Ordinary differential equations : from calculus to dynamical systems
Author(s)
Bibliographic Information
Ordinary differential equations : from calculus to dynamical systems
（MAA textbooks）
The Mathematical Association of America, c2014
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Note
Includes index
Description and Table of Contents
Description
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.
Table of Contents
- 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.
by "Nielsen BookData"