Jean-Luc Thiffeault

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

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 `Rⁿ`; Cross product; Orientation of bases
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

Math 321: Applied Mathematical Analysis I (Fall 2019)
(Vector and Complex Calculus for the Physical Sciences)