Description
Book SynopsisThis 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.
Table of ContentsIntroduction to the Tutorials. Graphs of Functions.
1. Plotting a Function.
2. Plotting Several Curves.
3. Piecewise-Defined Functions.
4. Engineering Functions.
First-Order ODEs.
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.
Second-Order ODEs.
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.
Additional Topics.
23. Plotting Partial Sums: Fourier Series.
24. Fourier Coefficients.
25. Recursion Relations: Series Solutions.
Glossary.
Common Functions and Constants in Mathematica.
Index of Mathematica Commands.
