1. 
Introduction 
1 
2. 
Getting Started with Mathematica 
7 
3. 
Doing Mathematics with Mathematica 
13 
4. 
Using Mathematica Notebooks 
31 

Problem Set A: Practice with Mathematica 
41 
5. 
Solutions of Differential Equations 
45 
6. 
A Qualitative Approach to Differential Equations 
59 

Problem Set B: First Order Equations 
69 
7. 
Numerical Methods 
79 
8. 
Features of Mathematica 
97 

Problem Set C:Numerical Solutions of Differential Equations 
121 
9. 
Solving and Analyzing Second Order Linear Equations 
129 

Problem Set D: Second Order Equations 
145 
10. 
Series Solutions 
159 
10. 
Laplace Transforms 
167 

Problem Set E: Series Solutions and Laplace Transforms 
177 
11. 
Higher Order Equations and Systems of First Order Equations 
189 
12. 
Qualitative Theory for Systems of Differential Equations 
205 

Problem Set F: Systems of Equations 
213 

Glossary 
229 

Sample Solutions 
239 

Index 
261 
