Ordinary differential equations : from calculus to dynamical systems
著者
書誌事項
Ordinary differential equations : from calculus to dynamical systems
（MAA textbooks）
The Mathematical Association of America, c2014
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注記
Includes index
内容説明・目次
内容説明
Techniques for studying ordinary differential equations (ODEs) have become part of the required toolkit for students in the applied sciences. This book presents a modern treatment of the material found in a first undergraduate course in ODEs. Standard analytical methods for first- and second-order equations are covered first, followed by numerical and graphical methods, and bifurcation theory. Higher dimensional theory follows next via a study of linear systems of first-order equations, including background material in matrix algebra. A phase plane analysis of two-dimensional nonlinear systems is a highlight, while an introduction to dynamical systems and an extension of bifurcation theory to cover systems of equations will be of particular interest to biologists. With an emphasis on real-world problems, this book is an ideal basis for an undergraduate course in engineering and applied sciences such as biology, or as a refresher for beginning graduate students in these areas.
目次
- Preface
- Sample course outline
- 1. Introduction to differential equations
- 2. First-order differential equations
- 3. Second-order differential equations
- 4. Linear systems of first-order differential equations
- 5. Geometry of autonomous systems
- 6. Laplace transforms
- Appendix A. Answers to odd-numbered exercises
- Appendix B. Derivative and integral formulas
- Appendix C. Cofactor method for determinants
- Appendix D. Cramer's rule for solving systems of linear equations
- Appendix E. The Wronskian
- Appendix F. Table of Laplace transforms
- Index
- About the author.
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