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basic_tools:vector_calculus [2017/12/16 14:27]
jakobadmin [Why is it interesting?]
basic_tools:vector_calculus [2022/09/07 01:15] (current)
laserblue
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 ====== Vector Calculus ====== ====== Vector Calculus ======
  
-<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. 
- 
----- 
  
-**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]] 
-  * [[basic_tools:​vector_calculus:​stokes_theorem]] 
  
-<​tabbox ​Layman+<​tabbox ​Intuitive
  
 <note tip> <note tip>
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 </​note>​ </​note>​
   ​   ​
-<​tabbox ​Student+<​tabbox ​Concrete
   * [[http://​www2.eng.cam.ac.uk/​~alj3/​vc.pdf|A Survival Guide to Vector Calculus]] by Aylmer Johnson   * [[http://​www2.eng.cam.ac.uk/​~alj3/​vc.pdf|A Survival Guide to Vector Calculus]] by Aylmer Johnson
  
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-  * 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]]+  * Vector Calculus, Linear Algebra, and Differential Forms: ​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   * 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   * [[http://​www.physics.miami.edu/​~nearing/​mathmethods/​|Mathematical Tools for Physics]] by James Nearing
-<​tabbox ​Researcher+ 
 +**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> <note tip>
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   ​   ​
-<​tabbox ​Examples+<​tabbox ​Why is it interesting?​
  
---> Example1#+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.
-<--+
  
---Example2:#+<​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 FAQ> ​ 
-  ​ 
 <tabbox History> ​ <tabbox History> ​
  
basic_tools/vector_calculus.1513430837.txt.gz · Last modified: 2017/12/16 13:27 (external edit)