“All the little bits”
I bought this book when I was taking calc based physics. I never thought I would laugh so much at a math book! Educational and hilarious!
Can an idiot ask what book that is?
calculus made easy?
lol, in my defence I used to be in print publishing and I didn’t catch that. I did say idiot.
That said, that’s ambiguous design and I’ll be briefly uncomfortable on that hill.
The symbols are the most intimidating part of mathematics for me. They are beautiful and mysterious.
This reading actually helped me understand calculus a bit better, thanks for sharing!
Honestly, me too! You’re welcome :)
Is the from a book by Sylvanus P. Thompson?
The online version can be found at https://calculusmadeeasy.org/
35 years after graduating from engineering school, this book helped me finally understand why calculus works, instead of just learning how to mechanically apply it.
RDRR
but wouldn’t “the sum of all the little bits of x” just be… x? Like what the fuck Calculus?! Speak plainly.
Yes, that’s the whole point of calculus. It’s useful for finding x if you don’t have other easier ways to do so.
Here’s an example of how dividing the area under a curve up into smaller and smaller bits helps to find a value for the area.
I mean, the idea is simple enough to understand. The actual execution is what fucks idiots like me, especially when the exam is full of shit like
integral sin(e ^ (x^2 * cos(e)) * tan(sqrt 5x)That’s been an argument among educators. You can teach the basic concepts of Calculus to a fourth grader. What makes it difficult is rigor, but we don’t necessarily need to teach rigor to fourth graders.
“dMonica in my life”
All the little bits by my side…
“All the, derivatives. True care. Truth brings.”
I have finally discovered my niche content: math texts that are irreverent and also defiantly uncomplicated.
Read “a mathematicians lament”, by Paul Lockhart. It was originally a short essay (25 pages you can find free online), but expanded into a book that I haven’t read yet.
In a similar vein is Shape, by Jordan Ellenberg.
I read a short paper called “Lockheart’s Lament”, but I didn’t realize he had expanded on it. I might have cried about that one. Thanks for the reccomendations!
Thank you for this beautiful example of using “defiantly” correctly!
He defiantly used it properly, definitely.
Math is never irrelevant
Irreverent not irrelevant
What’s this about the ears on an elephant?
A little confused, but they’ve got the spirit.
Minor nitpick: the “d” is an operator, not a variable. So it’s “dx”, not “dx”… But there are so many textbooks that don’t get this right, that I’m aware that I’m charging windmills here.
This is the nicest I’ve seen this info presented.
They didn’t even need to draw a chart of decreasing deltas and partitions, or talk about tangents and secants.
I would’ve absolutely paid more attention in maths if the learning material was this utterly contemptuous of “ordinary mathematicians” haha
also full Project Gutenberg text is here https://calculusmadeeasy.org/, thanks for sharing!
Mille mercis !
I’m a chemical engineer and I now better understand calculus slightly better from this post. I did a whole lot of “okkayyy …let’s just stick to the process and wait for this whole thing to blow over”
I know what they were asking me to do but I never really fully understood everything.
okkayyy…let’s just stick to the process and wait for this whole thing to blow over
This is such a classic engineer brain solution to the problem. It just warms my heart.
When I started algebra in something like 5th grade I had a huge issue with f(x) and the best answer my teacher gave me was that “the equation is a function of x” and couldn’t explain it differently and I couldn’t get over the fact that we are not multiplying whatever f is by X. “If we’re going to set precedent with notation at least be fucking consistent” - 5th grade me probably
I also studied chemical engineering, and throughout high school and university that was exactly it. Calculus was a kind of magic, and you just had to learn all the spells.
With this book I finally understood why the derivative of x^2 is 2x.
I tried to figure it out myself back in high school but the best I came up with is X^2 -->2x because it just fucking does.
Ok I’m no mathematician but I’ll still can’t see why d(x^2) = 2x.
This exact explanation is in the book: https://calculusmadeeasy.org/4.html
Calculus was never an issue for me. I could do double-integral calculus in my head clear into my forties. I’ve just gotten rusty since then, likely with a spot of practice I could pull off that party trick again.
No, the only part of math that ever struck fear into my heart was trigonometry. Sin, cos, tan, that kind of stuff. For some reason I have never been able to grok, on a fundamental level, the basics of trig. I understand things on a high/intellectual level, just not on an instinctual level.
Wait what? It’s all triangles. We just know the ratios because of the way they are. I can arcsin my way through all my problems.
Physics is what made Calc make sense. Trig is what made physics make sense.
All of geometry is a cult. The only kind I like. Math cult. Good people. Great orgies.
I oppose math cults because I’m a member of bean cults. Our orgies are better, it’s the health benefits of beans
It’s all triangles.
Sure. They relate different properties of triangles or periodic phenomena.
But can you explain what a “sine” operation is actually doing? Algebra and calculus can pretty much all be explained in terms of basic operations like addition, subtraction, multiplication, and division. But I’m in the same boat as @[email protected] - trig operations feel like a black box where one number goes in and a different number comes out. I am comfortable using them and understand their patterns, but don’t really get them.
I’ve always just thought of it as derivatives describe the rate of change and integrals the total of whatever it is that has been done.
Like if we’re talking about an x that describes position in terms of t, time, dx/dt is the rate of change of position over change in time, or speed. Then ddx/dt is change in speed over change in time, or acceleration. And dddx/dt is rate of change in acceleration over change in time (iirc this is called jerk). And going the opposite way, integrating jerk gets acceleration, then speed, then back to position. But you lose information about the initial values for each along the way (eg speed doesn’t care that you started 10m away from the origin, so integrating speed will only tell you about the change in position due to speed).
That’s how I thought of it too. I really liked calculus; being able to measure another part of the graph was interesting to me.
Calculus is just piling stones.
