/sci/ - Science & Math

[Anonymous No.10390559]

What are some cool/fun things you can do with low (introductory) level calculus? I'm taking calc 1 right now and we just finished the chapter about derivatives of logarithmic functions and implicit differentiation. We took the derivatives of some interesting looking relations.

But what can calculus be used for that is fun and is a learning experience?

[Anonymous No.10390566]

>>10390559
Nothing, calculus is a hoop they make you jump through before you learn the secrets of the universe, or as they call it in school, topology.

[Anonymous No.10390568]

>>10390559
With basic, single variable calculus the coolest thing you can pretty much do is solve related rates problems, or calculate the volume of an object of rotation (or its surface area).

[Anonymous No.10390573]

>>10390559
How to make the area under that curve infinity

[Anonymous No.10390578]

>>10390559
Winning those guess how many beans are in this jar. Never found a use for it outside that desu

[Anonymous No.10390580]

>He actually thinks you can do things with math

[Anonymous No.10390586]

Apply to Law School and work in financial law

[Anonymous No.10390589]

Learn some physics. Basic kinematics and dynamics. That's what calculus was invented for.

[Anonymous No.10390597]

>>10390559
Nothing. It's intended to be a dry weedout class

[Anonymous No.10390601]

>>10390597
Why is it a weedout class?

[Anonymous No.10390609]

>>10390601
It's intended to scare dumb people away from STEM

[Anonymous No.10390668]

>>10390559
Wheres the differential? If delta is then
[eqn]Life=\int_{death}^{birth}\displaystyle\frac{H}{t}\;dt, then Life=(happiness)ln(birth)-(happiness)ln(death)[/eqn] i dont understand this.

[Anonymous No.10390687]

>>10390668
Is happiness a function of time tho?

[Anonymous No.10390710]

>>10390687
for each time you could determine a persons happiness so yes obviously.

[Anonymous No.10390725]

>>10390568
min/max problems is one of the most powerful results from single variable calc

[Anonymous No.10390726]

learn about probability distributions but you probably need to take a class for that

[Anonymous No.10390739]

>>10390668
You switched the limits, also agreed, this equation assumes happiness is constant across life, which is wrong.

[Anonymous No.10391115]

>>10390559
Integrate irl

[Anonymous No.10391134]

>>10390559
Assuming you know the basic rules, anti-derivatives, and the fundamental theorem, you can show where many of the basic newtonian physics functions and ideas come from.
eg proving conservation of energy is trivial.

[Anonymous No.10391158]

This is a nice puzzle for beginner who learn calculus. Try to solve this without reading the solution in the textbook.

int log(x) dx = ?

Putnam calculus problems:
1987B1, 1993A5, 2005A5

Here's a challenging problem: prove that pi is irrational using calculus.

[Anonymous No.10391260]

>>10390668
>assuming happiness remains constant throughout life

[Anonymous No.10391811]

One fun thing you can do with early calculus is show the paradoxical result of Gabriel's Horn: a shape with infinite surface area but only finite volume. https://en.wikipedia.org/wiki/Gabriel%27s_Horn

[Anonymous No.10392646]

>>10390559
Find the optimal shape for a wine barrel.
Trivially deduce all area and volume that highschool books make look like a big deal, but are easy

[Anonymous No.10392699]

>>10391115
that circuit differentiates dumbass
>>10390559
You can justify a lot of theoretical stuff about polynomials. You can solve minimization problems. Taylor series can also be used to model many natural phenomena empirically.

[Anonymous No.10392856]

>>10390559

With calc I you can prove a lot of the stuff you learned previously in math. Like the area of a circle or sphere.

Proving all the derivative and integral rules are fun too. You can also prove the SUVAST equations in physics.

There are a lot of fun problems out there. Some in physics and some pure math.


Here is a challange for you:

Try to minimize the area between two curves.

[Anonymous No.10393007]

>>10390589

true that

but did anybody read PRINCIPIA?

is obscure and sloppy . fucking alchemist-nerd -genius

[Anonymous No.10393154]

>>10390601
Because there are people that are literally too dumb to pass Calc 1-2, so it's best to keep them out of upper level courses where they're just going to take up space and waste everyone's time.

[Anonymous No.10393180]

>>10392699
>justify a lot of theoretical stuff about polynomials
Brainlet here learning math from scratch, can't wait to start calc 1

[Anonymous No.10393377]

>>10392699
Orthogonal polynomials and numerical integration tricks using them are cool

[Anonymous No.10393409]

>>10390559
You can start learning analysis.
No, I'm serious. Knowing the results of calc 1 prime you to learn analysis from the get go.

[Anonymous No.10393420]

>>10390559
Also
>Delta time on a continuous representation
You are like little baby

[math] \text{Life} = \lim_{\Delta x\to\infty} sum_{birth}^{death} \frac{H(t)}{t} \Delta t[/math]

[Anonymous No.10393422]

>>10390559
Also
>Delta time on a continuous representation
You are like little baby


\text{Life} = \lim_{\Delta x\to\infty} \sum_{birth}^{death} \frac{H(t)}{t} \Delta t

[Anonymous No.10393429]

>>10390559
Also
>Delta time on a continuous representation
You are like little baby

[math]\text{Life} = \lim_{\Delta x\to\infty} \sum_{birth}^{death} \frac{H(t)}{t} \Delta t[/math]

[Anonymous No.10393439]

>>10393429
where's x?

[Anonymous No.10393441]

>>10393439
Meant to make it a t, made it an x out of habit :(

[Anonymous No.10393443]

The logic introduced to you with implicit differentiation is, in it's essence, the motivation behind differential equations. You need practice with integral and multivariate calculus before being able to actually solve differential equations, but learning about implicit differentiation gives you a taste of diff. eq. which is one of the coolest things you can do with calculus.

[Anonymous No.10393450]

>>10391115
You can propagate wave functions with Trig too.

[Anonymous No.10393455]

>>10393439
also whoops, wanted to make it approach 0, not infinity

[Anonymous No.10393461]

>>10393007
Newton... "the planets orbit around the sun in ellipses"
How do you know?
"Calculus"
What dafuq dude...

[Anonymous No.10393464]

>>10393455
why not just t approaching infinity

[Anonymous No.10393474]

>>10393464
Because thats not how Reimann sums work

[Anonymous No.10393511]

>>10393474