic of iteration -- Appendix C: Vector fields as differential operators -- Appendix D: Coordinate systems and canonical forms -- Appendix E: Parametrized curves and arclength -- Appendix F: Smoothness with respect to inital conditions -- Appendix G: Canonical form for linear operators -- Appendix H: Runge-Kutta methods -- Appendix I: Multistep methods -- Appendix J: Iterative interpolation and its error.

Subjects

Differential equations -- Numerical sol… Differential equations, Linear -- Numer… Differentialgleichung -- Numerische Mat… Équations d'évolution Équations différentielles -- Solutions … Équations différentielles linéaires -- … Evolution equations Evolutionsgleichung Gewöhnliche Differentialgleichung Lineare Differentialgleichung Mécanique Mechanics mechanics (physics) Mechanik -- Mathematische Methode Numerische Mathematik -- Differentialgl… Numerisches Verfahren Variationsrechnung