LEC # | TOPICS | KEY DATES |
---|---|---|

I. Vectors and matrices | ||

0 | Vectors | |

1 | Dot product | |

2 | Determinants; cross product | |

3 | Matrices; inverse matrices | |

4 | Square systems; equations of planes | Problem set 1 due |

5 | Parametric equations for lines and curves | |

6 | Velocity, acceleration Kepler's second law | |

7 | Review | Problem set 2 due |

Exam 1 (covering lectures 1-7) | ||

II. Partial derivatives | ||

8 | Level curves; partial derivatives; tangent plane approximation | |

9 | Max-min problems; least squares | Problem set 3 due |

10 | Second derivative test; boundaries and infinity | |

11 | Differentials; chain rule | |

12 | Gradient; directional derivative; tangent plane | Problem set 4 due |

13 | Lagrange multipliers | |

14 | Non-independent variables | |

15 | Partial differential equations; review | Problem set 5 due |

Exam 2 (covering lectures 8-15) | ||

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

16 | Double integrals | Problem set 6 due |

17 | Double integrals in polar coordinates; applications | |

18 | Change of variables | |

19 | Vector fields and line integrals in the plane | Problem set 7 due |

20 | Path independence and conservative fields | |

21 | Gradient fields and potential functions | |

22 | Green's theorem | Problem set 8 due |

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

24 | Simply connected regions; review | |

Exam 3 (covering lectures 16-24) | Problem set 9 due | |

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

25 | Triple integrals in rectangular and cylindrical coordinates | |

26 | Spherical coordinates; surface area | |

27 | Vector fields in 3D; surface integrals and flux | Problem set 10 due |

28 | Divergence theorem | |

29 | Divergence theorem (cont.): applications and proof | |

30 | Line integrals in space, curl, exactness and potentials | |

31 | Stokes' theorem | Problem set 11 due |

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

Exam 4 (covering lectures 25-32) | ||

33 | Topological considerations Maxwell's equations | Problem set 12 due |

34 | Final review | |

35 | Final review (cont.) | |

36 | Final exam |