✎ Vector Calculus [The Physics Travel Guide]

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====== Vector Calculus ======

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
</note>
  
<tabbox Concrete> 
  * [[http://www2.eng.cam.ac.uk/~alj3/vc.pdf|A Survival Guide to Vector Calculus]] by Aylmer Johnson

**Recommended Textbooks:**

* http://mathinsight.org/thread/vector_algebra
  * A nice introduction can be found in Section 3 of Vol. 2 of Feynman's Lectures on Physics, which are available [[http://www.feynmanlectures.caltech.edu/II_03.html|here]]
  * A Student's Guide to Vectors and Tensors by Daniel A. Fleisch
  * DIV, Grad, Curl, and All That: An Informal Text on Vector Calculus by H. M Schey
  * [[http://www.physics.miami.edu/~nearing/mathmethods/|Mathematical Tools for Physics]] by James Nearing
<tabbox Abstract>

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

Vector calculus is an important tool, whenever we want to understand systems where directions play a role. A vector is an arrow that points in some direction. Thus, a vector is a tool to denote a direction.

This is needed, for example, to describe in which spatial direction a ball moves or how a fluid flows.

<blockquote>A vector is the mathematical representation of a physical entity that may be
characterized by size (or “magnitude”) and direction. In keeping with this definition, speed (how fast an object is going) is not represented by a vector, but velocity (how fast and in which direction an object is
going) does qualify as a vector quantity. Another example of a vector quantity
is force, which describes how strongly and in what direction something is being
pushed or pulled. But temperature, which has magnitude but no direction, is not
a vector quantity<cite>A Student's Guide to Vectors and Tensors by Daniel A. Fleisch
</cite></blockquote>

https://en.m.wikipedia.org/wiki/A_History_of_Vector_Analysis

</tabbox>

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