**SECTION** |
**MATERIAL ON FINAL EXAM** |

12.1–12.4 |
Background information only. |

12.5 |
Everything execpt angles between planes. |

13.1 |
Background information only. |

13.2 |
Everything except "Ideal Projectile Motion" |

13.3 |
Everything |

14.1 |
Background information only. |

14.2 |
Background information only. |

14.3 |
Background information only. |

14.4 |
**NOT ON FINAL ** |

14.5 |
Everything except the "Algebra Rules for Gradients" |

14.6 |
Background information only. |

14.7 |
Be able to apply Theorem 11 (Second Derivative Test); ignore extrema on closed bounded regions. |

14.8 |
Apply Lagrange's Method with one constraint (Ignore material on two constraints.) |

15.1 |
Know everything |

15.2 |
Know everything |

15.3 |
Know everything |

15.4 |
Know everything |

15.5 |
Know everything |

15.6 |
Everything, except no moments of inertia. |

15.7 |
Know everything |

16.1 |
Everything except moment and intertia calculations. |

16.2 |
Everything up to (and including) Work; but you can ignore circulation and flux here. (They're in 16.4) |

16.3 |
Everything except material on exact differentials. |

16.4 |
Be able to use Green's theorem to compute line integrals. (You do not need to know its physical interpretations.) |

16.5 |
Be able to find surface area. (But you can ignore material on implicitly defined surfaces.) |

16.6 |
Be able to compute surface integrals for all but implicitly defined surfaces. (But ignore material on flux, moments and inertia.) |

16.7 |
Be able to use Stokes' theorem. (But you can ignore all material AFTER Example 5.) |

16.8 |
**NOT ON FINAL ** |