Tensor Calculus and the Calculus of Moving Surfaces

Video Lectures

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