6 ms·

I am the fool who is mortally afraid of calculus. I am not kidding when I say that I still get nightmares of sitting in a Calculus exam. I am 37 years old The

I am the fool who is mortally afraid of calculus. I am not kidding when I say that I still get nightmares of sitting in a Calculus exam. I am 37 years old The first chapter turned on a light bulb in my head when it said d which merely means “a little bit of.” ∫ which is merely a long S, and may be called (if you like) “the sum of.” I am gonna bookmark it and read it to the end so that when my son grows up, I can teach him.

yann2 5y ago
Infinite Powers by Steven Strogatz would be a much better option.
loftyal 5y ago
I would recommend watching 3Blue1Bown series on calculus. Its very easy to understand and somes with some great visuals. https://www.youtube.com/watch?v=WUvTyaaNkzM https://www.youtube.com/watch?v=WUvTyaaNkzM
Chris2048 5y ago
from my perspective, integrals are continuous forms of summations. so Σ(6;n=1) f(n) becomes ∫(6;x=1) f(x) or ∫(6;1) f(x) dx The dx term always confused me, especially when it started being used in unfamiliar ways e.g g = (dt+1)/dx - but if you think of it as the step variable/component of a summation term I think it helps.
- globular-toast 5y ago
  One of the confusing things with integration is the difference between definite and indefinite integrals. What you're describing is a definite integral which is indeed a continuous sum. Indefinite integrals are maybe better called antiderivatives and it's less clear what it's all about. Most people just remember a set of rules for calculating derivatives and antiderivates (like integration by parts, the chain rule etc.). I find this really throws people off as it's like two separate concepts both, confusingly, called integration.
  - jamesmaniscalco 5y ago
    They're not totally separate concepts though, no? The definite integral is the difference of two values of the indefinite integral (antiderivative). I suppose if you're talking about solving them computationally, you can calculate/approximate the definite integral by taking the limit of the sum as you reduce the step size, whereas performing the indefinite integral requires a different method (chain rule etc.). But when doing them by hand usually the first step in calculating a definite integral is finding the antiderivative.
    - globular-toast 5y ago
      That's the thing. What tends to stick in people's heads is the bit that hurts. You can tell someone that integration is "just a continuous sum" and you might see a ligthbulb go on. But then the bad news: you still need to find this magical function F(x) and to do that requires intuition and guesswork. Understanding it's "just a sum" doesn't help at all with finding the antiderivative.
      - Chris2048 5y ago
        > Understanding it's "just a sum" doesn't help at all with finding the antiderivative No, but you can still integrate computationally (difference method).
  - Chris2048 5y ago
    if definite integrals can be represented as a sum of a finite series, I can't see why an Indefinite integral isn't the sum of an infinite series. You can just take any definite integral and replace it's interval with variables. Now it's just algebraic, much like if you replaced numbers in an equation with variables. > Indefinite integrals are maybe better called antiderivatives but why? I can't see why definite integrals aren't equally better called antiderivatives over an interval. Concepts wrt calculus, and method of solving them are separate things to me - you can understand how gravity works in general, without the specific means of solving orbital equations.
agentwiggles 5y ago
It's so funny how much of an impression bad experiences in school make on you. I occasionally have dreams where it's finals week and I realize that I haven't attended any sessions or completed any of the homework for some class. (Sadly all too realistic, I really struggled to have my shit together in college.) I've often thought that if I ever became wealthy enough to not have to work, I'd like to go back to school and do a better job of it. Looking back, I kick myself for wasting so much of a period of time where I could have been filling my brain with useful knowledge. Oh well, though - I got enough education to land my first programming job, so it wasn't a total waste. And a lot of fun was had along the way. Hindsight can be a bit illusory.
PebblesRox 5y ago
I read/summarized chapter one to my 4yo today and we had a nice conversation: Me: If x = the beach then dx = a piece of sand on the beach and ∫dx = all the little pieces of sand 4yo: ...and all of the parts of the ocean because that's the whole beach I'm also excited to do more with him as he gets older :)

yann2 5y ago

Infinite Powers by Steven Strogatz would be a much better option.

loftyal 5y ago

I would recommend watching 3Blue1Bown series on calculus. Its very easy to understand and somes with some great visuals. https://www.youtube.com/watch?v=WUvTyaaNkzM https://www.youtube.com/watch?v=WUvTyaaNkzM

Chris2048 5y ago

from my perspective, integrals are continuous forms of summations. so Σ(6;n=1) f(n) becomes ∫(6;x=1) f(x) or ∫(6;1) f(x) dx The dx term always confused me, especially when it started being used in unfamiliar ways e.g g = (dt+1)/dx - but if you think of it as the step variable/component of a summation term I think it helps.

globular-toast 5y ago
One of the confusing things with integration is the difference between definite and indefinite integrals. What you're describing is a definite integral which is indeed a continuous sum. Indefinite integrals are maybe better called antiderivatives and it's less clear what it's all about. Most people just remember a set of rules for calculating derivatives and antiderivates (like integration by parts, the chain rule etc.). I find this really throws people off as it's like two separate concepts both, confusingly, called integration.
- jamesmaniscalco 5y ago
  They're not totally separate concepts though, no? The definite integral is the difference of two values of the indefinite integral (antiderivative). I suppose if you're talking about solving them computationally, you can calculate/approximate the definite integral by taking the limit of the sum as you reduce the step size, whereas performing the indefinite integral requires a different method (chain rule etc.). But when doing them by hand usually the first step in calculating a definite integral is finding the antiderivative.
  - globular-toast 5y ago
    That's the thing. What tends to stick in people's heads is the bit that hurts. You can tell someone that integration is "just a continuous sum" and you might see a ligthbulb go on. But then the bad news: you still need to find this magical function F(x) and to do that requires intuition and guesswork. Understanding it's "just a sum" doesn't help at all with finding the antiderivative.
    - Chris2048 5y ago
      > Understanding it's "just a sum" doesn't help at all with finding the antiderivative No, but you can still integrate computationally (difference method).
- Chris2048 5y ago
  if definite integrals can be represented as a sum of a finite series, I can't see why an Indefinite integral isn't the sum of an infinite series. You can just take any definite integral and replace it's interval with variables. Now it's just algebraic, much like if you replaced numbers in an equation with variables. > Indefinite integrals are maybe better called antiderivatives but why? I can't see why definite integrals aren't equally better called antiderivatives over an interval. Concepts wrt calculus, and method of solving them are separate things to me - you can understand how gravity works in general, without the specific means of solving orbital equations.

agentwiggles 5y ago

It's so funny how much of an impression bad experiences in school make on you. I occasionally have dreams where it's finals week and I realize that I haven't attended any sessions or completed any of the homework for some class. (Sadly all too realistic, I really struggled to have my shit together in college.) I've often thought that if I ever became wealthy enough to not have to work, I'd like to go back to school and do a better job of it. Looking back, I kick myself for wasting so much of a period of time where I could have been filling my brain with useful knowledge. Oh well, though - I got enough education to land my first programming job, so it wasn't a total waste. And a lot of fun was had along the way. Hindsight can be a bit illusory.

PebblesRox 5y ago

I read/summarized chapter one to my 4yo today and we had a nice conversation: Me: If x = the beach then dx = a piece of sand on the beach and ∫dx = all the little pieces of sand 4yo: ...and all of the parts of the ocean because that's the whole beach I'm also excited to do more with him as he gets older :)