| Softcover ISBN: | 978-0-8218-2138-1 |
| Product Code: | STML/51 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-1220-3 |
| Product Code: | STML/51.E |
| List Price: | $49.00 |
| Individual Price: | $39.20 |
| Softcover ISBN: | 978-0-8218-2138-1 |
| eBook: ISBN: | 978-1-4704-1220-3 |
| Product Code: | STML/51.B |
| List Price: | $108.00 $83.50 |
| Softcover ISBN: | 978-0-8218-2138-1 |
| Product Code: | STML/51 |
| List Price: | $59.00 |
| Individual Price: | $47.20 |
| eBook ISBN: | 978-1-4704-1220-3 |
| Product Code: | STML/51.E |
| List Price: | $49.00 |
| Individual Price: | $39.20 |
| Softcover ISBN: | 978-0-8218-2138-1 |
| eBook ISBN: | 978-1-4704-1220-3 |
| Product Code: | STML/51.B |
| List Price: | $108.00 $83.50 |
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Book DetailsStudent Mathematical LibraryIAS/Park City Mathematics SubseriesVolume: 51; 2009; 313 ppMSC: Primary 34; 65; 70
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.ReadershipUndergraduate and graduate students interested in ordinary differential equations and numerical methods.
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Table of Contents
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Chapters
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Introduction
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Chapter 1. Differential equations and their solutions
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Chapter 2. Linear differential equations
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Chapter 3. Second-order ODE and the calculus of variations
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Chapter 4. Newtonian mechanics
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Chapter 5. Numerical methods
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Appendix A. Linear algebra and analysis
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Appendix B. The magic of iteration
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Appendix C. Vector fields as differential operators
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Appendix D. Coordinate systems and canonical forms
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Appendix E. Parametrized curves and arclength
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Appendix F. Smoothness with respect to initial conditions
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Appendix G. Canonical form for linear operators
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Appendix H. Runge-Kutta Methods
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Appendix I. Multistep methods
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Appendix J. Iterative interpolation and its error
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Additional Material
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Reviews
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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
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
Undergraduate and graduate students interested in ordinary differential equations and numerical methods.
-
Chapters
-
Introduction
-
Chapter 1. Differential equations and their solutions
-
Chapter 2. Linear differential equations
-
Chapter 3. Second-order ODE and the calculus of variations
-
Chapter 4. Newtonian mechanics
-
Chapter 5. 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 initial conditions
-
Appendix G. Canonical form for linear operators
-
Appendix H. Runge-Kutta Methods
-
Appendix I. Multistep methods
-
Appendix J. Iterative interpolation and its error
-
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
