The notes below represent summaries of the lectures as written by Professor Auroux to the recitation instructors.

LEC # | TOPICS | LECTURE NOTES |
---|---|---|

I. Vectors and matrices |
||

0 1 2 |
Vectors
Dot product Determinants; cross product |
Week 1 summary (PDF) |

3
4
5 |
Matrices; inverse matrices
Square systems; equations of planes Parametric equations for lines and curves |
Week 2 summary (PDF) |

6 |
Velocity, acceleration Kepler’s second law |
Week 3 summary (PDF) |

7 | Review | |

II. Partial derivatives |
||

8 | Level curves; partial derivatives; tangent plane approximation | Week 4 summary (PDF) |

9 | Max-min problems; least squares | |

10 | Second derivative test; boundaries and infinity | |

11 | Differentials; chain rule | Week 5 summary (PDF) |

12 | Gradient; directional derivative; tangent plane | |

13 | Lagrange multipliers | |

14 | Non-independent variables | Week 6 summary (PDF) |

15 | Partial differential equations; review | |

III. Double integrals and line integrals in the plane |
||

16 | Double integrals | Week 7 summary (PDF) |

17 | Double integrals in polar coordinates; applications | |

18 | Change of variables | Week 8 summary (PDF) |

19 | Vector fields and line integrals in the plane | |

20 | Path independence and conservative fields | |

21 | Gradient fields and potential functions | Week 9 summary (PDF) |

22 | Green’s theorem | |

23 | Flux; normal form of Green’s theorem | |

24 | Simply connected regions; review | Week 10 summary (PDF) |

IV. Triple integrals and surface integrals in 3-space |
||

25 | Triple integrals in rectangular and cylindrical coordinates | Week 10 summary (PDF) |

26 | Spherical coordinates; surface area | Week 11 summary (PDF) |

27 | Vector fields in 3D; surface integrals and flux | |

28 | Divergence theorem | |

29 | Divergence theorem (cont.): applications and proof | Week 12 summary (PDF) |

30 | Line integrals in space, curl, exactness and potentials | Week 13 summary (PDF) |

31 | Stokes’ theorem | |

32 | Stokes’ theorem (cont.); review | |

33 |
Topological considerations Maxwell’s equations |
Week 14 summary (PDF) |

34 | Final review | |

35 | Final review (cont.) |