advanced_tools:differential_forms
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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 ====== | ||
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| - | <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> | ||
| Line 24: | Line 8: | ||
| </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> | ||
| Line 35: | Line 23: | ||
| </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)
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