Metric tensors

Tensors in curvilinear coordinates

Curvilinear coordinates can be formulated in tensor calculus, with important applications in physics and engineering, particularly for describing transportation of physical quantities and deformation of matter in fluid mechanics and continuum mechanics. (Wikipedia).

Video thumbnail

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

From playlist Physics

Video thumbnail

Visualization of tensors - part 1

This video visualizes tensors. It shows some introduction to tensor theory and demonstrates it with the Cauchy stress tensor. Future parts of this series will show more theory and more examples. It talks about the term 'tensor' as used in physics and math. In the field of AI the term 'te

From playlist Animated Physics Simulations

Video thumbnail

Tensor Calculus For Physics Majors 006 | The Metric Tensor pt. 1

Today I talk about the metric tensor and how it relates coordinate displacement to distance. I also show how to calculate the components of the metric tensor in spherical coordinates. Link to Tensor Calculus for Physics Book: https://www.amazon.com/gp/product/1421415658/ref=as_li_tl?ie=UT

From playlist New To Tensors? Start Here

Video thumbnail

Tensors as a Sum of Symmetric and Antisymmetric Tensors

In the last tensor video, I mentioned second rank tensors can be expressed as a sum of a symmetric tensor and an antisymmetric tensor. Today we prove that.

From playlist New To Tensors? Start Here

Video thumbnail

Calculus 3: Tensors (1 of 28) What is a Tensor?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a tensor. A tensor is a mathematical representation of a scalar (tensor of rank 0), a vector (tensor of rank 1), a dyad (tensor of rank 2), a triad (tensor or rank 3). Next video in t

From playlist CALCULUS 3 CH 10 TENSORS

Video thumbnail

Given a Vector in Component Form, Find the Unit Vector

Learn how to determine the unit vector of a vector in the same direction. The unit vector is a vector that has a magnitude of 1. The unit vector is obtained by dividing the given vector by its magnitude. #trigonometry#vectors #vectors

From playlist Vectors

Video thumbnail

Calculus 3: Tensors (13 of 45) What is the Inertia Tensor?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the inertia tensor relating the physical inertia activity and the tensor component notation. Next video in the series can be seen at: https://youtu.be/-chgCHuEI4Y

From playlist CALCULUS 3 CH 10 TENSORS

Video thumbnail

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: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te

From playlist Introduction to Tensor Calculus

Video thumbnail

Einstein's General Theory of Relativity | Lecture 5

Lecture 5 of Leonard Susskind's Modern Physics concentrating on General Relativity. Recorded October 20, 2008 at Stanford University. This Stanford Continuing Studies course is the fourth of a six-quarter sequence of classes exploring the essential theoretical foundations of modern phys

From playlist Lecture Collection | Modern Physics: Einstein's Theory

Video thumbnail

Tensor Calculus Lecture 10c: The Second Order Normal Derivative

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: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te

From playlist Introduction to Tensor Calculus

Video thumbnail

Is geophysical fluid motion Newtonian? - Dubos - Workshop 1 - CEB T3 2019

Dubos (Ecole Polytechnique) / 10.10.2019 Is geophysical fluid motion Newtonian? Geophysical hydrodynamics rely on a variety of models which approximate classical, Newtonian fluid motion in rotating frames. Even accurate approximations, especially pertaining to the Coriolis pseudo-f

From playlist 2019 - T3 - The Mathematics of Climate and the Environment

Video thumbnail

3. Tensors continued.

MIT 8.962 General Relativity, Spring 2020 Instructor: Scott Hughes View the complete course: https://ocw.mit.edu/8-962S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP629n_3fX7HmKKgin_rqGzbx More on tensors, derivatives, and 1-forms. Contraction of tensor indices; th

From playlist MIT 8.962 General Relativity, Spring 2020

Video thumbnail

6. The principle of equivalence.

MIT 8.962 General Relativity, Spring 2020 Instructor: Scott Hughes View the complete course: https://ocw.mit.edu/8-962S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP629n_3fX7HmKKgin_rqGzbx Introduction to the principle of equivalence: freely falling frames to gener

From playlist MIT 8.962 General Relativity, Spring 2020

Video thumbnail

Lec 4b - Phys 237: Gravitational Waves with Kip Thorne

Watch the rest of the lectures on http://www.cosmolearning.com/courses/overview-of-gravitational-wave-science-400/ Redistributed with permission. This video is taken from a 2002 Caltech on-line course on "Gravitational Waves", organized and designed by Kip S. Thorne, Mihai Bondarescu and

From playlist Caltech: Gravitational Waves with Kip Thorne - CosmoLearning.com Physics

Video thumbnail

Calculus 3: Tensors (2 of 28) Tensors Represented in a Matrix

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain and visually show how tensors, scalar, vector, dyad, and triad, are represented by a matrix. Next video in the series can be seen at: https://youtu.be/brnzaYNFJ1w

From playlist CALCULUS 3 CH 10 TENSORS

Video thumbnail

Tensor Calculus Lecture 6c: The Covariant Derivative 2

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: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te

From playlist Introduction to Tensor Calculus

Video thumbnail

Einstein's General Theory of Relativity | Lecture 4

October 13, 2008, Stanford's Felix Bloch Professor of Physics, Leonard Susskind, discusses covariant and contra variant indices, tensor arithmetic, algebra and calculus, and the geometry of expanding space time. This Stanford Continuing Studies course is the fourth of a six-quarter sequ

From playlist Lecture Collection | Modern Physics: Einstein's Theory

Video thumbnail

5. The stress energy tensor and the Christoffel symbol.

MIT 8.962 General Relativity, Spring 2020 Instructor: Scott Hughes View the complete course: https://ocw.mit.edu/8-962S20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP629n_3fX7HmKKgin_rqGzbx More on the stress-energy tensor: symmetries and the physical meaning of str

From playlist MIT 8.962 General Relativity, Spring 2020

Video thumbnail

Calculus 3: Tensors (5 of 28) Tensor for Crystal Structure: Orthorombic

Visit http://ilectureonline.com for more math and science lectures! In this video I will show how to apply tensors to a crystal structure, the orthorombic-which is a cube where all the angles are 90 degrees. Next video in the series can be seen at: https://youtu.be/fS1FumZgMKQ

From playlist CALCULUS 3 CH 10 TENSORS

Video thumbnail

Thomas Dubos: High performance climate modelling : mimetic finite differences, and beyond ?

Abstract: Climate models simulate atmospheric flows interacting with many physical processes. Because they address long time scales, from centuries to millennia, they need to be efficient, but not at the expense of certain desirable properties, especially conservation of total mass and ene

From playlist Numerical Analysis and Scientific Computing

Related pages

Curl (mathematics) | Line integral | Covariant derivative | Tensor calculus | Invariant (mathematics) | Gradient | Albert Einstein | Chain rule | Frenet–Serret formulas | Surface integral | Kronecker delta | Maxwell's equations | Identity function | Divergence | Determinant | Del in cylindrical and spherical coordinates | Christoffel symbols | Cartesian coordinate system | Euclidean space | Orthogonality | Scalar (mathematics) | Cross product | Curvilinear perspective | Levi-Civita symbol | Manifold | Metric tensor | Einstein notation | Orthogonal coordinates | Space | Vector calculus | Curvilinear coordinates | Vector field