CiNii 図書 - Ordinary differential equations : from calculus to dynamical systems

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.

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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Ordinary differential equations : from calculus to dynamical systems

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