I want to learn tensor calculus in order to study more advanced mathematics and physics such as; General Relativity, Differential Geometry, Continuum Mechanics etc. Moore, Displacement effect of a three-dimensional boundary layer, N. You can look at Barrett O'Neill's Elementary Differential Geometry as well. More advanced studies of the properties of mathematical and physical objects which are invariant with respect to the choice of coordinate systems led to a generalization of vector calculus —. I've heard good things about Pressley's Elementary Differential Geometry and O'Neill's Elementary Differential Geometry, but I've never read either of them However, I have read another of O'Neill's books, and I liked it. Moore, Displacement effect of a three-dimensional boundary layer, N.
Have you studied linear algebra now? Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, special types of space, relative tensors, ideas of volume, and more. The displacement effect of the boundary layer is also discussed. Tensor calculus dover books on mathematics book 5 ebook j l synge a schild amazonin and for those interested in the applications of tensor calculus to mathematical physics and engineering revised and updated second edition dover books on mathematics. You could also try jumping right into Gallot, Hulin and Fontaine's Riemannian Geometry straight away - the first chapter will teach you the langauge - its always a good idea to work at a level above your comfort zone when you are starting out because math gets harder as you become more advanced also there's not much time. Dec 15 2018 epub document about mathematical expositions no 5 tensor calculus second edition 324 pp download is available on print and digital edition this pdf ebook is one of digital edition of mathematical expositions no 5 tensor calculus second edition 324 pp by j l synge download that can be tensor calculus mathematical expositions no.
This view is the reason you were taught from the O'Neill's book in your undergrad. Whereas Barrett O'Neill manages gets to some serious differential geometry while working over low-dimensions. You might give it a shot for something a little more tractable. You will do annoying computations which I don't find particularly enlightening, and you will work with lots of ugly coordinates and parametrizations. Differential geometry is a beautiful field and really rewarding to study! Connection is a sophisticated idea: orders of magnitude harder to grasp than anything in Lee's basic text.
Mangler, Zusammenhang zwischen ebenen und rotationssymmetrischen Grenzschichten in kompressiblen Flüssigkeiten, Z. All posts and comments should be directly related to mathematics. Description: ix, 324 pages : illustrations ; 21 cm Contents: Introduction -- Spaces and tensors -- Basic operations in Riemannian space -- Curvature of space -- Special types of space -- Applications to classical dynamics -- Applications to hydrodynamics, elasticity, and electromagnetic radiation -- Relative tensors, ideas of volume, green-strokes theorems -- Non-Riemannian spaces. It actually helped me understand the calculus of curvature a lot, and made other texts on it more accessible. Zee's book is basically the opposite of a mathematical viewpoint. And your understanding of it will be a million times more mature than someone who suffered through O'Neill I had to read it for 2 classes in undergrad differential geometry and it still haunts my worse nightmares.
Now, Barrett O'Neill's book has sophisticated mathematical ideas I know of no other book where Cartan's is so simply presented written in the language that even a person with a calculus and linear algebra background can understand, whereas Lee's book has very few differential geometric ideas in it since its job is to set up the vocabulary. Vector calculus comprises vector algebra and vector analysis. Derivation of the equations for flow along a general curved surface, Philos. Vector calculus originated in the 19th century in connection with the needs of mechanics and physics, when operations on vectors began to be performed directly, without their previous conversion to coordinate form , ,. Lee's book, nice though it is, being a book on basic manifold theory is a language book with respect to differential geometry - not even covariant derivatives are defined in it differential geometry needs to have differentiation happening.
It might not be the best book to learn from, but it's good to know what the 'right' way is, even if you don't end up learning that way in depth Also, my advice would be to stay away from any book e. Consider a voluminous body with internal stresses. What are you talking about? I have met many a mathematicians in my life but honestly how many you think read 5 volumes? You could also look at Barrett O'Neill's Semi-Riemannian Geometry: its primarily a book on Relativity I haven't read it but I know a guy who swears by it. The invariance properties of these equations are found using the concept of subtensors. I certainly wouldn't use either as a first introduction. This is simply not true.
Conditions for the Cartesian form of the equations are given and a criterion for no secondary flow is found in terms of the geodesies of the body surface. No surprise to me it's hard, but I'm not an analyst. Evidently your profs agree with me. Also, I have to disagree with your recommendation for Zee's book. Do not ask or answer this type of question in.
Don't waste your time too much here. General political debate is not permitted. Schild, Tensor calculus, University of Toronto Press, Toronto, 1949, pp. In my opinion, totally boring and uninteresting. The flow near a stagnation point, Philos.
Don't mistake the fact that you can read its definition with understanding it. I think it was the standard first course undergrad differential geometry book for many years, I could be wrong. Hayes, The three-dimensional boundary layer, Nav. This includes reference requests - also see our lists of recommended and. You're asking on so you are getting a lot of overly technical recommendations imho.
Fundamental introduction for beginning student of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. All of these sources seem quite different and seem like I require much more advanced topics in mathematics in order to understand. My suggestion would be to look at do carmo's and Kreszyg's books, and pick one which you like better. Kuo, On the flow of an incompressible viscous fluid past a flat plate at moderate Reynolds numbers, J. Even Schutz seems to develop things in a more careful and coherent way, even if it does it more slowly than other texts. The boundary layer equations are not tensor equations but subtensor equations. Thefirst five chapters--comprising tensor algebra, the line element, covariant differentiation, geodesicsand parallelism, and curvature tensor--develop their subjects without undue rigor.