Help understanding the basic, core rule of calculus.

[mbear]

I bombed out of Calculus in college for a variety of reasons, but I've recently started a project that requires it. I've found a bunch of resources at Hackaday.com of all places that talk about calculus, but I'm one of those people who really doesn't understand something until I understand the 50,000 foot view.

I also do some Python and JavaScript programming at my day job, which is what led me to the following statement:

A calculus problem (integral or derivative) can be represented in programming as a recursive function Wikipedia link.

Thanks!

Edit: I should also point out that I've downloaded and printed Calculus Made Easy by Silvanus P. Thompson from Project Gutenberg.

[dgorsman]

It's old, but I still find it useful.  There's a series on introductory university math and physics called "The Mechanical Universe".  It demonstrates equation solving and principles through primitive (for today) CGI.

Edit: episodes 3 and 7, which should be on Youtube.

[Daryk]

The key insights for me when I was learning calculus were that derivatives give you the slope of the function, while integrals are the area underneath it.  That may simply be a comment on how my brain works, but I hope they help.

[skiltao]

mbear, do you still need the 50,000 foot view?

A calculus problem (integral or derivative) can be represented in programming as a recursive function Wikipedia link.

There's a few things this could mean. It could be referring to how you break an equation into chunks, or one of the various ways to do a "close enough" approximation without solving an equation exactly, or something to do with how certain curves can be converted into Riemann sums... out of context, it's hard to tell what exactly the statement was going for.

Edit: I should also point out that I've downloaded and printed Calculus Made Easy by Silvanus P. Thompson from Project Gutenberg.

Hahahahaha just opened the pdf and saw the title page. Love the full title and the prologue.

[Bedwyr]

It could be referring to how you break an equation into chunks, or one of the various ways to do a "close enough" approximation without solving an equation exactly, or something to do with how certain curves can be converted into Riemann sums... out of context, it's hard to tell what exactly the statement was going for.

Integrals: "Take a bunch of little tiny slices and add them up."
Derivatives: "Cut the distance between the two points of the line slope again, again, gain, till it's infinitesimally small."
And the relationship between the two: I still support moving between a position function, velocity, and acceleration showing how tangent slopes and area under the curve work on each.

[skiltao]

Yeah, if I were to describe the basic function of calculus, I'd start with an image of a "close enough" approximation too.

[mbear]

OK. I think I've got it. Thanks everyone.

Hahahahaha just opened the pdf and saw the title page. Love the full title and the prologue.

Yeah, that was one of the things that attracted me to it. Someone who was saying "This really isn't as difficult as you've been made to think it is" without the word "dummy" or "idiot" in the title. (Not that I haven't done idiotic or dumb things in the past, but still.)

[ANS Kamas P81]

Hahahahaha just opened the pdf and saw the title page. Love the full title and the prologue.

"Ancient Simian Proverb."  That one killed me.