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Wtf is calculus?

Anonymous Sun 20 Oct 03:23:17 2019 No.11075452 View Reply Original Report

Quoted By: >>11075461 >>11075462 >>11075482 >>11076916 >>11076936 >>11076942 >>11076946 >>11077047 >>11077276

Hey there, I'm currently 1st year math major, and actually going fine with >80 on midterms and overall good grades.
But the problem is I don't know what Calculus essentially is. I can solve anything that I should, but I'm afraid that it will backfire on the long term. I had Calc in high school, and I didn't know it even back then. What do I do, folks? Should I kill myself or transfer to CS?

Anonymous

Anonymous Sun 20 Oct 2019 03:26:52 No.11075461 Report

Quoted By:

>>11075452
if you don't want to live in a box under the bridge you should transfer to CS.

Anonymous

Anonymous Sun 20 Oct 2019 03:27:10 No.11075462 Report

Quoted By: >>11075483

>>11075452
Calculus is the most intuitive of all higher mathematics. If you're having trouble here you're screwed

Tuba Jam

Tuba Jam Sun 20 Oct 2019 03:40:38 No.11075482 Report

Quoted By: >>11075486

>>11075452
What exactly are you having trouble with? You say you can solve anything you need, which implies that you know it, yet you also say that in high school you "didn't know it even back then", which implies you don't know it now.

Anonymous

Anonymous Sun 20 Oct 2019 03:40:42 No.11075483 Report

Quoted By: >>11075500

>>11075462
Fuck :c Am I really?
Maybe there are online courses that will explain what it is really about?
Khan Academy and other bullshit only explains how to solve problems, with which I have no struggle

Anonymous

Anonymous Sun 20 Oct 2019 03:42:17 No.11075486 Report

Quoted By: >>11075490 >>11075500 >>11075507

>>11075482
I mean that that I don't get it. If you tell me to take a derivative, an integral or to compute a limit, I will. But I don't understand why? I just learned this shit by heart

Anonymous

Anonymous Sun 20 Oct 2019 03:43:25 No.11075490 Report

Quoted By: >>11075496 >>11075500

>>11075486
You dont really see the usefulness of areas under curves or rates of change?

Anonymous

Anonymous Sun 20 Oct 2019 03:48:42 No.11075496 Report

Quoted By: >>11075499

>>11075490
I'm glad you asked about areas under curves. It was actually on physics class, when I realised I don't understand integrals and calculus in general. I know that integral = area, but wtf?

Anonymous

Anonymous Sun 20 Oct 2019 03:50:14 No.11075499 Report

Quoted By:

>>11075496
I dont know what you're talking about. The area under the velocity of a particle is the distance it had traveled. This is extremely elementary.

Tuba Jam

Tuba Jam Sun 20 Oct 2019 03:51:55 No.11075500 Report

Quoted By: >>11077031

>>11075490
I think he sees the usefulness, he just doesn't understand why, e.g. the quotient rule is what it is (am I right OP?)

>>11075486
You might want to whet your appetite with https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw. If this is still not enough, I'll refer you to https://4chan-science.fandom.com/wiki/Mathematics#Single_Variable_Calculus and gen.lib.rus.ec

>>11075483
Ignore him, the fact that you care about where this all comes from (where most of your classmates are fine grinding problems with whatever they're given) is precisely the mindset needed to do upper level math with proofs. (speaking of which, the page I linked has a lot of good books on problems, problem solving, and proofs).

Anonymous

Anonymous Sun 20 Oct 2019 03:58:06 No.11075507 Report

Quoted By: >>11076932

>>11075486
Calculus is the study of stuff moving, things not staying the same, what happens when items are projected through time. Think of the derivative as a little number tied to an object calculating the change of something, and the integral as the concrete change observed, i.e. the physical effect of a car going from here to there,

Anonymous

Anonymous Sun 20 Oct 2019 16:13:09 No.11076916 Report

Quoted By:

>>11075452
Its when you do algebra and geometry with infinite sequences, and convergence. By understanding how a sequence of approximations converges, its sometimes possible to express that convergence in closed form (for example, the integral of x^2 on [a,b] is (1/3)*(b^3 - a^3). By understanding calculus, you can realize when an infinite sequence has a closed form convergence, and that can save you a fuckload of time when computing the best approximation of something.

Anonymous

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Anonymous Sun 20 Oct 2019 16:15:23 No.11076923 Report

Quoted By:

Essence of Calculus by 3b1b on youtube might help you. You may also want to work through a more rigorous book.

Anonymous

Anonymous Sun 20 Oct 2019 16:20:18 No.11076932 Report

Quoted By: >>11078570

First semester CS major here.
I got similar questions as OP does.
I understand the basic gist about Calculus being that of representing change quite similar to what is explanained >>11075507, but I've got lots of specific questions or doubts about things like how the formal definition of a limit gives way to power rule and chain rule, or what exactly is the relationship between antiderivatives and integrals.
Most of the Algebra or Calculus textbooks I've come across can teach people how to use mathematical procedures or formulas, but I've never seen any books that attempt to verbally explain mathematical proofs in common language.

Anonymous

Anonymous Sun 20 Oct 2019 16:22:31 No.11076936 Report

Quoted By: >>11078570

>>11075452
You won't know what calculus is until you take Real Analysis

Anonymous

Anonymous Sun 20 Oct 2019 16:23:49 No.11076942 Report

Quoted By:

>>11075452
a way to describe physical systems, think of something like a differential equation as describing a physical system, the only reason it exists is because it is relatively tidy in describing more complex systems that cane be be described explicitly such as in the form y = f(x)

Anonymous

Anonymous Sun 20 Oct 2019 16:25:09 No.11076946 Report

Quoted By:

>>11075452
To understand calculus first you need to have an honest understanding of what functions are in your heart. Do you actually really both intuitively and formally know in your heart what functions are? When I say "function" does your brain go to a long definition or does it go to some esoteric abstract image of what a "function" is that is already burned permanently into your brain?

If you have that image in your brain, then Calculus is just the study of functions that are continuous and/or differentiable. Calculus studies all the fun stuff that you can do with these functions that, in general, you can't do with the other functions.

Anonymous

Anonymous Sun 20 Oct 2019 16:53:22 No.11077031 Report

Quoted By:

>>11075500
Do you know what are the differences between Apostol and Courant is?
Which one would be better for a applied math student?

Anonymous

Anonymous Sun 20 Oct 2019 16:58:58 No.11077047 Report

Quoted By: >>11077052

>>11075452
just watch the fucking 3blue1brown calculus series already, it animates everything and it's short

Anonymous

Anonymous Sun 20 Oct 2019 17:00:55 No.11077052 Report

Quoted By:

>>11077047
HERE OP. GET FUCKING STARTED ALREADY.
https://www.youtube.com/watch?v=WUvTyaaNkzM

Anonymous

Anonymous Sun 20 Oct 2019 18:21:59 No.11077276 Report

Quoted By:

>>11075452
Broadly speaking, calculus is the application of analysis. Basically, you want to make statements about how things change over time, and calculus helps you handle that. Sometimes you don’t just vary time, but other quantities too. Calculus introduces you to the behavior of functions in the real numbers. It’s not always intuitive, and you need to use some sophisticated machinery to actually talk about it (which is the subtle difference between a limit and “evaluating at a point / evaluating at infinity”)

Derivatives roughly correspond/analogize into the rate at which something changes, while the integral roughly (very rough, not always true) corresponds to finding area or “recovering” a function, but this analogy has serious limitations. Limits tell you about how a function behaves at a particular point or towards infinity. All of these will start to make more sense as you ease into analysis. These analogies are rough and sometimes misleading, so it’s best to actually look at a lot of examples and analogize on a case by case basis.

Anonymous

Anonymous Mon 21 Oct 2019 01:55:31 No.11078517 Report

Quoted By:

OP here, if anybody is still up. Thanks to every single soul who tried to explain it. 3B1B videos do work with me. Watched the whole playlist, math is beautiful

Anonymous

Anonymous Mon 21 Oct 2019 02:16:43 No.11078570 Report

Quoted By:

>>11076932
See:>>11076936
Real analysis is where you'll learn point-set topology, epsilon-delta definitions of limits, continuity and field axioms, more rigorous algebraic definitions of derivatives, differentiability, partitions, the fundamental theorems, convergence of series and all the fun stuff that comes with all of that like the supremum, infimum, archimedean property, definitions of closed and open sets, limit points, closure, interior and so on and so forth. Also elementary measure theory if your professor is an asshole who wants to see your suffer even more. Be glad you haven't had to do any proofs yet, while you still have your mathematical virginity you don't have to look at the literally infinite line of proofs ahead of you and have the soul-crushing pressure to make just an infinitesimally small mark on the mathematical landscape. Real analysis is where you can choose to take the blue pill and continue on with your life, or take the red pill and see how deep the rabbit hole goes.

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