Solving ODE's with Maple V

This handy resource manual/lab book shows students how to use the MapleĻ computer algebra system to solve problems in ordinary differential equations. Projects, exercises, and explanations show readers how to get the most out of the Maple computer algebra system when solving differential equations.

• Basic Maple commands that deal with differential equations are included in Chapters 1, 4, 5, 6, and 8.
• Exercises that illustrate the use of Maple commands appear at the end of each chapter
• Chapters 3 and 7 include applications, and Chapter 10 contains projects (more extended applications that use Maple to simplify the computations and to provide graphical insight.
• A quick review of Maple commands is given in Chapter 0.

Table of Contents:

0. MAPLE REVIEW.

Assignment Statements and Arithmetic. Expressions versus Functions. Plots. Solving Equations. Differentiation. Integration. Taylor Approximations.

1. DIFFERENTIAL EQUATIONS AND MAPLE.

Maple Commands. Examples. Exercises.

2. NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS.

Numerical Algorithms. The Order of Convergence for Some Numerical Methods. A Finite Difference Method for a 2-Point Boundary Value. Problem. Exercises.

3. APPLICATIONS.

Art History. Rural Water Supplies. Growth of Microorganisms: Linear and Nonlinear.

4. SYSTEMS.

Analyzing a First Order Linear System with Two Unknowns. A Mixing Problem which Gives Geometric Insight into Eigenvectors. An Introduction to Maple's Linear Algebra Package. Homogeneous First Order Linear Systems. Nonhomogeneous First Order Linear Systems. Determining the Stability of a Nonlinear System. Nuts and Bolts. Exercises.

5. NUMERICAL SOLUTIONS OF SYSTEMS.

Numerical Solution of Systems of First Order Equations. Two-Dimensional Motion of a Projectile with Friction. Exercises.

6. HIGHER ORDER EQUATIONS.

Homogenous Equations. Nonhomogeneous Equations. Exercises.

7. APPLICATIONS OF HIGHER ORDER EQUATIONS.

Beats and Resonance. Damped Forced Vibrations. Exercises.

8. LAPLACE TRANSFORMS.

Definition of the Laplace Transform. Derivatives. Initial Value Problems. Step Functions. Impulse Functions. The Convolution Integral. The Transfer Function. Exercises.

9. QUALITATIVE THEORY AND NONLINEAR SYSTEMS.

The Phase Plane: Linear Systems. Autonomous Systems. Competing Species. The Predator-Prey Equations. Exercises.

10. PROJECTS.

Heat-Seeking Particles. Autonomous Differential Equations. The Tennis Serve. Modeling Lake Pollution. Shooting a Projectile. Rocket Propulsion. The Laplace Transform and Square Waves. Taylor Series Methods for Differential Equations. Controlling the Motion of a Cart.

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