This text is for a first undergraduate course in ordinary differential equations. While the exposition develops a fairly rigorous theoretical foundation, this text also includes an emphasis on modeling and computation. Embedded Sage cells allow readers to perform computations directly within the book, and each chapter ends with a collection of rich projects that integrate recently developed ideas and illustrate current uses of them. Each section includes reading questions and several activities to support an active learning environment. Given the amount of content, classroom use will require choosing between topics, such as nonlinear systems and Laplace transforms.
Note:
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PDF Version updated June 24, 2023
- Title
- The Ordinary Differential Equations Project
- Author(s)
- Thomas W. Judson
- Published
- 2023-07-24
- Edition
- 1
- Format
- eBook (pdf, epub, mobi)
- Pages
- 407
- Language
- English
- License
- GNU FDL
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
Preface Acknowledgements A First Look at Differential Equations Modeling with Differential Equations Separable Differential Equations Geometric and Quantitative Analysis Analyzing Equations Numerically First-Order Linear Equations Existence and Uniqueness of Solutions Bifurcations Projects for First-Order Differential Equations Systems of Differential Equations Modeling with Systems The Geometry of Systems Numerical Techniques for Systems Solving Systems Analytically Projects for Systems of Differential Equations Linear Systems Linear Algebra in a Nutshell Planar Systems Phase Plane Analysis of Linear Systems Complex Eigenvalues Repeated Eigenvalues Changing Coordinates The Trace-Determinant Plane Linear Systems in Higher Dimensions The Matrix Exponential Projects Systems of Linear Differential Equations Second-Order Linear Equations Homogeneous Linear Equations Forcing Sinusoidal Forcing Forcing and Resonance Projects for Second-Order Differential Equations Nonlinear Systems Linearization Hamiltonian Systems More Nonlinear Mechanics The Hopf Bifurcation Projects The Laplace Transform The Laplace Transform Solving Initial Value Problems Delta Functions and Forcing Convolution Projects for Laplace Transforms Appendices GNU Free Documentation License Hints and Answers to Selected Exercises Notation Back Matter Readings and References Index
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