#Math-Physics Forum

1 messages · Page 1 of 1 (latest)

lone cloak
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As per someone's idea, gonna do like a daily (maybe not daily but smth like it) lesson or smth like that, and then do like a work assignment on it. No idea how many people would actually do it but fuck it; i like teaching stuff so its cool with me.

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vivid roost
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Cool

lone cloak
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well then what to start with huh

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i could try and follow my math doc i made a little while back

vivid roost
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Start with something "easy" ig

lone cloak
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but i might just let people join for now

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and then ill get started on smth

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hmm

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logarithms could be nice

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i could do some trig stuff

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or go head first into calculus

sick turret
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This is the onkel containment forum

vivid roost
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Containment class: keter

sick turret
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Technically? It's not wrong.

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Well, considering our resources at least.

vivid roost
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But w(a)³⁰h techonologies will find a better way to contain it soon

sick turret
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Of course. This is a great source of energy.

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Oi, onkel, how much enkephalin do you produce?

lone cloak
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idk

sick turret
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Well, calculate it.

lone cloak
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...

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nah

sick turret
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Oh, not that

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The fancy enkephalin

hallow delta
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Start with baics please

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I can’t get a 100 if I don’t know what the curly a means

lone cloak
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this symbol?
∂

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thats way out of the scope currently if so

vivid roost
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isn't that a symbol for thickness or was that smth else

lone cloak
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thats the symbol for a partial derivative

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or at least part of it

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e.g. ∂/∂x is a partial derivative with respect to x

vivid roost
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uhhh i kinda get it i think

tight flame
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hey Onkel
I have a theory
1/0.1=10 ; 1/0.01=100 ; 1/0.0001=10 000
see the smaller the divider the bigger the quotient
so could this mean that 1/0=infinity ???
(just entered high school so I might be missing some obvious things)

sick turret
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not onkel, but don't think so.

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or rather, it's def not so

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1/(1/infinity) would be infinity since infinity*1/infinity = 1, but no number times 0 equals 1

lone cloak
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That’s taking the limit from the right side so your getting smaller into the positives

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If you try getting smaller into the negatives you get negative infinity

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Therefore it suggests that negative infinity = infinity which is a contradiction

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Hence 1/0 is undefined because it simply cannot be defined by a concept or number

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But it’s good that your thinking that way though

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You accidentally stumbled upon the concept of a limit

sick turret
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I wonder if that's how it was discovered at first

lone cloak
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Not too sure myself

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Might have to investigate the Wikipedia page then

sick turret
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Oh no, the horror

tight flame
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I'm so smart 😏

sick turret
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It was all calculated

paper maple
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can I use this chat to get homework help

sick turret
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Yep

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Onkel won't be able to resist

lone cloak
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first order of business, lets try and see what peeps' avg level of education is (in broard strokes)

steep gladeBOT
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**:bar_chart: What is your rough education level in Maths and or Physics? **

🇦 Middle School
🇧 Lower High School
🇨 Upper High School
🇩 College/University

lone cloak
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just so i can determine where to start]

vivid roost
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Whats the differents between all of them

lone cloak
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i mean its levels of schooling so its pretty rough

tight flame
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you forgor kindergarten for Cj

lone cloak
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tru

vivid roost
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i'll just do middle school ig

lone cloak
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the first 'lesson' is already 6pages long

vivid roost
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Oh no

sick turret
lone cloak
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its introduction basic trig so i could do more

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but i want to focus on building intuition first tbh than complexity

lone cloak
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have fun

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ask questions and all that while im awake :)

vivid roost
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i'll do it tomorrow if ya don't mind

lone cloak
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all up to u

vivid roost
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K

hallow delta
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btw googles inbuilt calculator uses radians

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bro i gotta rember sohcahtoa now 💀

lone cloak
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You can switch between radians and degrees iirc

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There’s a button

hallow delta
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Where

lone cloak
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just click the 'deg'

unknown.png
hallow delta
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This would’ve been so useful 2 years ago

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😭

paper maple
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@lone cloak found this at my class board this morning do you have any idea what it represents?

20220921_083233.jpg
lone cloak
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that is schrodingers equation

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with the hamiltonian operator expanded

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thats a lot of words idk if i could explain

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might as well go left to right then

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i, thats the imaginary unit defined as i^2 = -1 (rigorous definition), or i = sqrt(-1) (simpler definition)

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h-bar, is the reduced planks constant. around like 1.05?x10^-34

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the curly-d/a are the partial 'signs' that make up the partial derivative of the wave function, psi.

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the wave functions describes how an object described by it behaves

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this is then equal to (usually) the hamiltonian operator operating on the wave function psi

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in its expanded form you have the kinetic energy on the left side of the + and the potential energy on the right side of the +

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m is just the mass of the thing, and more often that not you'll see the second partial derivative of psi with respect to space as just del^2.

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then as potential energy's equations/formulae vary on what object is being described you just asign it as a general potential function V that depends on x and its acting on the wave function psi.

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heres the equation in its non-expanded hamiltonian form, dw about the weird brackets around the psi that just indicates in a way what 'state' a particle is in

unknown.png
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as the psi is in a 'ket', its just a normal/standard state

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heres the expanded form

unknown.png
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i use the term 'expanded' loosely here

paper maple
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ohh

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thanks!

steel jewel
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onkel

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u are a good teacher

lone cloak
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eh not really but thx

lone cloak
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ill update the gdoc this weekend

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been busy with application to uni stuff

hallow delta
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What g mean

IMG_6263.jpg
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Gravity?

hallow delta
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And what does bizarre mark in the sqrt 1/2gx^2/y-x?????35

sick turret
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Is that just very poorly written tan?

lone cloak
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Ye it’s my poorly written tan

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And g is just acceleration due to gravity

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So 9.81ms^-1

sick turret
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Like, that line is a t? The a looks like c or e, and the n looks like a cross between a squished m and a y.

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My phys teacher would've stabbed me with her metal ruler for that.

lone cloak
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its just that my a's and e's usually get conjoined with the next letter so they look sorta similar in my handwriting if im 'rushing'

sick turret
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Uh huh

lone cloak
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Still working on it btw

hallow delta
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Uuuh

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What’s an integral

lone cloak
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do you know what differentiation is?

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its the opposite of that

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and for a simple graphical use of it, it can be used to find the exact area under a curve

hallow delta
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Ok so

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Derivative s

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It’s how you find the slope on a particular point on a graph yes?

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and to do that you find its limit?

hallow delta
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halb
😭

unknown.png
lone cloak
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thats not too bad

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it looks like a lot due to the symbols

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but its really just integrating a function, differentiating a function and the adding them alongisde some constants with its original function (also multiplied by a constant)

lone cloak
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for lack of a better word

hallow delta
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What is integratin a function

lone cloak
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finding the area under the curve of that function

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just like how differentiating is finding the gradient/slope of that function

hallow delta
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how does it work

lone cloak
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like how do you do it? or the proof/justification behind it?

hallow delta
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Specifically the ki integral thing e(t)dt, both would be cool to know

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I know that the ki is a constant

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And et is error from which I can tell is basically a constant

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And Dt is Chang in time

lone cloak
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the way you integrate it depends on the function itself so i cant really say how you would integrate a general function e(t)

hallow delta
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But I don’t know what the big goofy s thing Symbol means or what it does

lone cloak
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that the integral sign

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so you want me to teach you how integrals work then?

hallow delta
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Pretty much

lone cloak
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okay let me prepare some things first

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bare with me for a few more mins

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okay

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first order of buisness

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lets take a general function f(x)

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lets say the function looks smth like this

unknown.png
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now if we wanted to find the area under this graph between, lets say 2 and 6, we could estimate with a varying number of trapeziums, triangles, rectangles etc

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so between this section here

unknown.png
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to highlight it, this section here

unknown.png
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lets consider this little slice of the graph

unknown.png
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we can turn this area into a bunch of these little slices, which i am not gonna painstakingly draw out on desmos rn

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this little slice as a width of, lets say, 𝛿x (delta x)

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like so

unknown.png
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now if we consider what happens when this 𝛿x gets really small, then the f(𝛿x) essentially becomes the y-value at the point thats 'picked' out from the x-axis

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damn you dirac delta function, forever ruining the word 'pick' for me

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so if we make all of these little slices of the area have width 𝛿x, then as we take the limit as this width apporaches zero, then it essentially does the same thing

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we make these slices so thin that we essentially get a continuous area, instead of a mere approximation

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now of cause to actually get an area, we need to multiply this 𝛿x 'space' thats been shrunk by the 'height' of this space.

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or in other words, the y-value thats being picked out

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we then add up the areas of these little small slices, and we get the area

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boom thats integration

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at least an explaination of it

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and this can be algebraically defined by this blury ass img here

unknown.png
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the area is equal to the sum of all the areas of these slices

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which is equivalent to

unknown.png
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where dx is the 𝛿x and the weird-s symbol is the idea of taking this infinite sum

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all good then?

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at least so far?

lone cloak
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?

hallow delta
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Was in internet shadow realm

hallow delta
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But it all make sense now

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I’m having a revelation

paper maple
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integration!!!

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hey onkel look at this

Screenshot_20221011_210717.jpg
lone cloak
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yeah electricity sucks

vivid roost
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wdym i like electricity

hallow delta
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Thank you btw

tight flame
unborn tendon
paper maple
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we study in french

tight flame
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Interesting

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I don't think I'd like studying sciences in a foreign language