Differential Geometry (2015) by James Cook

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source: James Cook      2015年6月2日

Differential Geometry: Lecture 1: overview 5:23
Lecture 2 part 1: points, vectors, directional derivative 23:30
Lecture 2 part 2: points, vectors, directional derivative 39:18
Lecture 3 Part 1: differential forms 39:42
Lecture 3 Part 2: differential forms 12:21
Lecture 3 Part 3: differential forms 2:56
Lecture 4 part 1: curves and velocity 32:59
Lecture 4 part 2: Jacobian and push-forward 36:29
Lecture 5 part 1: frames and components in R3 53:32
Lecture 5 part 2: attitude matrix and calculus along curve 46:28
Lecture 6 part 1: Frenet Serret Equations 57:01
Lecture 6 part 2: Frenet Serret for nonconstant speed 20:09
Lecture 7 part 1: covariant derivative in R3 31:08
Lecture 7 part 2: connection form in R3 17:50
Lecture 7 part 3: matrices of forms 32:26
Lecture 8: coframes and structure equations for R3 59:51
Lecture 9 part 1: Euclidean geometry of Rn 25:00
Lecture 9 part 2: push forward of isometries 28:30
Lecture 10: Frenet Curves in Rn 34:46
Lecture 11 Part 1: pushing around vectors in R3 27:28
Lecture 11 Part 2: congruence of curves in R3 51:13
Lecture 12 part 1: surfaces in R3 11:00
Lecture 12 part 2: 19:03
Lecture 12 part 3: surfaces 8:38
Lecture 12 part 4: calculus on surface 16:17
Lecture 12 part 5: TpM the tangent space 49:12
Lecture 13 part 1: differential forms on surface in R3 40:23
Lecture 13 part 2: push-forward of cartesian frame 5:19
Lecture 13 part 3: 41:33
Lecture 13 part 4: diffeomorphism of surfaces 10:49
Lecture 13 part 5 19:08
Lecture 13 part 6 11:16
Lecture 14 part 1: topological trivia for surfaces 43:03
Lecture 14 part 2: proof and manifolds 15:25
Lecture 15 part 1: Shape Operator Defined 41:05
Lecture 15 part 2: normal curvature 35:05
Lecture 15 part 3: Gaussian and Mean curvature 38:50
Lecture 16: calculation of K and H 35:02
Lecture 17: on principal,aymptotic and geodesic curves 56:22
Lecture 18: adapted frame fields of surfaces in R3 41:47
Lecture 19: theorems for surfaces 13:32
Lecture 20 part 1: isometries of surfaces 26:31
Lecture 20 part 2: Gauss' Awesome Theorem 23:35
Lecture 21 part 1: orthogonal patches and Gaussian Curvature 43:03
Lecture 21 part 2: total Gaussian curvature 13:02
Lecture 22: congruence of surfaces 6:33
Lecture 23: metric on geometric surface 26:58
Lecture 24: curved abstract surfaces 42:03
Lecture 25: covariant derivatives again 41:17
Lecture 26: geodesics on geometric surfaces 29:57
Lecture 27 part 1: Gauss Bonnet Theorem 55:55
Lecture 27 part 2: euler characteristic of torus 3:43
Lecture 28: applicationa of Gauss Bonnet 18:18
Lecture 29: I, II and III form notation 17:08