My oldest is retaking calc, struggling with understanding derivatives. He wants to really get how they work, not just push symbols. He has a low tolerance for frustration; I try to explain and he throws his hands in the air. It was the same when he took it in high school. So I’ll be spending my flight to LA digging into my old calc book to see if I can improve my explanations.
That said, anyone here know of a good source to explain this stuff in a technical but digestible way?
[2501.04219] Framing the Fundamental Theorem of Calculus Through Physics-Based Quantities #ITeachPhysics #ITeachMath #Calculus #Physics
Bob Miller's Calc for the Clueless: Calc I & II, 1997
The first calc study guides that really give students a clue. Bob Miller's student-friendly Calc for the Clueless features quickly-absorbed, fun-to-use information and help. Students will snap up Calc for the Clueless as they discover: Bob Miller's painless and proven techniques to learning Calculus Bob Miller's way of anticipating problems.
How much total drag does my truck create while moving down the highway?
Measure it indirectly!
Run cellphone GPS logger at 1-second interval. Get truck up to speed on flat section of highway, put transmission in neutral, foot off the gas. Let the truck slow down 30 - 45 seconds to get a decent number of data points. Make another data run on same section, but opposite direction to average out effects of wind and any slope.
Import GPS log into spreadsheet.
A linear fit gives you a straight line slope...good enough to determine deceleration...then apply that to F = m * a (you need to know truck's weight) Now you know total drag force at one speed.
Total drag is air resistance (varies with square of speed) plus rolling friction (assume it's constant). OK, do a quadratic/polynomial fit. Now you know rolling friction. Subtract from total drag, and you can determine area-drag (Cd * frontal area) of your truck.
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Deriving the Reactance Formulas - If you’ve dealt with reactance, you surely know the two equations for computing in... - https://hackaday.com/2025/04/28/deriving-the-reactance-formulas/ #radianfrequency #mischacks #reactance #calculus #math
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!
Today I accidentally learned that limacons are inversions of conic sections!
"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.
This makes sense, right? (Trying to better understand arclength in polar.)
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
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!)
There is a point on every #calculus that all other stones may stack upon.
That is #balance.
That is #negotiation.
That is #compromise.
"In #Latin, "calculus" means "small pebble" or "pebble," which is where the mathematical term gets its name from as ancient Romans used pebbles for counting on an #abacus."
#math
#nature
#history
**The Jagged, Monstrous Function That Broke Calculus**
Solomon Adams
_“Weierstrass discovered a function that, according to Ampère’s proof, should have been impossible: It was continuous everywhere yet differentiable nowhere.”_
https://www.quantamagazine.org/the-jagged-monstrous-function-that-broke-calculus-20250123/.
every vector has a basis is implied by
#calculus
Wrapped up the last day of the semester in #Calculus with a topic that never fails to blow my mind: Fourier Series!
university. Her accomplishments were tremendous in her short but astonishing life.⠀
Born Sofia Korvin-Krukovskaya, in Moscow, she attributed her early aptitude for #calculus to a shortage of wallpaper, which lead her father to have the nursery papered with his old differential and integral analysis notes. Her parents nurtured her early interest in #math, and hired her a tutor. The local priest’s son introduced her to #nihilism. So both her bent for revolutionary politics and passion for math 
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