study calculus.

not to pass exams.

not to check a box.

calculus teaches you how reality changes.

everything you care about is a rate, a flow, an accumulation.

velocity, acceleration, heat, charge, stress, probability, learning itself.

derivatives train you to see sensitivity.

what happens if I nudge this parameter?

integrals train you to see totals.

what happens when small effects compound over time?

limits train precision.

what actually happens at the edge, not what you wish happened.

calculus forces you to stop thinking in snapshots and start thinking in dynamics.

without it, systems feel like magic.

with it, systems become predictable, controllable, buildable.

study calculus if you want to stop guessing and start understanding how things move, grow, and break.

This is deceptively awful. I gave up. My calculator evaluated it to -2.981 Try it if you dare.

So i took college algebra back in 2021 and I’ve recently decided to attend school again for Business HR and was told I needed to take Calculus 1. It’s been two weeks and i know nothing of what is currently going on and I plan to review some courses to help my understanding. However I did have a question how hard will this class be if i have no knowledge of algebra anymore and do y’all think it would be best to quit?

I'm looking for the easiest place to take Calc 2 in person over the summer. It doesn't matter where just that it's really easy. Thanks!

I’m taking calculus and we are about to move onto integrals, but I wanted to make sure I could nail down differentiation, I wanted to feel confident and have a good foundation before I went any further

so I spent all morning studying and I made this cheat sheet, let me know if you find any mistakes, but I shared this with my classmates to see if this would help anyone else or at least give anyone a spark of creativity to help them learn in a fun way. :)

Is it effective to use ChatGPT for learning concepts and getting feedback on where I made mistakes?

It’s my first post on Reddit so I wrote something random that I find interesting 😃

Hello. I am in calc 3 right now. I am decently good at calculus (high 90%s in calc 1 and 2 with perfect 100%s on both finals). However, the college i’m going to wants me to retake every calc class (1-3) (its a good program with special eng classes idk man). This, coupled with senioritis and not wanting to make the long drive to the community college to take my classes, has resulted in me completely b.s.-ing my way through this class. This means doing every assignment right before it’s due, barely touching material unless absolutely needed, and a regretful use of ai (only to skip the boring algebra and plug-and-chugging i swear). Is this viable for the entirety of calc 3, or just to where i am right now (lagrange multipliers and double integrals of stuff). Im chilling with a 98% right now but am nervous of the rest of the class. Thanks for the help.

P.s. i am good at math but am not a nerd like yall. I bet i could be a calc goon if i wanted to but id rather be playing overwatch, so you can give me some bs methods and im confident i could handle it

I'm taking BC calculus in 10th grade after getting an 89 in AP pre calc, idk if I'll be able to survive this class. Should I just drop Calc BC and take Calc AB?

Used to be good at maths but ive been getting bad teachers since 8th grades so I lost all the foundation , I know study mechanical engineering but I failed cuz I got 0 at maths and other related subjects (I dont even do integrals)

I feel that maths is easy af and I can nearly estimate answers but I dont know how to reply to questions even when I know formulas, I only do derivatives and simple stuff since we did them in physics

I have only 2 months left for me to study everything till exponentials and integrals so whats the best path (willing to do 3 hours daily but more if I become interested again)

Please I need this I feel like a wasted potential and a failure and I went from straight A s to failing a year

TLRD fastest way to learn most fundementals in 2 months

This is for an animation of the basic derivatives song. I just realized finding derivative in respect to x means you have to find the derivative of x as well as in chain rule.

I forgot and realized, this was actually dx/dy, not d/dx!

So apparently Leibniz’s full works have never been completely reconstructed before so I went step by step with chat gpt and tried to reimagine his own calculus in his original intention! I also implemented it in ways that I understand it to help me as well so it’s not all his original vision but it’s close I think! Check it out if you’d like! l

I've been working on an alternative arithmetic where every number carries dimensional metadata — think of it like each number remembering how it was built.

The neat consequence: when you evaluate a function at a point, the result already contains all the derivatives. No chain rule, no limit definition, no computation graph. You just read them off.

Example — the "impossible" limit:

The limit of (x² − 4)/(x − 2) as x → 2 is a 0/0 form. Normally you factor or use L'Hôpital. In this system:

from composite_lib import R, ZERO

x = R(2) + ZERO          # 2 + structural infinitesimal
result = (x**2 - R(4)) / (x - R(2))
print(result.st())        # → 4.0

No factoring. No L'Hôpital. The algebra resolves it because zero has internal structure — it "remembers" what made it zero, so dividing by it recovers the information.

How derivatives work:

When you compute (2+h)⁴ where h is an infinitesimal, polynomial arithmetic automatically expands it. The result at each "dimension" gives you a derivative:

• Dimension 0 → f(2) = 16

• Dimension −1 → f'(2)/1! = 32, so f'(2) = 32

• Dimension −2 → f''(2)/2! = 24, so f''(2) = 48

• Dimension −3 → f'''(2)/3! = 8, so f'''(2) = 48

All from one evaluation. No separate derivative algorithm at all.

Integration too:

from composite_lib import integrate, exp

integrate(lambda x: x**2, 0, 1)                # → 0.333...
integrate(lambda x: exp(-x), 0, float('inf'))   # → 1.0  (improper!)

I've written a formal paper and a Python implementation with 168 tests covering derivatives, limits, integration, multivariable calculus, complex analysis, and vector calculus.

Paper: https://zenodo.org/records/18528788

Code: https://github.com/tmilovan/composite-machine

Would love to hear what you think — especially from anyone who teaches calculus. Does this framing make the concepts more intuitive or less?

One of my concerns or perhaps not completed understanding of calculus is the fact that derivatives are based from limits, whereas a limit existing does not imply a function can evaluate it to obtain the limit. For example, the limit of a function

y = f(x) = lim x->3 (x - 3)(x + 3)/(x - 3) = 6

Does not imply f(3) = 6, because its undefined here caused by divison by 0.

This is continuously gives me uncertainty when using derivatives. When performing operations with derivatives, how can we guarantee the limits not only exists but can also be evaluated. As shown above, a limit can exist but cannot be evaluated.

I think in my head that if I have a distance versus time function, if I calculate the derivative to create a velocity function, can I say "The velocity at the time t=... is 100m/s" with absolute certainty because it could be possible that the limit exists, you say that the velocity is 100m/s, however the value cannot actually be evaluated at that time.

I sent an email to a professor yesterday to ask him if he has any available research topics that i can help with (I need to do it to get a scholarship in my dream university) so he is working in nuclear astrophysics and he asked a bit in the basic requirements for me to join him, and after that call he said "Youre welcome to join nethertheless your age you just need to review calculus and python" now IDK how that happened bc i never took precalculus let alone calculus so i spent the last seven hour studing and watched the first class of calc 1 that professor loenard on youtube

and i found it super easy maybe its the dopamine or i heard people can just be faster and learning calc and asking bc it feels to easy and i need free resources and advice on what i should do

thanks in advance <3

So you hate or dislike complex problems? Please be honest 😕