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Invidious > Channel > MathTheBeautiful

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YT 1 hour 1 minute 39 seconds MathTheBeautiful Why Tensor Calculus? YT 1 minute 1 second MathTheBeautiful An Alert for My Tensors Textbook YT 40 minutes 5 seconds MathTheBeautiful Geometric vectors as the starting point for Tensor Calculus. Vector-valued functions and more!

YT 36 minutes 5 seconds MathTheBeautiful Tensor Calculus 2: The Two Conflicting Definitions of the Gradient YT 11 minutes 56 seconds MathTheBeautiful Tensor Calculus 2b: Two Geometric Gradient Examples (Torricelli's and Heron's Problems) YT 37 minutes 1 second MathTheBeautiful Tensor Calculus 3a: The Covariant Basis

YT 39 minutes 13 seconds MathTheBeautiful Tensor Calculus 3b: Change of Coordinates YT 1 hour 28 minutes 39 seconds MathTheBeautiful Tensor Calculus 4a: The Tensor Notation YT 29 minutes 41 seconds MathTheBeautiful Tensor Calculus 4b: Position Vector, Covariant Basis, Covariant Metric Tensor, Contravariant Basis

YT 18 minutes 50 seconds MathTheBeautiful Tensor Calculus 4c: A Few Tensor Notation Exercises YT 11 minutes 43 seconds MathTheBeautiful Tensor Calculus 4d: Quadratic Form Minimization YT 13 minutes 25 seconds MathTheBeautiful Tensor Calculus 4e: Decomposition by Dot Product in Tensor Notation

YT 6 minutes 7 seconds MathTheBeautiful Tensor Calculus 4f: The Relationship Between the Covariant and the Contravariant Bases YT 25 minutes 49 seconds MathTheBeautiful Tensor Calculus 4g: Index Juggling YT 1 hour 42 minutes 5 seconds MathTheBeautiful Tensor Calculus 5a: The Tensor Property

YT 9 minutes 56 seconds MathTheBeautiful Tensor Calculus 5b: Invariants Are Tensors YT 21 minutes 6 seconds MathTheBeautiful Tensor Calculus 6a: The Christoffel Symbol YT 50 minutes 11 seconds MathTheBeautiful Tensor Calculus 6b: The Covariant Derivative

YT 43 minutes 51 seconds MathTheBeautiful Tensor Calculus Lecture 6c: The Covariant Derivative 2 YT 43 minutes 11 seconds MathTheBeautiful Tensor Calculus 6d: Velocity, Acceleration, Jolt and the New δ/δt-derivative YT 1 hour 8 minutes 49 seconds MathTheBeautiful Tensor Calculus Lecture 7a: Determinants and Cofactors

YT 18 minutes 2 seconds MathTheBeautiful Tensor Calculus Lecture 7b: Relative Tensors YT 9 minutes 41 seconds MathTheBeautiful Tensor Calculus Lecture 7c: The Levi-Civita Tensors YT 20 minutes 7 seconds MathTheBeautiful Tensor Calculus Lecture 7d: The Voss-Weyl Formula

YT 34 minutes 42 seconds MathTheBeautiful Tensor Calculus Lecture 8: Embedded Surfaces and the Curvature Tensor YT 32 minutes 44 seconds MathTheBeautiful Tensor Calculus Lecture 8b: The Surface Derivative of the Normal YT 30 minutes 57 seconds MathTheBeautiful Tensor Calculus Lecture 8c: The Curvature Tensor On The Sphere Of Radius R

YT 12 minutes 33 seconds MathTheBeautiful Tensor Calculus 8d: The Christoffel Symbol on the Sphere of Radius R YT 50 minutes 4 seconds MathTheBeautiful Tensor Calculus Lecture 8e: The Riemann Christoffel Tensor & Gauss's Remarkable Theorem YT 59 minutes 42 seconds MathTheBeautiful Tensor Calculus Lecture 9a: The Equations of Surface and the Shift Tensor

YT 16 minutes 53 seconds MathTheBeautiful Tensor Calculus Lecture 9b: The Components of the Normal Vector YT 50 minutes 19 seconds MathTheBeautiful Tensor Calculus Lecture 10a: The Covariant Surface Derivative in Its Full Generality YT 31 minutes 13 seconds MathTheBeautiful Tensor Calculus Lecture 10b: The Normal Derivative

YT 17 minutes 4 seconds MathTheBeautiful Tensor Calculus Lecture 10c: The Second Order Normal Derivative YT 36 minutes 27 seconds MathTheBeautiful Tensor Calculus Lecture 11a: Gauss' Theorema Egregium, Part 1 YT 23 minutes 8 seconds MathTheBeautiful Tensor Calculus Lecture 11b: Gauss' Theorema Egregium, Part 2

YT 18 minutes 47 seconds MathTheBeautiful Tensor Calculus Lecture 12a: Linear Transformations in Tensor Notation YT 6 minutes 41 seconds MathTheBeautiful Tensor Calculus Lecture 12b: Inner Products in Tensor Notation YT 11 minutes 16 seconds MathTheBeautiful Tensor Calculus 12c: The Self-Adjoint Property in Tensor Notation

YT 8 minutes 30 seconds MathTheBeautiful Tensor Calculus Lecture 13a: Integration - The Arithmetic Integral YT 20 minutes 13 seconds MathTheBeautiful Tensor Calculus Lecture 13b: Integration - The Divergence Theorem YT 12 minutes 53 seconds MathTheBeautiful Tensor Calculus Lecture 14a: Non-hypersurfaces

YT 11 minutes 23 seconds MathTheBeautiful Tensor Calculus Lecture 14b: Examples of Curves in 3D YT 10 minutes 46 seconds MathTheBeautiful Tensor Calculus Lecture 14c: Non-hypersurfaces - Relationship Among The Shift Tensors YT 12 minutes 8 seconds MathTheBeautiful Tensor Calculus Lecture 14d: Non-hypersurfaces - Relationship Among Curvature Tensors 1

YT 16 minutes MathTheBeautiful Tensor Calculus Lecture 14e: Non-hypersurfaces - Relationship Among Curvature Tensors 2 YT 17 minutes 52 seconds MathTheBeautiful Tensor Calculus Lecture 14f: Principal Curvatures YT 13 minutes 57 seconds MathTheBeautiful Tensor Calculus Lecture 15: Geodesic Curvature Preview

YT 21 seconds MathTheBeautiful Derivative of a Basis Vector Illustrated (e_r in polar coordinates)