The Riemann Christoffel Tensor & Gauss's Remarkable Theorem 
The Riemann Christoffel Tensor & Gauss's Remarkable Theorem
by MathIsBeautiful
Video Lecture 28 of 48
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Views: 1,155
Date Added: April 3, 2016

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,

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Course Index

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

Course Description


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