## 2018-03-13

### Advanced Calculus (Fall 2017) by James Cook at Liberty University

source: James Cook      2017年8月29日

59:51 Advanced Calculus: linear algebra, norms, limits: 8-28-17, part 1
30:08 linear algebra, norms, limits: 8-28-17, part 2
59:51 limits, differentiation: 9-1-17, part 1
30:16 limits, differentiation: 9-1-17, part 2
20:12 differentiation from defn: 9-4-17, part 1
11:55 linearity and chain rule: 9-4-17, part 2
9:31 partial derivatives, Jacobian matrix: 9-1-17, part 3
21:58 continuously diff. implies diff theorem: 9-4-17, part 4
14:33 product rule: 9-4-17, part 5
10 59:51 calculus on an algebra: 9-9-17, part 1
11 28:05 calculus on an algebra: 9-9-17, part 2
12 59:51 theft for NLS, inverse mapping theorem, 9-11-17
13 26:50 implicit mapping theorem not explained well, 9-11-17
14 59:51 implicit diff, manifolds, tangents, normals, 9-15-17, part 1
15 31:24 implicit diff, manifolds, tangents, normals, 9-15-17, part 2
16 11:58 orthogonal complements, 9-18-17, part 1
17 18:25 tangents to curves on manifold form vec. space, 9-18-17, part 2
18 21:59 Lagrange Multipliers, 9-18-17, part 3
19 8:28 quadratic forms, 9-18-17, part 4
20 11:47 multivariate critical pt. analysis, 9-18-17, part 5
21 59:51 variational calculus, 9-22-17, part 1
22 26:40 variational calculus, 9-22-17, part 2
23 59:51 central forces, differential geometry begins, 9-25-17, part 1
24 22:43 tangent space ideas unfinished!, 9-25-17, part 2
25 59:51 abstract manifolds, differentiation, 9-29-17, part 1
26 28:44 abstract manifolds, differentiation, 9-29-17, part 2
27 59:51 differentiation on the manifold examples, 10-2-17, part 1
28 24:12 differentiation and push-forward examples, 10-2-17, part 2
29 59:51 vector fields and flows, 10-9-17 part 1
30 24:04 vector fields and flows, 10-9-17 part 2
31 59:51 dual space, tensors, exterior calc in R3, 10-13-17 part 1
32 27:45 dual space, tensors, exterior calc in R3, 10-13-17 part 2
33 59:51 wedges from determinants, ext derivative, 10-20-17, part 1
34 30:54 wedges from determinants, ext derivative, 10-20-17, part 2
35 59:51 fun with pull backs, substitution to Poincare Lemma, 10-23-17, part 1
36 29:31 fun with pull backs, substitution to Poincare Lemma, 10-23-17, part 2
37 59:51 form integration, start of E and M in diff forms, 10-27-17 part 1
38 28:43 form integration, start of E and M in diff forms, 10-27-17 part 2
39 59:51 potential forms, interior products 10-30-17, part 1
40 26:44 potential forms, interior products 10-30-17, part 2
41 59:51 Lie Derivatives and flow loops, 11-3-17, part 1
42 31:49 Lie Derivatives and flow loops, 11-3-17, part 2
43 59:51 gradient on Riemannian manifold, metric construction, 11-6-17, part 1
44 30:29 gradient on Riemannian manifold, metric construction, 11-6-17, part 2
45 59:51 connection coefficients, calculations, 11-10-17, part 1
46 22:47 derivative along a curve in Riemannian space, 11-10-17, part 2
47 59:51 parallel transport idea, curvature sketch, 11-13-17, part 1
48 16:04 parallel transport idea, curvature sketch, 11-13-17, part 2
49 59:51 isometries and fun, 11-17-17, part 1
50 25:53 isometries and fun, 11-17-17, part 2
51 59:51 contact forms and distributions in R3, 11-27-17, part 1
52 19:51 contact forms and distributions in R3, 11-27-17, part 2
53 59:51 review session for Test 2, 12-1-17, part 1
54 12:17 review session for Test 2, 12-1-17, part 2
55 59:51 contact geometry, Reeb field etc. 12-8-17, part 1
56 24:44 contact geometry, Reeb field etc. 12-8-17, part 2
57 18:15 on Frenet frame for curves, 12-11-17 part 1
58 33:56 overview of Gauss Bonnet Theorem, 12-11-17 part 2