# i'm 15 and I really want to start learning calculus, I know geometry, a little trig, and algebra 1 and 2 what is the best way to go about this? [closed]

like the title said i'm looking for the best way for me(a 15 year old) to go about learning calculus, thank you :)

• Obtain a copy of Rudin's "Principles of Mathematical Analysis" and start reading it from the very first page, when you encounter a statement (can be a proposition or theorem) try to prove it by yourself, at least for a day, if you don't came up with an idea, then the following day you can check the proof in the book. Or ask for help here in MSE. You will learn a lot in this way – Warlock of Firetop Mountain Jan 17 '18 at 17:14

Go straight to Khan Academy and start with their beginner courses. It's by far one of the most effective ways to learn things. I'm a CS student in university and keep coming back to Khan Academy to help with things from limits or L'Hopital's Rule. So for someone who wants to start learning Calculus Khan Academy is the way to go.

Also maybe borrow a book from your library to get an idea of the things you need to study and make sort of a layout. Best of luck!

You could take a look at the online Pre-Calculus course of the Technical University in Delft. https://online-learning.tudelft.nl/courses/pre-university-calculus/ I think this will fit your academic and enthusiasm level perfect!

Cheers! Wessel

1. While you are studying calculus (or anything else), study yourself. How do you learn best? What are your strengths, your goals etc.?

2. Always ask yourself, "what is the big idea?” Summarize for yourself the steps in any solution and extract the important concepts.

2a. Keep in mind that calculus itself is one of the giant big ideas in science and it consists of two giant big ideas, which is the derivative as an instantaneous rate of change, the integral as an accumulation of change, and the connection between these two, which is the fundamental theorem of calculus. Never lose sight of this in all the detail.

1. There are many sources for the basic material, and you can get materials cheap. Buy a couple of 20 year old or 50 year old textbooks and work through them systematically. Compare this source with Khan academy or whatever is available online, and see what serves you best.

2. Your goals should change as you progress. If your goal is to sort of know something about calculus, that’s fine. If your goal evolves to knowing calculus thoroughly, in the sense of being able to do any calculation and pass any reasonable test, you will have to devote a lot of time to practice and thinking. But your goal may progress beyond this to wanting a deeper understanding. Then you will need better materials: classic books by Spivak, Courant and Apostol.

Also: this might be useful: Am I too young to learn more advanced math and get a teacher?

Also this: MIT online course by Gilbert Strang with textbook, https://ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/

• About 2a, calculus introduces another big idea to students: treating functions as things to be considered, not the individual points on the function. So instead of making a statement about $f(x)$, you make statements about $f$. Some students have trouble adapting to this, especially when the coursework doesn't make it clear. – DanielV Jan 17 '18 at 17:08
• @DanielV What do you mean by "making a statement about f(x), you make statements about f."? – Botond Jan 17 '18 at 21:11

3Blue1Brown's Essence of calculus is a good starting point: https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr
And for a lot of excercises, you can check blackpenredpen: https://www.youtube.com/user/blackpenredpen