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jby
Any books recommended for dummies? All books that I've found starts with contraviant and covariant tensor, which seems misleading to me.
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Originally posted by jby
Any books recommended for dummies? All books that I've found starts with contraviant and covariant tensor, which seems misleading to me.
Originally posted by marcus
my private sentiment is that the word "tensor" is misleading
(probably "dingus" would do as well and it is just some
historical accident that they started saying tensor-----but covar
and contravar are descriptive names, therefore could be helpful to understand what they mean.
Originally posted by marcus
however a trajectory or path in X is COvariant because the map f will transform it into an image path in Y. And taking the derivative of some real-valued function defined on X at a point along that path translates into taking the derivative of a function defined on Y along the image path.
so the solemn ritual of taking a derivative of whatever and in whatever direction goes along WITH the map, getting carried along from X to Y in the same direction as the map goes.
Originally posted by jcsd
While your here, i found these on-line notes on 'Modern Relativity' extermely useful as a refernce work whilst working on the computer:
http://www.geocities.com/zcphysicsms/
Originally posted by jby
Any books recommended for dummies? All books that I've found starts with contraviant and covariant tensor, which seems misleading to me.
Originally posted by pmb
Use caution when using these notes. They were written by a well known crackpot. Most of it is okay I guess (simple stuff copied from texts) but other parts are very wrong.
The author used to post here for a short time. He came here and imediately started flaming me when he couldn't convince me that a scalar was not defined in modern physics/math as a tensor of rank zero. He was banished when he started to flame the moderator. He was warned to cease flaming but continued and was tossed out.
Pete
Some but not all.Originally posted by jcsd
I haven't looked over all of them, but they do seem okay to me, I've the feeling he might of lifted them from a textbook.
Originally posted by pmb
It goes on and on and on. He's just a crackpot - plain and simple.
Contravariant and covariant tensors are two types of mathematical objects used in the study of tensors. The main difference between them is their transformation properties under coordinate transformations. Contravariant tensors transform in the opposite direction as the coordinate system, while covariant tensors transform in the same direction as the coordinate system.
Contravariant and covariant tensors are related through the metric tensor, which is a mathematical object that defines the inner product between two vectors. The metric tensor is used to raise and lower indices of tensors, converting between contravariant and covariant representations.
Contravariant and covariant tensors are used in various fields such as physics, engineering, and computer science. In physics, they are used to describe the physical properties of objects and their interactions. In engineering, they are used in the study of stress and strain in materials. In computer science, they are used in image and signal processing algorithms.
Contravariant and covariant tensors can be manipulated using index notation and tensor algebra. This involves raising and lowering indices, contracting tensors, and performing operations such as addition and multiplication. It is important to follow the rules of tensor algebra to ensure the correct transformation of tensors.
Yes, contravariant and covariant tensors can have different dimensions. In general, tensors are multidimensional arrays of numbers, and the number of indices and their dimensions can vary. For example, a 2nd-order tensor may have a different number of rows and columns for its covariant and contravariant representation. However, the dimensions of the covariant and contravariant representations must match for a tensor to be well-defined.