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basic_tools:vector_calculus [2017/04/14 11:44]
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basic_tools:vector_calculus [2022/09/07 01:15] (current)
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 ====== Vector Calculus ====== ====== Vector Calculus ======
  
-===== Why is it interesting?​ ===== 
  
-===== Layman ===== 
  
-===== Student===== 
  
-==== Recommended Readings ====+<tabbox Intuitive> ​
  
 +<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:​**
 + 
 +
 +  * Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach by John H. Hubbard and Barbara Burke Hubbard - Extremely student friendly, lots of margin notes that talk about the "​soft"​ stuff that's so crucial to the actual practice of math. Reading just the margins jumps your mathematical maturity by 2 years.
 +  * 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   * 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
 +
 +**Geometric Calculus:**
 +  *[[https://​geocalc.clas.asu.edu/​| Geometric Calculus R & D]] website
 +
 +**Geometric Calculus videos:**
 +  *[[https://​www.youtube.com/​watch?​v=-JQxOYL3vhY| Geometric Calculus 0]] Alan Macdonald
 +  *[[https://​www.youtube.com/​watch?​v=ItGlUbFBFfc| Tutorial on Geometric Calculus]] David Hestenes
 +
 +<tabbox Abstract> ​
 +
 +<note tip>
 +The motto in this section is: //the higher the level of abstraction,​ the better//.
 +</​note>​
 +
 +  ​
 +<tabbox Why is it interesting?> ​
 +
 +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>​
 +
 +
 +<tabbox History> ​
 +
 +https://​en.m.wikipedia.org/​wiki/​A_History_of_Vector_Analysis
  
-===== Researcher=====+</​tabbox>​
  
-===== Examples ===== 
  
-===== History ===== 
basic_tools/vector_calculus.1492163099.txt.gz · Last modified: 2017/12/04 08:01 (external edit)