Tensor Calculus and the Calculus of Moving Surfaces

Course Description

Tensor Calculus and the Calculus of Moving Surfaces
The textbook written by Prof. Pavel Grinfeld is used as this basis for this course.
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Video Lectures & Study Materials

# Lecture Play Lecture
1 Introduction to Tensor Calculus Play Video
2 The Rules of the Game Play Video
3 The Two Definitions of the Gradient Play Video
4 Two Geometric Gradient Examples Play Video
5 The Covariant Basis Play Video
6 Change of Coordinates Play Video
7 The Tensor Notation Play Video
8 Fundamental Objects in Euclidean Spaces Play Video
9 A Few Tensor Notation Exercises Play Video
10 Quadratic Form Minimization Play Video
11 Decomposition by Dot Product Play Video
12 The Relationship Between the Covariant and the Contravariant Bases Play Video
13 Index Juggling Play Video
14 The Tensor Property Play Video
15 Invariants Are Tensors Play Video
16 The Christoffel Symbol Play Video
17 The Covariant Derivative Play Video
18 The Covariant Derivative II Play Video
19 Velocity, Acceleration, Jolt and the New δ/δt-derivative Play Video
20 Determinants and Cofactors Play Video
21 Relative Tensors Play Video
22 The Levi-Civita Tensors Play Video
23 The Voss-Weyl Formula Play Video
24 Embedded Surfaces and the Curvature Tensor Play Video
25 The Surface Derivative of the Normal Play Video
26 The Curvature Tensor On The Sphere Of Radius R Play Video
27 The Christoffel Symbol on the Sphere of Radius R Play Video
28 The Riemann Christoffel Tensor & Gauss's Remarkable Theorem Play Video
29 The Equations of Surface and the Shift Tensor Play Video
30 The Components of the Normal Vector Play Video
31 The Covariant Surface Derivative in Its Full Generality Play Video
32 The Normal Derivative Play Video
33 The Second Order Normal Derivative Play Video
34 Gauss' Theorema Egregium (Part 1) Play Video
35 Gauss' Theorema Egregium (Part 2) Play Video
36 Linear Transformations in Tensor Notation Play Video
37 Inner Products in Tensor Notation Play Video
38 The Self-Adjoint Property in Tensor Notation Play Video
39 Integration: The Arithmetic Integral Play Video
40 Integration: The Divergence Theorem Play Video
41 Non-hypersurfaces Play Video
42 Examples of Curves in 3D Play Video
43 Non-hypersurfaces: Relationship Among The Shift Tensors Play Video
44 Non-hypersurfaces: Relationship Among Curvature Tensors I Play Video
45 Non-hypersurfaces: Relationship Among Curvature Tensors II Play Video
46 Principal Curvatures Play Video
47 Geodesic Curvature Preview Play Video


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