✎ Vector Calculus [The Physics Travel Guide]

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

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.

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**Important Vector Calculus Concepts:**

* [[basic_tools:vector_calculus:curl]]
  * [[basic_tools:vector_calculus:gradient]]
  * [[basic_tools:vector_calculus:flux]]
  * [[basic_tools:vector_calculus:divergence]]
  * [[basic_tools:vector_calculus:dot_product]]
  * [[basic_tools:vector_calculus:cross_product]]
  * [[basic_tools:vector_calculus:gauss_theorem]]

<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 Student> 
  * [[http://www2.eng.cam.ac.uk/~alj3/vc.pdf|A Survival Guide to Vector Calculus]] by Aylmer Johnson

**Recommended Textbooks:**

* A perfect 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 Researcher>

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

--> Example1#

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--> Example2:#

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

</tabbox>

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