## 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 | ||