Tensor analysis?

[Freeman]

Does anyone know a good book for lay people on tensor calculus? I have tried reading a grad book on it and it was focused primarily on the algebra of tensors...rather disappointing really.

 

Or, on the other hand, does anyone know tensor analysis? I have tried googling it several times.

[DQW]

Does anyone know a good book for lay people on tensor calculus?

Does a "lay person" know the math of vector spaces, matrices, and (scalar and vector) calculus ?

[MetaFrizzics]

The perfect book for someone with a high-school education is

About Vectors by Hoffmann (Dover reprint <$10)

 

This little gem takes a reader with no real grasp of vectors at all, right to tensors (last chapter). The book is in a class by itself, superior to

Div, Grad, Curl, and All That by Schey.

 

Either of these books is almost a prerequisite to squeaking through 1st or 2nd year Engineering, but About Vectors really lays all the key (and controversial) topics before the student in a lively and friendly way with thorough but not too wordy discussions that are easy to understand.

 

pm me if you want help with getting up to speed. Vectors are critically important for virtually all of Mechanics and Electrical Engineering (Electronics).

 

By the way, Vectors were almost singlehandedly invented by Heaviside, who took Maxwell's messy and impenetrable Electromagnetic Theory based upon quaternions, and reduced Maxwell's original 12 - 20 equations to an efficient four! (The ones everyone thinks are Maxwell's!) In the process, Heaviside virtually invented the whole field of Electrical Engineering, as well as Vectors, by deconstructing quaternions into bite-size and practical pieces, and inventing nine out of ten electrical terms, like resistivity, permeability etc.

 

If you want to understand things, ignore Maxwell and grab Heaviside.

[Freeman]

Does a "lay person" know the math of vector spaces, matrices, and (scalar and vector) calculus ?

All of it but vector calculus.

[DQW]

I would recommend Vector Analysis, by Murray Spiegel.

 

It deals extensively with vector calculus and finishes up with tensor analysis.

[MetaFrizzics]

All of it but vector calculus.

In that case, Div, Grad, Curl, and All That by Schey might be the better book. It is a small and informal but speedy and complete text on vector calculus meant to supply the missing course for those in the sciences. Typically other textbooks or coursebooks only cover a brief set of basics, leaving the student to find out details on his own via secondary texts on mathematical methods for engineers.