Tensors | Differential geometry | Tensors in general relativity
In differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing from one coordinate system to another (see tensor field), except that it is additionally multiplied or weighted by a power W of the Jacobian determinant of the coordinate transition function or its absolute value. A tensor density with a single index is called a vector density. A distinction is made among (authentic) tensor densities, pseudotensor densities, even tensor densities and odd tensor densities. Sometimes tensor densities with a negative weight W are called tensor capacity. A tensor density can also be regarded as a section of the tensor product of a tensor bundle with a density bundle. (Wikipedia).
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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
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What is Density? | Gravitation | Physics | Don't Memorise
Understanding the concept of Density is very important in order to understand Physics. Watch this video to fully grasp the idea of density. To get access to the entire course based on Gravitation, enroll here: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&u
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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
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From playlist High School Geometry | High School Math | Khan Academy
(November 26, 2012) Leonard Susskind derives the Einstein field equations of general relativity and demonstrates how they equate spacetime curvature as expressed by the Einstein tensor, with the energy and momentum within that spacetime as expressed by the stress-energy tensor. This serie
From playlist Lecture Collection | General Relativity
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Tensor Calculus for Physics Ep. 14 | Covariant Curl
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