## Table of Contents

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 | ||