Ordinary differential equations using Matlab

Cover
Title page
Preface
1. Introduction to MATLAB
Numerical Expressions
Mathematical Functions
Output Format
Comp1ex Arithmetic
Recording Your Work
Exercises
2. Plotting in MATLAB
EZ plotting
Matrices and Vectors in MATLAB
Addition, Subtraction, and Multiplication by Scalars
Array Operations and Array Smart Functions
Plotting in MALAAS Using the plot Command
Editing Graphics
Saving, Printing, and Exporting Your Plot
Script M-files
Text strings in MATLAB
A Little Programming
Other Issues with M-files
Handle graphics
Exercises
3. Introduction to DFIELD6
Starting DFIELD6
The Direction Field
Initial Value Problems
Existence and Uniqueness
Qualilative Analysis
Using MATLAB While DFIELD6 is Open
Subscripts and Greek Letters
Editing Ihe Display Window
Other Features of DFIELD6
Exercises
Appendix: Downloading and Installing the Software Used in This Manual
4 The Use of Function M-Files
New functions in MATLAB
Function M-files, Computational Exercices and Graphics
Functions of Several Variables
Naming and Organizing Files
Exercises
5. Numerical Methods for ODEs
Euler's Method
Euler's Method Versus the Exact So1ution
Changing the Step Size - Using Script M-Files
Numerical Error Analysis
The Second Order Runge-Kutta Method
The Fourth Order Runge-Kutta Method
Comparing Euler, RK2, and RK4
Exercises
Appendix: M-files for Numerical Methods
6 Advanced Use of DFIELD6
Step Functions
Step Functions in DFIELD6
Using Funetion M-files in DFIELD6
The Square Wave Function
Solvers and Solver Settings in DFIELD6
Exercices
7. Introduction to PPLANE6
Starting PPLANE6
Changing the System - Using the PPLANE6 Setup Window
Plotting Solution Curves
Other Propertiesof PPLANE6
Exercices
8. Solving ODEs in MATLAB
MATLAB's ODE Suite
Single First Ordcr Differential Equations
Function M-File Drivers and Subfunctions
Systems of First Order Equations
Second Order Differential Equations
The Lorenz System and Passing Parameters
Improving Accuracy
Behavior Near Discontinuities
Stiff Equations
Other Possibilities
Exercices
Student Projects
9. Introduction to ODESOLVE
Staning ODESOlVE
Oplions in ODF.50lVE
Exercises
10. The Symho!ic Toolbox
Algebraic Expressions and Symbolic Objects
Verifying Solutions to Differential Equations
Solving Ordinary Differential Equations
Solving Systems of Ordinary Differential Equations
Interpreting Ihe Output of DSOLVE
The Solve Command
Exercices
11. Linear Algebra Using MATLAB
Systems of Linear Equations
Linear Combinations of Vectors and the Matrix-Vector Product
Matrix Multiplication
Solving Systems of Equations and Row Operations
MatrixIndexing in MATLAB and Row Operations
The Rational Format
Elimination and Backsolving
Determined Systems of Equations
The Determinant and Systems
The Nullspaçe of a Matrix
Linear Dependence and Independence
The Nullspace and Dependence
Exercices
12. Homogeneous Linear Systems of ODEs
Eigenvalues Using MATLAB
Eigenvectors Using MATLAB
MATLAB's eig Command
Tying It All Together - Solving Systems of ODEs
Complex Eigenvalues
The Exponential or a Matrix
Solving Systems with Repeated Eigenvalues
Exercices
13. Advanced Use of PPLANE6
Nullclines
Equilibrium Points
Linear Systemw
Nonlinear Systems
Separatrices
Limit Sets or Solution Curves
Other Options in PPLANE6
Exercises
Appendix: A Summary of Equilibrium Point Messages