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--- basic_tools:calculus [2017/09/24 11:18]
jakobadmin [Researcher]
+++ basic_tools:calculus [2022/09/07 00:59] (current)
laserblue
@@ Line 1: / Line 1: @@
 ====== 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)}}]
+** 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>
@@ Line 23: / Line 36: @@
 </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
@@ Line 39: / Line 56: @@
 They are neither finite quantities nor quantities infinitely small, nor yet nothing. May
 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  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.
-===== 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>

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