
Ordinary Differential Equations Using MATLAB, 2/e
John Polking, Rice University Published May, 1999 by Prentice Hall Engineering/Science/Mathematics
 
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1. Introduction to Matlab. Numerical Expressions. Mathematical Functions. Output Format. Complex Arithmetic. Recording Your Work. Exercises. 2. Introduction to DFIELD5. Starting DFIELD5. Initial Value Problems. Existence and Uniqueness. Qualitative Analysis. Zooming and Stopping. Using MATLAB While DFIELD5 is Open. Changing the Size and Appearance of the Display Window. Personalizing the Display Window. Printing, Quitting, and Using Clipboards. Exercises. 3. Vectors, Matrices, and Array Operations. Matrices in MATLAB. Addition, Subtraction, and Scalar Multiplication. Vectors in MATLAB. Linear Combinations of Vectors. Matrix Multiplication. Array Operations. Plotting in MATLAB. Printing Your Plot. Simple Function Mfiles. Exercises. 4. Numerical Methods for ODEs. Euler's Method. Euler's Method Versus the Exact Solution. Changing the Step SizeScript Files. Further Error Analysis. The Second Order RungeKutta Method. The Fourth Order RungeKutta Method. Comparing Euler, RK2, and RK4. MATLAB'S ODE45 Routine. Exercises. Appendix: Mfiles for Numerical Methods. 5. Advanced Use of DFIELD5. Step Functions. Step Functions in DFIELD5. Using Function Mfiles in DFIELD5. Solvers and Solver Settings in DFIELD5. Exercises. Appendix: SQW.M. 6. Introduction to PPLANE5. Starting PPLANE5. Changing the Differential SystemUsing the PPLANE5 Setup Window. Plotting Solution Curves. Personalizing the Display Window. Saving Systems and Galleries. Exercises. 7. Solving ODEs in MATLAB. MATLAB'S ODE Suite. Single First Order Differential Equations. Systems of First Order Equations. Second Order Differential Equations. The Lorenz System. Improving Accuracy. Kinky Plots. Behavior Near Discontinuities. Stiff Equations. Other Possibilities. Exercises. Student Projects. 8. The Symbolic Toolbox. Symbolic Objects. The Default Symbolic Variable. Verifying Solutions to Differential Equations. Solving Ordinary Differential Equations. Solving Systems of Ordinary Differential Equations. Interpreting the Output of DSOLVE. The Solve command. Exercises. 9. Linear Algebra Using MATLAB. Systems of Linear Equations. Matrix Indexing in MATLAB and Row Operations. The Rational Format. Solving Linear Equations. Determined Systems of Equations. The Determinant and Systems. The Nullspace of a Matrix. Linear Dependence and Independence. The Nullspace and Dependence. Exercises. 10. Homogeneous Linear Systems of ODEs. Eigenvalues Using MATLAB. Eigenvectors Using MATLAB. MATLAB's EIG command. Tying It TogetherSolving Systems. Complex Eigenvalues. The Exponential Matrix. Repeated Eigenvalues. Exercises. 11. Advanced Use of PPLANE5. Nullclines. Equilibrium Points. Linear Systems. Separatices. Improving Accuracy. A Summary of Equilibrium Point Messages. Exercises. Index..
