**Student Mathematical Library**

Volume: 51;
2009;
313 pp;
Softcover

MSC: Primary 34; 65; 70;

Print ISBN: 978-0-8218-2138-1

Product Code: STML/51

List Price: $51.00

Individual Price: $40.80

**Electronic ISBN: 978-1-4704-1220-3
Product Code: STML/51.E**

List Price: $51.00

Individual Price: $40.80

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#### Supplemental Materials

# Differential Equations, Mechanics, and Computation

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*Richard S. Palais; Robert A. Palais*

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

#### Table of Contents

# Table of Contents

## Differential Equations, Mechanics, and Computation

- Cover Cover11 free
- Title page i2 free
- Contents v6 free
- IAS/Park City Mathematics Institute ix10 free
- Preface xi12 free
- Acknowledgments xiii14 free
- Introduction 116 free
- Differential equations and their solutions 520 free
- Linear differential equations 3752
- Second-order ODE and the calculus of variations 6378
- Newtonian mechanics 91106
- Numerical methods 133148
- Linear algebra and analysis 225240
- The magic of iteration 233248
- Vector fields as differential operators 243258
- Coordinate systems and canonical forms 247262
- Parametrized curves and arclength 255270
- Smoothness with respect to initial conditions 257272
- Canonical form for linear operators 259274
- Runge-Kutta Methods 263278
- Multistep methods 281296
- Iterative interpolation and its error 303318
- Bibliography 307322
- Index 311326 free
- Back Cover Back Cover1329

#### Readership

Undergraduate and graduate students interested in ordinary differential equations and numerical methods.

#### Reviews

This volume in the IAS/Park City Mathematical Subseries of the Student Mathematical Library shares with many other volumes of that series an approach that is freshly considered, accelerated and challenging. The authors take their cue from Richard Feynman: 'Imagine that you are explaining your ideas to your former smart, though ignorant, self, at the beginning of your studies!' . . . The authors are clearly intent on building a deeper conceptual understanding and offering correspondingly sophisticated tools. . . . [T]he treatment is subtle and aimed at developing a mature appreciation of important applications. . . . This book offers a sophisticated introduction to differential equations that strong student would likely find very attractive. It would also function nicely for independent or guided self-study.

-- Bill Satzer, MAA Reviews