Lecture Description
This video lecture, part of the series Tensor Calculus and the Calculus of Moving Surfaces by Prof. , does not currently have a detailed description and video lecture title. If you have watched this lecture and know what it is about, particularly what Mathematics topics are discussed, please help us by commenting on this video with your suggested description and title. Many thanks from,
- The CosmoLearning Team
- The CosmoLearning Team
Course Index
- Introduction to Tensor Calculus
- The Rules of the Game
- The Two Definitions of the Gradient
- Two Geometric Gradient Examples
- The Covariant Basis
- Change of Coordinates
- The Tensor Notation
- Fundamental Objects in Euclidean Spaces
- A Few Tensor Notation Exercises
- Quadratic Form Minimization
- Decomposition by Dot Product
- The Relationship Between the Covariant and the Contravariant Bases
- Index Juggling
- The Tensor Property
- Invariants Are Tensors
- The Christoffel Symbol
- The Covariant Derivative
- The Covariant Derivative II
- Velocity, Acceleration, Jolt and the New δ/δt-derivative
- Determinants and Cofactors
- Relative Tensors
- The Levi-Civita Tensors
- The Voss-Weyl Formula
- Embedded Surfaces and the Curvature Tensor
- The Surface Derivative of the Normal
- The Curvature Tensor On The Sphere Of Radius R
- The Christoffel Symbol on the Sphere of Radius R
- The Riemann Christoffel Tensor & Gauss's Remarkable Theorem
- The Equations of Surface and the Shift Tensor
- The Components of the Normal Vector
- The Covariant Surface Derivative in Its Full Generality
- The Normal Derivative
- The Second Order Normal Derivative
- Gauss' Theorema Egregium (Part 1)
- Gauss' Theorema Egregium (Part 2)
- Linear Transformations in Tensor Notation
- Inner Products in Tensor Notation
- The Self-Adjoint Property in Tensor Notation
- Integration: The Arithmetic Integral
- Integration: The Divergence Theorem
- Non-hypersurfaces
- Examples of Curves in 3D
- Non-hypersurfaces: Relationship Among The Shift Tensors
- Non-hypersurfaces: Relationship Among Curvature Tensors I
- Non-hypersurfaces: Relationship Among Curvature Tensors II
- Principal Curvatures
- Geodesic Curvature Preview
Course Description
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