Vector Calculus: Dots, Crosses & Triple Products Explained

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Discussion Overview

The discussion revolves around recommendations for books covering vector calculus topics, specifically focusing on dot products, cross products, triple products, and related concepts such as gradient and divergence. The scope includes theoretical and applied aspects of vector calculus.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests book recommendations for topics including vectors, gradients, and their applications.
  • Another participant suggests a specific online resource and recommends using linear algebra for vectors and multivariable calculus for gradients.
  • A participant mentions "div, grad, curl, and all that," which is interpreted as a book title, leading to confusion among others.
  • Some participants express frustration over the clarity and relevance of replies, questioning the appropriateness of certain responses.
  • Several participants list various calculus textbooks that cover the requested topics, including titles like Stewart, Edwards-Penney, and Feynman, emphasizing their relevance to both mathematics and physics.
  • One participant notes that many calculus books contain theorems related to vector calculus, suggesting that the fundamental theorem of calculus is particularly significant.

Areas of Agreement / Disagreement

Participants generally agree on the need for book recommendations, but there is disagreement regarding the relevance and quality of certain replies. Some responses are viewed as unhelpful or commercial in nature, while others defend their relevance to the original request.

Contextual Notes

Some responses may lack clarity or context, leading to misunderstandings about the nature of the replies. The discussion does not resolve the appropriateness of certain recommendations or the perceived quality of the responses.

Who May Find This Useful

Readers interested in vector calculus, particularly students seeking textbooks for study or reference, may find this discussion useful.

pona24
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Can anybody please suggest me a good book which covers following topics in detail

Vectors - Dots, Cross and triple products, Gradient, divergence and applications.

thnx in advance
 
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"div, grad, curl, and all that"
 
thrill3rnit3 said:
"div, grad, curl, and all that"

What kind of reply is that?
 
AC130Nav said:
What kind of reply is that?

Lol, it's a book title... google it :smile:
 
I don't really see your problem with the reply. The OP was asking for books, the reply gave a book...
 
Essentially all several variable calculus books cover these topics: Stewart, Edwards-Penney, Hass Weir Thomas, either at the end or in volume 2. Stronger treatments are in apostol vol.2, Courant vol.2, Fleming, or even spivak's calculus on manifolds, or the derivative evrsion in guillemin and pollack. Indeed almost every differential geometry book on ym shelf covers this material. I found 10-15 books on my shelf with this theorem in it. this must be the most important theorem in mathematics. Of course that is no surpriz=se since it is the general fundamental theorem of calculus. (Stokes thm).

So if you own almost any calculus book, look in it for this stuff.

Physics books are also good for telling you what the theorem means physically. E.g. after learming the vector algebra try Feynman vol 2.
 
  • #10
thnk u all
 

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