LEC # | TOPICS | READINGS |
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I. Vectors and matrices |
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0 | Vectors | Text: Section 12.1 |

1 | Dot product | Text: Section 12.2 |

2 | Determinants; cross product |
Text: Section 12.3 Notes: Section D |

3 | Matrices; inverse matrices | Notes: Sections M.1 and M.2 |

4 | Square systems; equations of planes |
Text: Pages 798-800 Notes: Section M.4 |

5 | Parametric equations for lines and curves | Text: Sections 12.4 and 10.4 |

6 |
Velocity, acceleration Kepler's second law |
Text: Section 12.5, page 818 Notes: Section K |

7 | Review | |

II. Partial derivatives |
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8 | Level curves; partial derivatives; tangent plane approximation |
Text: Sections 13.2 and 13.4 Notes: Section TA |

9 | Max-min problems; least squares |
Text: Pages 878-881, 884-885 Notes: Section LS |

10 | Second derivative test; boundaries and infinity |
Text: Section 13.10, through page 930 Notes: Section SD |

11 | Differentials; chain rule | Text: Sections 13.6-13.7 |

12 | Gradient; directional derivative; tangent plane | Text: Section 13.8 |

13 | Lagrange multipliers | Text: Section 13.9, through page 922 |

14 | Non-independent variables | Notes: Section N |

15 | Partial differential equations; review | Notes: Section P |

III. Double integrals and line integrals in the plane |
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16 | Double integrals |
Text: Section 14.1-14.3 Notes: Section I.1 |

17 | Double integrals in polar coordinates; applications |
Text: Sections 14.4-14.5 Notes: Section I.2 |

18 | Change of variables |
Text: Section 14.9 Notes: Section CV |

19 | Vector fields and line integrals in the plane |
Text: Section 15.2 Notes: Section V1 |

20 | Path independence and conservative fields | Text: Section 15.3 |

21 | Gradient fields and potential functions | Notes: Section V2 |

22 | Green's theorem | Text: Section 15.4 |

23 | Flux; normal form of Green's theorem | Notes: Sections V3 and V4 |

24 | Simply connected regions; review | Notes: Section V5 |

IV. Triple integrals and surface integrals in 3-space |
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25 | Triple integrals in rectangular and cylindrical coordinates |
Text: Sections 12.8, 14.6, and 14.7 Notes: Section I.3 |

26 | Spherical coordinates; surface area |
Text: Section 14.7 Notes: Sections I.4, CV.4, and G |

27 | Vector fields in 3D; surface integrals and flux | Notes: Sections V8 and V9 |

28 | Divergence theorem |
Text: Section 15.6 Notes: Section V10 |

29 | Divergence theorem (cont.): applications and proof |
Text: Section 15.6, Pages 1054-1055 Notes: Section V10 |

30 | Line integrals in space, curl, exactness and potentials |
Text: Pages 1017-1018 Notes: Sections V11 and V12 |

31 | Stokes' theorem |
Text: Section 15.7 Notes: Section V13 |

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

33 |
Topological considerations Maxwell's equations |
Notes: Sections V14 and V15 |

34 | Final review | |

35 | Final review (cont.) |