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 
