Change of Basis
We learned about how vectors can form a basis for a vector space, and we can express any vector within a vector space as a linear combination of the basis ...
Professor Dave Explains
Curvature tensor and Covariant derivative
An intuitive introduction to the curvature tensor plus a spontaneous definition of the covariant derivative.
Ahmed Isam
Tensor Calculus 5b: Invariants Are Tensors
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: ...
MathTheBeautiful
Contravariant and Covariant Vectors | 1/2
In this video, I describe the meaning of contravariant and covariant vector components. As mentioned in a previous video, tensors are invariant under coordinate ...
Faculty of Khan
Tensor Calculus 3b: Change of Coordinates
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: ...
MathTheBeautiful
Tensor Calculus 11: The Metric Tensor and Arc Lengths (flat space)
Tensors for beginners video on the Metric Tensor (for vector lengths): https://www.youtube.com/watch?v=C76lWSOTqnc.
eigenchris
Change of basis | Essence of linear algebra, chapter 13
Home page: https://www.3blue1brown.com/ How do you translate back and forth between coordinate systems that use different basis vectors? Full series: ...
3Blue1Brown
Tensor Calculus 1: The Rules of the Game
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: ...
MathTheBeautiful
Linear Algebra 20L: The Dot Product in Non-Cartesian Bases, the Gram Matrix or the Metric
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep ...
MathTheBeautiful
Tensors for Beginners 1: Forward and Backward Transformations (contains error; read description!)
WARNING: THERE ARE ERRORS IN THIS VIDEO!! The F and B matrices in this video are all "flipped" on their sides (that is, I accidently wrote out F-transpose ...
eigenchris
Tangent space
This video looks at the idea of a tangent space at an arbitrary point to any given manifold in which vectors exist. It shows how vectors expressed as directional ...
Tensor Calculus - Robert Davie
Tensor Calculus 4b: Position Vector, Covariant Basis, Covariant Metric Tensor, Contravariant Basis
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: ...
MathTheBeautiful
Essentials of Tensor Calculus – Part 1
In a series of five webinars, Dr. Robert Lopez will present the essential ideas of the tensor calculus. The central concepts are contained in three sections: ...
Maplesoft
Contravariant, covariant and physical components of tensors
This video looks at the ideas of contravariant, covariant and physical components and how to convert the first two component types into physical component ...
Tensor Calculus - Robert Davie
Tensors for Beginners 9: The Metric Tensor
Starting to lose steam again. I feel the way I'm editing videos is really inefficient. I have 3 more videos planned for the non-calculus videos. After that I'll take a ...
eigenchris
Variation of the metric determinant
This video looks at the process for deriving some useful expressions to be used in the variation of the determinant of the metric. The variation of the metric term is ...
Tensor Calculus - Robert Davie
What Is a Tensor?
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: ...
MathTheBeautiful
Tensor Calculus 3a: The Covariant Basis
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: ...
MathTheBeautiful
Linear Algebra 20k: Two Derivations of the Dot Product Component Space Expression
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep ...
MathTheBeautiful
Continuum Mechanics - Ch 0 - Lecture 1 - Introduction
The written media of the course (slides and book) are downloadable as: Multimedia course: CONTINUUM MECHANICS FOR ENGINEERS. Prof. Oliver's web ...
Online Course on Continuum Mechanics
Calcolo Tensoriale: Sistemi non ortogonali
Sistemi non ortogonali: Proiezioni parallele e proiezioni perpendicolari. Componenti controvarianti e covarianti. Sito web ufficiale: https://www.giuseppesottile.it/ ...
YouSciences Academy
Tensor Calculus 2: Cartesian/Polar Coordinates, and Basis Vectors
A review of cartesian and polar coordinate systems, and the basis vectors that we get from them (also called the "covariant basis" or "holonomic basis").
eigenchris
Tensor Calculus 17.5: Covariant Derivative (Component Definition) - Optional
Video 17 on Covariant Derivative in flat space: https://www.youtube.com/watch?v=U5iMpOn5IHw&index=19&list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx.
eigenchris
Introduction to tensors
Prof. Abhijit P Deshpande Department of Chemical Engineering IIT Madras.
Rheology - IITM
Linear Algebra 15h: The Derivative as a Linear Transformation
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep ...
MathTheBeautiful
The Similarity Relationship Represents a Change of Basis
Description: The formula P^-1AP=D is called similarity. We interpret this geometrically as being a change of basis. Learning Objective: Given two similar matrices ...
Trefor Bazett
Linear Algebra 7g: The Nullspace of a 3x3 Matrix with a Specific Pattern
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep ...
MathTheBeautiful
Tensors Explained Intuitively: Covariant, Contravariant, Rank
Tensors of rank 1, 2, and 3 visualized with covariant and contravariant components. My Patreon page is at https://www.patreon.com/EugeneK.
Physics Videos by Eugene Khutoryansky
Basis Vectors - Tensors #5
In this video I discuss the notion of a basis for a vector space and introduce the Einstein summation convention. Apologies for the harsh "ess" sounds, tried to ...
WHYBmaths
Linear Algebra 6b: Alternative Definition of Linear Indpendence
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep ...
MathTheBeautiful
Introduction to Tensors: Transformation Rules
In this video, I continue my introduction to tensors by talking about the transformation property that defines tensors, that tensors are invariant under a change of ...
Faculty of Khan
Vector triple product expansion (very optional) | Vectors and spaces | Linear Algebra | Khan Academy
A shortcut for having to evaluate the cross product of three vectors Watch the next lesson: ...
Khan Academy
Gram-Schmidt Orthogonalization and Legendre Polynomials
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep ...
MathTheBeautiful
Independent components of the Riemann tensor
This video investigates the symmetry properties of the Riemann tensor and uses those properties to determine the number of independent components it ...
Tensor Calculus - Robert Davie
But what is a partial differential equation? | DE2
The heat equation, as an introductory PDE. Home page: https://www.3blue1brown.com Brought to you by you: http://3b1b.co/de2thanks Infinite powers, ...
3Blue1Brown
Linear algebra introduction
A review of linear algebra as necessary for quantum mechanics, including vector properties, inner products, normalization, and representations of vectors in a ...
Brant Carlson
Linear Algebra 19f: The Heart of Component Spaces - Matrix Representation of a Linear Tranformation
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep ...
MathTheBeautiful
Lecture 22 : Tensor Product of Representation
Tensor Product of Representation.
IIT Bombay July 2018
Tensor Calculus 1: Multi-variable Calculus Review (Updated with correction)
Updated with a correction to the tangent vector magnitude formula. Thanks to Daniel McCammon for pointing out the error. A review of the multi-variable calculus ...
eigenchris
Vector transformations | Matrix transformations | Linear Algebra | Khan Academy
Introduction to the notion of vector transformations Watch the next lesson: ...
Khan Academy
Linear Algebra 6c: Second Definition of Linear Dependence Fixed!
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep ...
MathTheBeautiful
Linear Algebra 8e: A 3x3 Linear System
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep ...
MathTheBeautiful
