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advanced_tools:differential_forms [2017/07/15 16:30]
jakobadmin [Student]
advanced_tools:differential_forms [2023/01/27 15:41] (current)
yys [+ book VDGF]
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 ====== Differential Forms ====== ====== Differential Forms ======
- 
-<tabbox Why is it interesting?> ​ 
-<​blockquote>​ 
-P-forms are important, because they are exactly the objects that we need if we want to talk about areas and volumes (and higher dimensional analogues). 
- 
-<​cite>​http://​jakobschwichtenberg.com/​vectors-forms-p-vectors-p-forms-and-tensors/</​cite>​ 
-</​blockquote>​ 
- 
-<​blockquote>​ 
-‘Hamiltonian mechanics 
-cannot be understood without differential forms’ 
- 
-<​cite>​Mathematical methods of classical mechanics by Wladimir Igorewitsch Arnold, p. 163</​cite>​ 
-</​blockquote>​ 
- 
- 
  
  
-<​tabbox ​Layman?+<​tabbox ​Intuitive
  
 <note tip> <note tip>
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 </​note>​ </​note>​
   ​   ​
-<​tabbox ​Student+<​tabbox ​Concrete
  
-http://​jakobschwichtenberg.com/​vectors-forms-p-vectors-p-forms-and-tensors/​+Differential ​forms (co-vectors) are functions (elements of dual vector-space) which map vectors ​to real numbers.
  
-One of the best introductions can be found in “Geometrical methods of mathematical physics” by Bernard F. Schutz+  * For the basic idea, see http://​jakobschwichtenberg.com/​vectors-forms-p-vectors-p-forms-and-tensors/​ 
 +  * One of the best introductions can be found in “Geometrical methods of mathematical physics” by Bernard F. Schutz 
 +  * [[https://​web.archive.org/​web/​20180127144926/​http://​www.math.cornell.edu/​~sjamaar/​manifolds/​|Manifolds and Differential Forms]] lecture notes by Reyer Sjamaar 
 +  * 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. 
 +  * Another good introduction can be found in “Visual Differential Geometry and Forms: A Mathematical Drama in Five Acts”(2021) by Tristan Needham ​
 <tabbox Researcher> ​ <tabbox Researcher> ​
  
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 </​note>​ </​note>​
  
---Common Question 1#+<tabbox Why is it interesting?​
  
-  +<WRAP group> 
-<--+<WRAP half column>​ 
 +<WRAP quoteshadow>​ 
 +P-forms are important, because they are exactly the objects that we need if we want to talk about areas and volumes (and higher dimensional analogues).
  
---> ​Common Question 2#+<​cite>​http://​jakobschwichtenberg.com/​vectors-forms-p-vectors-p-forms-and-tensors/</​cite>​ 
 +</WRAP>
  
-  +</WRAP>
-<-- +
-   +
-<tabbox Examples+
  
---Example1#+<WRAP half column> 
 +<WRAP quoteshadow>​ 
 +‘Hamiltonian mechanics cannot be understood without differential forms’.
  
-  +<​cite>​Mathematical methods of classical mechanics by Wladimir Igorewitsch Arnold, p. 163</​cite>​ 
-<--+</WRAP>
  
---Example2:#​ +</WRAP
- +</WRAP>
-  +
-<-- +
-  ​ +
-<tabbox History+
  
 </​tabbox>​ </​tabbox>​
  
  
advanced_tools/differential_forms.1500129010.txt.gz · Last modified: 2017/12/04 08:01 (external edit)