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Course
Subject:
Mathematics
Topic:
Tensor Calculus
Views:
56,932
Educator
Name:
Pavel Grinfeld (MathIsBeautiful)
Type:
Individual
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Tensor Calculus and the Calculus of Moving Surfaces
Video Lectures
Displaying all 47 video lectures.
Lecture 1
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Introduction to Tensor Calculus
Lecture 2
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The Rules of the Game
Lecture 3
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The Two Definitions of the Gradient
Lecture 4
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Two Geometric Gradient Examples
Lecture 5
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The Covariant Basis
Lecture 6
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Change of Coordinates
Lecture 7
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The Tensor Notation
Lecture 8
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Fundamental Objects in Euclidean Spaces
Lecture 9
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A Few Tensor Notation Exercises
Lecture 10
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Quadratic Form Minimization
Lecture 11
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Decomposition by Dot Product
Lecture 12
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The Relationship Between the Covariant and the Contravariant Bases
Lecture 13
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Index Juggling
Lecture 14
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The Tensor Property
Lecture 15
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Invariants Are Tensors
Lecture 16
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The Christoffel Symbol
Lecture 17
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The Covariant Derivative
Lecture 18
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The Covariant Derivative II
Lecture 19
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Velocity, Acceleration, Jolt and the New δ/δt-derivative
Lecture 20
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Determinants and Cofactors
Lecture 21
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Relative Tensors
Lecture 22
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The Levi-Civita Tensors
Lecture 23
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The Voss-Weyl Formula
Lecture 24
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Embedded Surfaces and the Curvature Tensor
Lecture 25
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The Surface Derivative of the Normal
Lecture 26
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The Curvature Tensor On The Sphere Of Radius R
Lecture 27
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The Christoffel Symbol on the Sphere of Radius R
Lecture 28
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The Riemann Christoffel Tensor & Gauss's Remarkable Theorem
Lecture 29
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The Equations of Surface and the Shift Tensor
Lecture 30
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The Components of the Normal Vector
Lecture 31
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The Covariant Surface Derivative in Its Full Generality
Lecture 32
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The Normal Derivative
Lecture 33
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The Second Order Normal Derivative
Lecture 34
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Gauss' Theorema Egregium (Part 1)
Lecture 35
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Gauss' Theorema Egregium (Part 2)
Lecture 36
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Linear Transformations in Tensor Notation
Lecture 37
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Inner Products in Tensor Notation
Lecture 38
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The Self-Adjoint Property in Tensor Notation
Lecture 39
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Integration: The Arithmetic Integral
Lecture 40
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Integration: The Divergence Theorem
Lecture 41
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Non-hypersurfaces
Lecture 42
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Examples of Curves in 3D
Lecture 43
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Non-hypersurfaces: Relationship Among The Shift Tensors
Lecture 44
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Non-hypersurfaces: Relationship Among Curvature Tensors I
Lecture 45
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Non-hypersurfaces: Relationship Among Curvature Tensors II
Lecture 46
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Principal Curvatures
Lecture 47
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Tensor Calculus and the Calculus of Moving Surfaces