(Vector and Complex Calculus for the Physical Sciences)

Lecture Room: | B239 Van Vleck |

Lecture Time: | 9:30–10:45 TuTh |

Lecturer: | Jean-Luc Thiffeault |

Office: | 503 Van Vleck |

Email: | |

Office Hours: | see syllabus |

See the syllabus for information about the class, including textbook, homeworks, discussions, grading, midterm and exam dates.

The main course website is hosted on Canvas.

lecture |
date |
pages |
topic |

1 | 09/05 | 9–14 | Review of vectors in 2D and 3D |

2 | 09/10 | 14–22 | Addition and scaling of vectors; General vector spaces; Bases and components |

3 | 09/12 | 23–29 | Lines and planes; Medians of a triangle; Dot product |

4 | 09/17 | 30–39 | Orthonormal bases; Dot products and norms
in ; Cross product; Orientation of basesR^{n} |

5 | 09/19 | 37–47 | Triple vector product; Levi-Civita symbol; Index notation; Einstein convention |

6 | 09/24 | 48–63 | Mixed product and determinant; Lines and planes again (and spheres!); Orthogonal transformations and matrices |

7 | 09/26 | 61–67 | Matrices; Euler angles; Gram–Schmidt |

8 | 10/01 | 73–75 | Vector functions |

9 | 10/03 | 75–77 | Vector functions (cont'd) |

10 | 10/08 | 79–80 | Homework problems; Newtonian mechanics |

11 | 10/10 | 80–91 | Newtonian mechanics; Curves |

12 | 10/15 | 91–94 | Curvature and torsion; Integrals on curves |

13 | 10/17 | 94–99 | Integrals on curves; Surfaces |

14 | 10/22 | – | Review for midterm |

– | 10/24 | – | Midterm 1 |

15 | 10/29 | 99–106 | Surface integrals |

16 | 10/31 | 106–109 | Volumes |

17 | 11/05 | 109–111 | Curvilinear coordinates |

18 | 11/07 | 111–120 | Grad |

19 | 11/12 | 121–124 | Div, curl |

20 | 11/14 | 125–135 | Div, curl in polars; Green's theorem |

21 | 11/19 | 135–155 | Stokes' theorem; Divergence theorem; Complex numbers |

– | 11/21 | – | Midterm 2 |

22 | 11/26 | 158–166 | Polar form; Complex roots; Cauchy–Riemann relations |

23 | 12/03 | 166–168, 179–181 | Cauchy's theorem; Contour integration |

24 | 12/05 | 181–189 | Poles; Residue theorem; Cauchy's formula |

25 | 12/10 | 190–195 | Using complex integration |