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basic_tools:calculus [2017/09/24 11:20] jakobadmin [Researcher] |
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====== Calculus ====== | ====== Calculus ====== | ||
- | ===== Layman ===== | + | <tabbox Intuitive> |
- | ===== Why is it interesting? ===== | + | <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> | ||
- | ===== Student===== | ||
[{{ :calculus_made_easy.jpg?nolink |Source: "[[http://djm.cc/library/Calculus_Made_Easy_Thompson.pdf|Calculus Made Easy]]" (1910)}}] | [{{ :calculus_made_easy.jpg?nolink |Source: "[[http://djm.cc/library/Calculus_Made_Easy_Thompson.pdf|Calculus Made Easy]]" (1910)}}] | ||
+ | ** Recommended Short Reads** | ||
- | ==== Recommended Books ==== | + | * [[https://betterexplained.com/articles/a-gentle-introduction-to-learning-calculus/|A Gentle Introduction To Learning Calculus]] by Kalid Azad |
+ | * [[https://betterexplained.com/calculus/|A Better Explained Guide To Calculus]] | ||
+ | |||
+ | **Recommended Books:** | ||
+ | |||
+ | * [[https://www.gutenberg.org/ebooks/33283|Silvanus P. Thompson, Calculus Made Easy]] | ||
+ | * [[https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/|Gilbert Strang, Calculus]] | ||
+ | * See also: https://www.physicsforums.com/insights/self-study-calculus/ | ||
+ | * [[http://www.physics.miami.edu/~nearing/mathmethods/|Mathematical Tools for Physics]] by James Nearing | ||
+ | * http://mathinsight.org/thread/multivar | ||
<blockquote> | <blockquote> | ||
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</blockquote> | </blockquote> | ||
- | ===== Examples ===== | ||
- | ===== Researcher===== | + | A nice video introduction is |
+ | * [[https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr|Essence of calculus]] by 3Blue1Brown | ||
+ | | ||
+ | * [[https://www.youtube.com/watch?v=-JQxOYL3vhY| Geometric Calculus 0]] by Alan Macdonald | ||
+ | |||
+ | <tabbox Abstract> | ||
<blockquote>A more appropriate analogy would be that of calculus in | <blockquote>A more appropriate analogy would be that of calculus in | ||
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we not call them the ghosts of departed quantities? | we not call them the ghosts of departed quantities? | ||
It was due to criticism like this that finally led to rigorous formulation of calculus in terms of $\epsilon$ and δ now | It was due to criticism like this that finally led to rigorous formulation of calculus in terms of $\epsilon$ and δ now | ||
- | dreaded by beginning mathematics students [7] <cite>Note: Where is the Commutation Relation Hiding in the Path Integral Formulation? byYen Chin Ong</cite></blockquote> | + | dreaded by beginning mathematics students [7] <cite>[[http://www.docslides.com/faustina-dinatale/note-where-is-the-commutation|Note: Where is the Commutation Relation Hiding in the Path Integral Formulation? byYen Chin Ong]]</cite></blockquote> |
and ref 7 is: J. V. Grabiber, [[http://www.mr-ideahamster.com/classes/assets/a_evepsilon.pdf|Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus]], the American Mathematical Monthly, March 1983, Vol.90, No.3, 185-194. | and ref 7 is: J. V. Grabiber, [[http://www.mr-ideahamster.com/classes/assets/a_evepsilon.pdf|Who Gave You the Epsilon? Cauchy and the Origins of Rigorous Calculus]], the American Mathematical Monthly, March 1983, Vol.90, No.3, 185-194. | ||
- | ===== History ===== | + | |
+ | See also https://www.physicsforums.com/insights/the-pantheon-of-derivatives-i/ and "The Cauchy-Schwarz Master Class" | ||
+ | |||
+ | |||
+ | <tabbox Why is it interesting?> | ||
+ | |||
+ | <blockquote>We usually take shapes and formulas at face value, as a single pattern. Calculus gives us two superpowers to dig deeper: | ||
+ | |||
+ | X-Ray Vision: You see the hidden pieces inside a pattern. You don't just see the tree, you know it's made of rings, with another growing as we speak. | ||
+ | |||
+ | Time-Lapse Vision: You see the future path of an object laid out before you (cool, right?). "Hey, there's the moon. In the next few days it'll be rising and changing to a nice red color. I'll wait 6 days and take the perfect photo then." | ||
+ | |||
+ | So why is Calculus useful? Well, just imagine having X-Ray or Time-Lapse vision to use at will. That object over there, how was it put together? What will happen to it? | ||
+ | |||
+ | <cite>[[https://betterexplained.com/calculus/|A Better Explained Guide To Calculus]]</cite> | ||
+ | </blockquote> | ||
+ | |||
+ | </tabbox> | ||
+ |