| |
| |
| Preface | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Guiding Philosophy | |
| |
| |
| |
| Student's Guide | |
| |
| |
| |
| Instructor's Guide | |
| |
| |
| |
| Maple | |
| |
| |
| |
| ODE Chapters | |
| |
| |
| |
| Computer Problem Sets | |
| |
| |
| |
| A Word about Software Versions | |
| |
| |
| |
| Getting Started with Maple | |
| |
| |
| |
| Platforms and Versions | |
| |
| |
| |
| Installation | |
| |
| |
| |
| Starting Maple | |
| |
| |
| |
| Maple Input | |
| |
| |
| |
| Online Help | |
| |
| |
| |
| Ending a Session | |
| |
| |
| |
| Doing Mathematics with Maple | |
| |
| |
| |
| Arithmetic | |
| |
| |
| |
| Symbolic Computation | |
| |
| |
| |
| Assignments | |
| |
| |
| |
| Working with Output | |
| |
| |
| |
| Recovering from Problems | |
| |
| |
| |
| Errors in Input | |
| |
| |
| |
| Aborting Calculations | |
| |
| |
| |
| Suppressing Output | |
| |
| |
| |
| The Restart Command | |
| |
| |
| |
| Equations | |
| |
| |
| |
| Solving Equations | |
| |
| |
| |
| Functions and Expressions | |
| |
| |
| |
| Built-in Functions | |
| |
| |
| |
| User-defined Functions | |
| |
| |
| |
| Expressions | |
| |
| |
| |
| Substitution | |
| |
| |
| |
| Sequences, Sets, and Lists | |
| |
| |
| |
| Packages | |
| |
| |
| |
| Graphics | |
| |
| |
| |
| Plotting Functions and Expressions | |
| |
| |
| |
| Plotting Multiple Curves | |
| |
| |
| |
| Plotting Points | |
| |
| |
| |
| Adding Text to a Plot | |
| |
| |
| |
| Parametric Plots | |
| |
| |
| |
| Implicit Plots | |
| |
| |
| |
| Contour Plots | |
| |
| |
| |
| Calculus | |
| |
| |
| |
| More on Sequences, Lists, and Sets | |
| |
| |
| |
| Procedures | |
| |
| |
| |
| Some Tips and Reminders | |
| |
| |
| |
| Using Maple Documents | |
| |
| |
| |
| The Maple Window | |
| |
| |
| |
| Organization of a Document | |
| |
| |
| |
| Document Blocks | |
| |
| |
| |
| Graphics | |
| |
| |
| |
| Preparing Homework Solutions | |
| |
| |
| |
| Practice with Maple | |
| |
| |
| |
| Solutions of Differential Equations | |
| |
| |
| |
| Finding Symbolic Solutions | |
| |
| |
| |
| Existence and Uniqueness | |
| |
| |
| |
| Stability of Differential Equations | |
| |
| |
| |
| Different Types of Symbolic Solutions | |
| |
| |
| |
| A Qualitative Approach to Differential Equations | |
| |
| |
| |
| Direction Field for a First Order Linear Equation | |
| |
| |
| |
| Direction Field for a Non-Linear Equation | |
| |
| |
| |
| Autonomous Equations | |
| |
| |
| |
| Examples of Autonomous Equations | |
| |
| |
| |
| First Order Equations | |
| |
| |
| |
| Numerical Methods | |
| |
| |
| |
| Numerical Solutions Using Maple | |
| |
| |
| |
| Some Numerical Methods | |
| |
| |
| |
| The Euler Method | |
| |
| |
| |
| The Improved Euler Method | |
| |
| |
| |
| The Runge-Kutta Method | |
| |
| |
| |
| Inside dsolve(..., numeric) | |
| |
| |
| |
| Round-off Error | |
| |
| |
| |
| Controlling the Error in dsolve(..., numeric) | |
| |
| |
| |
| Reliability of Numerical Methods | |
| |
| |
| |
| Features of Maple | |
| |
| |
| |
| Names and Values | |
| |
| |
| |
| Clearing Values | |
| |
| |
| |
| Vectors and Matrices | |
| |
| |
| |
| Solving Linear Systems | |
| |
| |
| |
| Calculating Eigenvalues and Eigenvectors | |
| |
| |
| |
| Plots for ODEs | |
| |
| |
| |
| Commands for Plotting Direction Fields | |
| |
| |
| |
| Plotting Families of Numerical Solutions of ODEs | |
| |
| |
| |
| More about D Eplot | |
| |
| |
| |
| Stopping Conditions | |
| |
| |
| |
| Numerical Solutions of Higher Order Differential Equations | |
| |
| |
| |
| Troubleshooting | |
| |
| |
| |
| The Common Mistakes | |
| |
| |
| |
| Error and Warning Messages | |
| |
| |
| |
| Numerical Solutions | |
| |
| |
| |
| Solving and Analyzing Second Order Linear Equations | |
| |
| |
| |
| Second Order Equations with Maple | |
| |
| |
| |
| Comparison Methods | |
| |
| |
| |
| The Interlacing of Zeros | |
| |
| |
| |
| Proof of the Sturm Comparison Theorem | |
| |
| |
| |
| A Geometric Method | |
| |
| |
| |
| The Constant Coefficient Case | |
| |
| |
| |
| The Variable Coefficient Case | |
| |
| |
| |
| Airy's Equation | |
| |
| |
| |
| Bessel's Equation | |
| |
| |
| |
| Other Equations | |
| |
| |
| |
| Second Order Equations | |
| |
| |
| |
| Series Solutions | |
| |
| |
| |
| Series Solutions | |
| |
| |
| |
| Singular Points | |
| |
| |
| |
| Laplace Transforms | |
| |
| |
| |
| Differential Equations and Laplace Transforms | |
| |
| |
| |
| Discontinuous Functions | |
| |
| |
| |
| Differential Equations with Discontinuous Forcing | |
| |
| |
| |
| Series Solutions and Laplace Transforms | |
| |
| |
| |
| Higher Order Equations and Systems of First Order Equations | |
| |
| |
| |
| Higher Order Linear Equations | |
| |
| |
| |
| Systems of First Order Equations | |
| |
| |
| |
| Linear First Order Systems | |
| |
| |
| |
| Using Maple to Find Eigenpairs | |
| |
| |
| |
| Phase Portraits | |
| |
| |
| |
| Plotting a Single Trajectory | |
| |
| |
| |
| Plotting Several Trajectories | |
| |
| |
| |
| Numerical Solutions of First Order Systems | |
| |
| |
| |
| Qualitative Theory for Systems of Differential Equations | |
| |
| |
| |
| Systems of Differential Equations | |
| |
| |
| Glossary | |
| |
| |
| Sample Solutions | |
| |
| |
| Index | |