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A Modeling Perspectiveby Courtney S. Coleman
Synopses & Reviews
This effective and practical new edition continues to focus on differential equations as a powerful tool in constructing mathematical models for the physical world. It emphasizes modeling and visualization of solutions throughout. Each chapter introduces a model and then goes on to look at solutions of the differential equations involved using an integrated analytical, numerical, and qualitative approach. The authors present the material in a way that's clear and understandable to students at all levels. Throughout the text the authors convey their enthusiasm and excitement for the study of ODEs.
With the modeling and graphical visualization as the central approach, this book introduces differential systems and numerical methods early on and encourages the use of numerical solvers from the very start. It covers modern topics such as sensitivity, long-term behavior, bifurcation, and chaos together with the basic solution formula techniques and theory.
Table of Contents
Introduction to the Tutorials.
Graphs of Functions.
1. Plotting a Function.
2. Plotting Several Curves.
3. Piecewise-Defined Functions.
4. Engineering Functions.
5. Numerical Solutions of ODEs.
6. Slope Fields.
7. Integral Curves.
8. Solution Formulas.
9. Euler's Method, Heun's Method, 4th-Order Runge-Kutta.
10. Laplace Transforms: Discontinuous Driving Terms.
11. Orbits, Solution Curves, Component Curves.
12. Time-State Curves.
13. Discontinuous Driving Terms.
14. Solution Formulas.
15. Laplace Transforms: Dirac-Delta Driving Terms.
Systems of First-Order ODEs.
16. Orbits and Component Graphs.
17. Time-State Curves.
18. Direction Fields.
19. System of Three or More ODEs.
20. Solution Formulas.
21. Fourth-Order Runge-Kutta.
22. System of ODEs in Polar Form.
23. Plotting Partial Sums: Fourier Series.
24. Fourier Coefficients.
25. Recursion Relations: Series Solutions.
Common Functions and Constants in Mathematica.
Index of Mathematica Commands.
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