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Teresita
Seen in a tutoring job ad:
"I have a final exam in AP calculus BS"
BS??? I see how much you *love* calculus.
(Probably meant BC.)
Some people use math just like they use people, to lie, cheat or steal. But math itself never lies, or cheats, or steals from me, thats why I love math.
My graph of the day. Inspired by the fact that
\[ \sum_{k=1}^{\infty}{\sin k} \]
is bounded but diverges, I've been exploring other similar sums. Here's the start of
\[ \sum_{k=1}^{\infty}{\tan k} \]
It's not shocking that it looks like \(y = \ln(\|\cos x\| ) \), but I definitely wonder if at some point it blows up down the line!
The first and most complete unification of classical integration techniques ever! Say hello to USM.
Draft article: https://drive.google.com/file/d/12DayP6cD1VwDIZCL-nMlcaNH2XUwHfAy/view?usp=drivesdk
Today I accidentally learned that limacons are inversions of conic sections!
It's really fucking aggravating when you try to compute an integral, get to a solution, and then when you look at the instructor's solution, you find him using a formula that WAS NEVER INTRODUCED BEFORE JUST NOW!
"I'm not sure if that's a line or if it's two rays", asked a student, validating the instructional design of my introduction to polar coordinates activity.
The Missing Introduction to Calculus for AI https://medium.com/effortless-programming/the-missing-introduction-to-calculus-for-ai-3d5e8df6efa3 #AI #calculus #NeuralNetworks
This makes sense, right? (Trying to better understand arclength in polar.)
Toying with an idea to do differentiation in #Python EG something like dif ** 2 might return lambda x: x*2, dif.log == lambda x: 1/x
&c.
EG
S = 123**2
de = dif **2
x = 100
for tran in range(100):
x -= (S-(x**2))/de(x)
Imaginary numbers aren't just mathematical curiosities. They simplify #trigonometry, #calculus, and #geometry, opening up new possibilities in #math and #science. A mathematician explains: https://theconversation.com/taking-a-leap-of-faith-into-imaginary-numbers-opens-new-doors-in-the-real-world-through-complex-analysis-233965
The USM 𝐢𝐧𝐜𝐨𝐫𝐩𝐨𝐫𝐚𝐭𝐞𝐬, 𝐞𝐱𝐭𝐞𝐧𝐝𝐬, 𝐣𝐮𝐬𝐭𝐢𝐟𝐢𝐞𝐬, and 𝐬𝐮𝐫𝐩𝐚𝐬𝐬𝐞𝐬 Euler's substitutions. In Euler's substitutions, the choice of signs based on the domain must be made manually, whereas in the USM, the supporting theorems prescribe which sign to use according to the domain. Moreover, the USM shows that Weierstrass substitutions and the use of complex exponentials for integration are merely two sides of the same coin. The USM not only 𝐮𝐧𝐢𝐟𝐢𝐞𝐬 these two techniques into one, but also 𝐠𝐞𝐧𝐞𝐫𝐚𝐥𝐢𝐳𝐞𝐬 them.
USM: https://geometriadominicana.blogspot.com/2024/03/integration-using-some-euler-like.html
A few weeks back I was complaining about this meme and we had a good discussion about it on here. I ended up making a lesson plan about taxes and my students really liked it so I will share it. (It is for students with a basic understanding of integration. But, you could probably rework it to skip that bit.)
https://drive.google.com/file/d/14xaQ1hMpqy0A68MAbxN49zK4HxK8m2R6/view?usp=sharing
(And if you have feedback let me know!)
As somebody who suffered the torture of the maths part of an Electronics Engineering degree, I can honestly say this is the only time a Laplace Transform has made me smile.
Bringing Vector Calculus to Life – With Your Support! 
https://www.patreon.com/posts/bringing-vector-115648637?utm_medium=clipboard_copy&utm_source=copyLink&utm_campaign=postshare_creator&utm_content=join_link
Bringing Vector Calculus to Life – With Your Support!
https://www.patreon.com/posts/bringing-vector-115648637?utm_medium=clipboard_copy&utm_source=copyLink&utm_campaign=postshare_creator&utm_content=join_link
The notation df/dx for the derivative was introduced by Leibniz in 1675. After 95 years, the notation f'(x) for the first derivative was used by Joseph Lagrange.
Vector fields in #geogebra, #desmos and #math3d
Coming soon!
https://www.patreon.com/jcponce
∞Tthanks for your support! #mathematics #visualization #vector #calculus
