Tensor analysis Definition and 77 Threads

Hello, some time ago I read that if we know the metric tensor g_{ij} associated with a change of coordinates \phi, it is possible to calculate the (Euclidean?) inner product in a way that is invariant to the parametrization. Essentially the inner product was defined in terms of the metric...

Show that a symmetric tensor has n(n+1) \ 2 quantities. In a symmetric tensor we have that Aij = Aji which means that A12 = A21 A23 = A32 and so on. Thus these n quantites are similar. What do we do next?

Hello, I know all my algebra, trig, and I'm still fine tuning calculus and I've solved ODEs using the Laplace transform. Now, my question is... what else must I know to study Tensor calculus/Tensor Analysis? I really want to know so that I have a true understanding of relativity(the famous...

So far I have only seen ∂/(∂y) as being interpreted as an operator being of no use unless it is applied to some vector etc. Now, however, my course literature asserts the following equality: y=∂/(∂y) What is the interpretation of the differentials in this case?

εHomework Statement show that the determinant of a matrix A can be calculated as followings: det[A]= 1/6 (A_ii A_jj A_kk + 2 A_ij A_jk A_ki - 3 A_ij A_ji A_kk Homework Equations The Attempt at a Solution use ε_pqr det[A]= ε_ijk A_ip A_jq A_kr ε_pqr...

Tensor analysis is backbone of General theory of relativity... But it is a difficult mathematical concept. How can i know more about tensor analysis not in just a pure mathematical way?

I had a badly taught Advanced Linear Algebra course and it covered tensor algebra, resulting in a knowledge gap. What books would you recommend, if any? Exterior algebra, exterior calculus, Clifford and Grassmann algebras included wouldn't be bad ideas as well.

Hello, Does anyone know of a REALLY good tensor analysis text. I am a chemical engineer who is working on a masters in EE and would like a text that covers fluids applications as well as rank 3 EE applications and even some rank 4 general relativity would be nice to see. It would also be...

Hey there, I am a Physics major and currently in my freshmen year. I would love to study General Relativity in the senior year of college. One of the requirements of General Relativity is the knowledge of tensors. But, which math courses should I take? I read in some blogs that Group Theory...

Homework Statement 1) Let e, e' be two orthonormal bases(not necessarily the standard basis). Prove that the matrix S = [Id]e-e' (direct transformation from e to e') is orthogonal, i.e. SS^T = S^TS = [Id]_3. SS^T is S * S transpose. 2) The moment of inertia tensor of a right circular cylinder...

Hi, I think I have been having this question for some time now. What is the difference between tensor calculus and linear algebra? Both seem to make frequent use of matrices, but they seem to be different subject matter. Can anyone please enlighten me on this issue?

Please introduce me a good book for my self_study of tensor analysis and group theory. I am a sophermore preparing to self-study them!

Hi All , I am looking for a book on introduction to tensor analysis . I do not have much of a background in mathematics .. I have an undergraduate degree in engineering . My aim is to understand General Relativity ... I would also like to understand Quantum Mechanics ... It feels odd that there...

Can anyone reccomend a good introductory text on tensor analysis? My college has neither a GR nor a tensor analysis course but i'd still like to read a good introductory text to prepare for an independent research project.

Hi all! I read about tensor analysis and came about following expressions, where also a questions arose which I cannot explain to me. Perhaps you could help me: I: Consider the following expressions: d\vec v=dc^k e^{(k)} d\vec v=dc^k e_{(k)} where: dc^k=dv^k+v^t\Gamma_{wt}^k dx^w...

Homework Statement I am having trouble solving this problem. From an analysis of the behavior of a general second-rank tensor under 90 degree and 180 degree rotations about the coordinate axes, show that an isotropic second-rank tensor in 3-D space must be a multiplier of delta ij...

I'm just starting out with learning a bit of general relativity and have read the first 3 chapters of Schutz's 'A first course in General Relativity' (up to and including the Tensor analysis chapter). I have managed to do about 90% of the exercises but I don't really feel confident with it. I've...

Could anyone tell me what a good book is that describes Tensor Analysis from the basics to the advanced material? It would be truly helpful.

Okay, second question - does anyone know of a good text that covers the basics of manipulating tensors without assuming a very extensive math background? I am reasonably good at linear algebra and taking a differential geometry class, but that's about the extent of my math background. I am in a...

I want to study 3 subjects on my own,the subjects are Group Theory, tensor analysis, and QFT. I know this might be a silly question, but regardless of what textbook material i have or how much I know, what is the best order to study these 3 subjects ? I feel I should leave QFT to the last...

what is the physical significance of the lie derivative? What is its purpose in tensor analysis?

why tensor analysis ? Hi Im studying tensor analysis this course but i don't know why we study it ? is it helpfull ? what is the history 4 it ? what tensor mean ? :confused: :confused: :confused: i hope i can find answer !

Im taking a course in contiuum mechanics and had some questions that I am sure are pretty basic but I'm not getting. We just started curvilinear coordinates and I was curious if someone could explain in a little simplier language of what the superscript and subscripts mean. Or if you...

Does anyone know good books on tensor analysis, especially need to learn it to understand continuum mechanics. Thank you.

When Enstein developed tensor analysis because all the other math fell apart, there was another type of math that was developed to measure the curvature of space. What is it? How does it work?

Ruslan Sharipov has a nifty online textbook on this subject. It's written in interactive do-it-yourself style. Give it a glance, and see what you think.

[SOLVED] Tensor Analysis - Request for opinion Seems that a few people refer to things like vectors and tensors as quantities which are invariant. For example Dr. Bertschinger (Cosmologist at MIT) has online notes at http://arcturus.mit.edu/8.962/notes/gr1.pdf "Introduction to Tensor...