Simply Beautiful Art's realm of calculus and analysis

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Andrew Li

01:02

Beep boop

@SimplyBeautifulArt Product to Sum and Sum to Product

Simply Beautiful Art

boop beep

ah...

not necessary at all

Andrew Li

Good. I struggle to remember them

Simply Beautiful Art

(especially once you learn Euler's formula)

Andrew Li

What's that?

Simply Beautiful Art

Euler's formula : Trig to exponentiation function

Andrew Li

01:03

Simply Beautiful Art

then you just need to remember basic exponential rules

and you can derive everything from there

Any who, so you found the derivatives of a few functions, pretty easy stuff?

Andrew Li

I really hate how they don't graphically teach trig in school

Simply Beautiful Art

mhm

Andrew Li

@SimplyBeautifulArt Yeah

Simply Beautiful Art

Did you see the power rule yet?

Andrew Li

01:05

d/dx of x^n = nx^(n-1)

Simply Beautiful Art

yup

Andrew Li

Also, cool video: youtube.com/watch?v=WUvTyaaNkzM

Simply Beautiful Art

Any other derivative rules you saw?

Andrew Li

Not yet. I'm quite busy atm

Simply Beautiful Art

kay

Will say videos are good, and I like that guy's math vids

:( I learned calc through text

Andrew Li

01:06

Heh

I liked the area of a circle example in the video.

Simply Beautiful Art

yeah, most people find it pretty cool

it's how you can derive formulas for volume and stuff

Andrew Li

You're never taught derivations of formulas in school. It's just mindless memorizing. Finding out derivation is really quite cool.

Simply Beautiful Art

Yes, I agree. To tell you the truth, I learned calculus just for one proof, which was the proof of Euler's formula

Andrew Li

Even just with things like completing the square in Algebra, finally seeing the graphical approach makes you realize the square you're completing

I'll have to look into that :)

Simply Beautiful Art

e^ix = cos(x) + i∙sin(x)

Euler's formula

Andrew Li

01:09

Oh man

Simply Beautiful Art

But it is so beautiful looking!

Andrew Li

It is

Simply Beautiful Art

And it is a tad beyond anything you can do with algebra

I know of three proofs of it, all of which require calculus

Andrew Li

Oh! Graphing on the complex plane gives a circular path

Rotations are cool

Simply Beautiful Art

Yup, since cos(x) + i∙sin(x) is like coordinates on the unit circle

Andrew Li

01:12

Wow

Simply Beautiful Art

Rotating complex numbers is actually easy once you start using Euler's form / polar form of complex numbers

Andrew Li

I'm currently going through the whole precalc curriculum for the final and that's what I'm reviewing next

Simply Beautiful Art

if you need help on any of that, I can help you too.... I think

Andrew Li

Okay, sure. Thanks :)

I'll be a afk for a while though

Simply Beautiful Art

but as you saw, calculus is pretty helpful for providing intuition for visual people

afk as in now? Or for the next few days? :P

Andrew Li

01:15

Now

Simply Beautiful Art

k mate

TheGreatDuck

yoyoyo

Simply Beautiful Art

@TheGreatDuck I like yoyo's

TheGreatDuck

lol

soda

Simply Beautiful Art

TheGreatDuck

01:24

lol-e-soda

what is a another name for soda?

Simply Beautiful Art

coke?

TheGreatDuck

pop

lol-e-pop

lollipop

anyways...

Q: Are all solutions to an ordinary differential equation continuous solutions to the associated implied differential equation and vice versa?

Now I have to heavily emphasize the fact that I have never studied differential algebra or the concept of other types of differentiation (which is what I believe is the concept behind a differential algebra). So, if I am abusing the terminology a little bit, please forgive me. Let us define a di...

Simply Beautiful Art

TheGreatDuck

any clue how to solve this?

it is literally the hardest problem I've ever attempted

Simply Beautiful Art

^_^ All you man

TheGreatDuck

01:26

im not at all prepared to solve it

i'm just wanting to determine if it is true or not.

Simply Beautiful Art

;)

TheGreatDuck

:-)

Simply Beautiful Art

honestly... you are putting up the hardest problem tagged with limits in the history of limit questions I've seen

TheGreatDuck

it's probably harder than the riemann hypothesis

Simply Beautiful Art

If you need a bounty....

TheGreatDuck

01:28

but dont tell anyone i said that

Simply Beautiful Art

okay

TheGreatDuck

im not joking

Simply Beautiful Art

probably not

TheGreatDuck

it would trivialize all differential equations involving step functions

that's way more powerful than some measly thing about prime number spacing

Simply Beautiful Art

lol

TheGreatDuck

01:30

only took me a year and a half to come up with the problem and another 6 months to write it in a way that could be competently understood

feel free to put up a bounty

might get some attention

i also put it on math overflow

might get some traction there

Simply Beautiful Art

ugh, as I just click away from the question, now you say that?

TheGreatDuck

Simply Beautiful Art

well, we'll see how this goes

Also, I'm teaching AndrewLi Calculus so he can skip it first year into high school xD

@AndrewLi It's also good for physics, intuitively, if you plan on taking that course.

Andrew Li

So do I have to always plug in the solutions I get for trig equations and inequalities to make sure they work?

I plan on taking Physics, yes

Simply Beautiful Art

@AndrewLi Depends on the problem

most inequalities and trig equations can be solved without plugging the solution back in at the end

Andrew Li

01:33

Oh yeah, so if it's a quadratic I have to?

Simply Beautiful Art

depends

Andrew Li

Ugh...

Simply Beautiful Art

I mean, honestly, if you can plug it in, you should

that's fastest way of checking

Andrew Li

Okay

Simply Beautiful Art

do all multiple choice inequality problems like that :P

Andrew Li

01:35

I'm just afraid I won't finish in time because I always check so I want to know which ones I should always check

Simply Beautiful Art

for pre-calc?

Andrew Li

Yeah

Simply Beautiful Art

hm...

give me a problem

Andrew Li

The one I just did: tan(x)+sqrt(3)=sec(x)

It turns out 5pi/6 doesn't work.

Simply Beautiful Art

ugh

you have to use sum of trig functions to solve it

Andrew Li

01:37

I solved it but one solution didn't work. Is there a reason why there's a solution that doesn't work?

It makes me want to bang my head on the wall

Simply Beautiful Art

x=π/6?

er, x=pi/6?

Andrew Li

The solutions are 5pi/6 and 11pi/6

Simply Beautiful Art

mhm, I see

well

I have to go to bed since it is late for me

@littlepootis Welcome to one of my realms

little pootis

Hey

Simply Beautiful Art

I shall answer any of your questions on the morrow @AndrewLi

Andrew Li

01:41

Bye @SimplyBeautifulArt o/

little pootis

01:58

Got an exam on Power series solutions, Laplace transforms, Beta, Gamma functions, and Legendre's polynomials.

17 hours later…

TheGreatDuck

19:17

@littlepootis what are you using laplace transforms for?

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