Tensor Calculus and the Calculus of Moving Surfaces

Video Lectures

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