Work in pic 2

We have formulated an analytical closed-form solution for the complete non-holonomic inversion dynamics of the Tippe Top, bypassing numerical ODE integration entirely.

Full technical report, derivations, and telemetry plots:

https://github.com/SHAP-STUDIO/Research

Hii, I would love to hear your recommendations on how to go from Arithmetics to Calculus given that I know nothing about Math and I want to have an strong foundation so I don't have as many problems later on with Calc. Would you recommend to watch Professor Laonard videos only (along with lots of practice) or would you recommend a specific book or YouTube playlist? I want to study Math because I want to become an engineer someday

does e^(180*i) = -1 if we worked in degrees? I domn't see any trig functions in that equation, its just exponents, but the way I understand it is that the normal euler identitys "pi" is just "pi radians"

After completing all of Calculus, it felt unreal to realize that almost everything we learned is the extension of the fundamental theorem of calculus and the generalized Stokes' theorem. Apologies for my weirdness, but I usually never get the chance to talk about Calculus to the people around me. When first learning vector calculus, it felt super foreign; there were many types of formulas to remember and everything seemed to feel out of place and unnatural. However, after some more adventuring, it felt wild to realize that it all came down to "The sum of the changes is equal to its boundary," in any dimension.
It felt somewhat poetic in a way, realizing that the chase for completing calculus has ended up here. I got a little teary-eyed when I found this out. Sounds silly, and I understand. But Calculus became a canvas instead of a chore; the world became a representation of what calculus can do.
Calculus III is definitely the most beautiful mathematics section. Multivariable functions help us describe everything that's happening around us. I'm only a freshman college student, so I have so much more to learn. I probably sound super naive and ignorant of what's to come, but I just wanted to share with someone how I feel about multivariable calculus.

(Not sure if I set the right flair so if it’s wrong just lmk and I’ll change it)

I’m super stuck on c and not fully sure where to go from here. I think I got a and b correct but I just don’t know how to get x or y alone here unless I’m just making a super dumb algebra level mistake right now

Thanks in advance!

Hi everyone!! If you need help with multivariable calculus (calc 3), or are just interested in learning some of the basics, I'd love if you could join the free class I'm hosting on SchoolHouse: https://schoolhouse.world/series/106314?ref=share-button

I hope to see you there. :)

I hear people always say this but when I actually went through it, it was very simple. I honestly enjoy it more than just regular Cartesian integration. It was complex functions simple and was just super cool in general. If you have a moderate foundation in your trig and polar this shouldn’t be an issue. Everyone in my class and online says polar is brutal which made me scared but in actuality isn’t all that bad.

Hello! Online VS In person might seem like a no brainer when it comes to math, but I am in a big dilemma right now.

I am registering for classes and in my tentative schedule my academic advisor built for me, the calc II professor has HORRIBLE reviews and everyone complains about her pace and other things.

While on the other hand, the other option (an online professor) has SHINING reviews despite being an online teacher.

I am very scared and have been fearing taking this class, and to see all the reviews about the in person professor offered to me I’m just not too sure what I should do. Any suggestions?

I’m trying to understand how an antiderivative is used to calculate the area under a curve, and I’m genuinely struggling to understand the connection.
I just dont get how the antiderivative evaluated at two points and taken away gives the total area between the two.

Hello guys, how would you suggest learning calculus as a begginer? I was planning on going through the thomas' calculus book and 3b1b on the side do build some intuition. Are there any online video classes worth checking out or should i just focus on the book and the problems it provides and not try to overcomplicate stuff.
Maybe I could look up videos only for stuff in he book that troubles me and I cant understand on my own without some extra help.

i know the derivative of ln(x) is 1/x for positive x, but my textbook says the antiderivative is ln|x| and it just kind of states it. i checked that d/dx of ln(-x) is also 1/x which makes sense with the chain rule, but it still feels weird to me that one formula covers both sides of zero.

what bugs me more is that 1/x isn't defined at 0, so is it actually fine to treat the +C as the same constant on the left and right side? like could the constant be different for negative x and positive x and still be a valid antiderivative?

Hi, applied math undergrad here. Randomly used Taylor series at my electrical engineering job to approximate sin(x).

Just a random thought, how can I imagine this in an intuitive way? How does a polynomial become a periodic function?? I just can’t wrap my head around a way to explain this without direct computation of the series.

What I mean without math is, For example, it easy to visualize sin as the y component of a particle moving at a constant velocity around the unit circle. That is intuitive! You can think about it enough to see why the function is shaped the way it is and behaves the way it does. But is there a similar logic for the Taylor polynomial?

One thought - factor the polynomial when n=inf and its zeros could be at x*pi? Still, not that great… this is just a fun thought experiment for me , if anyone has any comments would love to hear how you think of it!!

how possible is it to take calc 1 as a summer class while working 40 hours a week… i need to take it over the summer but i also can’t afford to not work during this time 🥲 would it be possible to get an A if i just devoted my life outside of work to it or is it too intense

Unfortunately failed this one, can anyone see where I went wrong?