We'll differentiate a rational expression using only (ugh!) the quotient rule. Then we'll do it again, first breaking the expression into partial fractions. Which route will be easier? Ref: Calculus Made Easy, Chapter XIII. (Free download: https://bit.ly/EasyCalculus ... https://www.youtube.com/watch?v=UWxIVw3G-_g
Impress your friends at parties with this quick proof of the irrationality of the square root of 2.
Life of Riley by Kevin MacLeod
Link: https://incompetech.filmmusic.io/song/3976-life-of-riley
License: https://filmmusic.io/standard-license
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https://www.youtube.com/watch?v=DsivAG_8v48
The first episode in our systematic study of Calculus, from Silvanus Thompson's classic text, Calculus Made Easy (bit.ly/EasyCalculus). We'll look at the take-things-apart symbol for differentiation, and the put-things-back-together symbol of integration.
Grab your free copy here: bit.ly/EasyCalculus
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https://www.youtube.com/watch?v=eTxQrwz2QvA
#Bitcoin #statistics #cryptocurrency
Guess what correlates with the price of Bitcoin? Suspicious use of statistics.
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https://www.youtube.com/watch?v=-_Cs-qt5Pl8
How can you find the area under a logarithm curve without using integration by parts? What is the easiest function in all of calculus? We'll use THAT.
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https://www.youtube.com/watch?v=buL3NFaheoU
Here's a quick derivation of the limit definition for the logarithm.
A previous video, https://youtu.be/bPmooEEXU_8 , relied on this definition.
You can read about this derivation here:
https://medium.com/mathadam/fall-in-love-with-e-all-over-again-2ddc5d03d4cc?sk=8f7111156005f8db169a628a91f8d7c0
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https://www.youtube.com/watch?v=g-buVItHro4
If p is a prime greater than 3, show that p² is congruent to 1 (MOD 24). This problem comes from U of T: https://www.math.toronto.edu/~herzig/putnam_nt_oct07.pdf
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https://www.youtube.com/watch?v=N-uelCUaNmk
Join Adam on this livestream as he demonstrates a much less convoluted piece of mathematics than he tried on the last livestream. TODAY is a good day to INTEGRATE... specifically, the inverse sine function between 0 and 1.
Notes on miro.com: https://miro.com/app/board/o9J_lEVnBGM=/
Desmos stuff: https://www.desmos.com/calculator/ttionwtppv
Visualizing IBP: https://srabbani.com/integration_parts.pdf
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https://www.youtube.com/watch?v=iYL43A7kX5o
Here we sneak up on the function 1/x to integrate it using the reverse power rule. Yes. It can be done.
My article showing the derivation of the log limit: https://medium.com/mathadam/fall-in-love-with-e-all-over-again-2ddc5d03d4cc?sk=8f7111156005f8db169a628a91f8d7c0
Life of Riley by Kevin MacLeod
Link: https://incompetech.filmmusic.io/song/3976-life-of-riley
License: https://filmmusic.io/standard-license
...
https://www.youtube.com/watch?v=bPmooEEXU_8