1. answering the question "how do we get the next x" for a function x=y.
If x=y, then if you increase x, you also increase y, so dx/dy=1. Figuring out dx/dy is fun when dealing with things like 3x^2+5x+7=y.
But take the game of Pong, for example. A simple Pong game has a ball and the direction of the ball can be controlled by two variables - horizonal velocity (H) and vertical velocity (V).
Each frame, you take the ball's X and Y and add H and V to it, to move the ball. When the ball collides with something, just multiply by -1 (to flip the sign) to reverse the ball.
If you divide V by something like 0.0001 each frame, you will implement gravity.
Want the ball to have a gravity or other "pull" that results in it hitting a point in a specific number of frames? Well ... someone who knew what they were doing would know what to do. That's all I got.
2. If you have a few points for x=y, you should be able to figure out dx/dy somehow. I think that's called integrals.
Oh sure, that's simple enough. How about gravity over a sphere in 3 dimensions? How about a custom physics and collision engine? How about some portals? How about some non linear spaces?
It is not that tough if you approach it in the right manner. Here is my "guaranteed understanding" 5-step recipe for Calculus :-)
a) Learn co-ordinate systems Geometry.
b) Learn Functions and Graphs.
c) Learn Derivatives.
d) Learn Integrals.
e) Learn Differential Equations.
Focus on understanding single-variable only and ignore everything else in the beginning.
You will find the following resources most helpful.
1) First refresh the basics from George Simmons' Precalculus Mathematics in a Nutshell : Geometry, Algebra, Trigonometry (it is less than 150 pages!) - https://archive.org/details/precalculusmathe00geor (pdfs are available elsewhere on the web) In particular; read the Trigonometry section thoroughly.
2) Higher Math for Beginners (Mostly Physicists and Engineers) by Zeldovich and Yaglom - https://archive.org/details/HigherMathForBeginners/mode/2up - Read everything from the beginning including Preface/Notes/etc. (which setup the Motivation) through chapter 1 (Functions and Graphs), chapter 2 (What is a Derivative) and chapter 3 (What is a Integral).
That's it! You now "know" Calculus; the rest is mere elaboration on this basic edifice. You should be able to do this in a week by just studying an hour or two everyday.
3) For a more Pictorial/Graphical help in understanding the above, get the book: Who Is Fourier?: A Mathematical Adventure by Transnational College of Lex. This is a manga-style book which gives a very intuitive understanding of Calculus and more.
Do not wait but get started today; You can thank me later :-)
"tough to learn outside of school and much older."
Be very careful with this way of thinking. People around me have used it to justify not taking the time to learn something as far as I can remember. In short, giving up before they try. This attitude will hinder any possible growth. I guarantee it.
What's tough is following thru, not the subject you are trying to learn. If you can't learn on your own take a class at a local college. It will force you to show up and try. But thinking that you can't learn because you are older is not true.
Obviously I've not looked at all of them but my main problem (especially with language books) is that there are so few good materials to learn from in self-study. Everything is "supporting the class room", or has some ridiculous split into (bad) contents and (worse) exercises that more often than not are the classic "draw three circles.. draw the rest of the owl".
And yes, people usually go on to recommend some vague resource that helped them understand just enough if they were starting from a decent problem already. (IMHO a good example here is vector math. If you do some stuff with 3d and games the problems are clear and most people will start from there and then learn enough to understand it. But just learning it in isolation is where people complain).
Sorry, but that's not any excuses for you not to start learning! Looks like your problem is procrastination which we all struggle with. Old age is also not as bad we're lead to believe for learning. It's all about getting into the habit of studying. That can come after an idea that turns into a goal and is kept in motion by brute force will. Alternatively the peer pressure from school or a course can keep you going and meeting goals effortlessly.
There are now many easily accessible online resources like 3blue1brown's "essence of" series [1], Khan academy [2], or Brilliant.org's courses [3].
I would actually start with a first pass at elementary linear algebra, before taking a serious crack at even single variable Calculus. Then let the key ideas marinate in your brain; develop some facility and intuition / insight.
Multivariable Calculus hardly makes any sense without a basic amount of linear algebra. It’s a bit of a historical accident that (Western) mathematics developed Calculus extensively prior to linear algebra taking shape as a significant subject. Don’t try to tackle Multivariable Calculus with a decent grip on matrices. Maybe do some computer graphics and learn how to build 2D & 3D shapes and animate them using matrices.
“Just” linear alg, LOL. I made it through calculus 2/3 in high school but linear algebra gives me fits, especially since I only ever learned it in a data science context. Linear algebra is freakin’ tough!
You need this book: Practical Linear Algebra: A Geometry Toolbox by Gerald Farin and Dianne Hansford. You can get older editions for pennies. The 1st edition was actually called The Geometry Toolbox for Graphics and Modeling.
You should also read Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares by Stephen Boyd and Lieven Vandenberghe: https://web.stanford.edu/~boyd/vmls/
You have the first prerequisite, the desire to learn! Try to find resources which nurture your interest, until it grows into the will to learn. I find the history of mathematics and how it came to be, its role in the rise of civilization, to be quite inspiring.
Between YouTube, and maybe the right blogs or online classes, it seems like a motivated person could learn almost anything online. There’s also a social aspect, we learn by talking about things with others, sometimes as pupils, other times as peers, and even teachers. Try to teach concepts you’ve learned to other people.
Finally, you can’t learn math just by reading or listening, any more than you can learn to play soccer just by watching matches. Math is a problem solving art, you have to resist the urge to peek at the answer until you’ve exerted serious effort and put in the time.
Why? There's so many resources now. I actually tried to relearn calculus recently. I ran into the same problem I had the first time in college, it felt like learning for learning sake and didn't have a strong enough motivation for it
