advanced_tools:differential_forms
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advanced_tools:differential_forms [2017/12/12 05:42] jakobadmin [Why is it interesting?] |
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 Intuitive> | ||
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| + | <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> | ||
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| + | <tabbox Concrete> | ||
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| + | Differential forms (co-vectors) are functions (elements of dual vector-space) which map vectors to real numbers. | ||
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| + | * 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> | ||
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| + | <note tip> | ||
| + | The motto in this section is: //the higher the level of abstraction, the better//. | ||
| + | </note> | ||
| <tabbox Why is it interesting?> | <tabbox Why is it interesting?> | ||
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| </WRAP> | </WRAP> | ||
| </WRAP> | </WRAP> | ||
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| - | <tabbox Layman?> | ||
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| - | <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> | ||
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| - | <tabbox Student> | ||
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| - | * 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 | ||
| - | * [[http://www.math.cornell.edu/~sjamaar/manifolds/|Manifolds and Differential Forms]] lecture notes by Reyer Sjamaar | ||
| - | <tabbox Researcher> | ||
| - | |||
| - | <note tip> | ||
| - | The motto in this section is: //the higher the level of abstraction, the better//. | ||
| - | </note> | ||
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| - | --> Common Question 1# | ||
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| - | <-- | ||
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| - | --> Common Question 2# | ||
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| - | <-- | ||
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| - | <tabbox Examples> | ||
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| - | --> Example1# | ||
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| - | <-- | ||
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| - | --> Example2:# | ||
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| - | <-- | ||
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| - | <tabbox History> | ||
| </tabbox> | </tabbox> | ||
advanced_tools/differential_forms.1513053732.txt.gz · Last modified: 2017/12/12 04:42 (external edit)
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