i want to study applied mathematics on my own, but i don't know where to start
That depends on "where" you are right now. What mathematics do you already know, and what level of school are you in, or have completed?
i know a little bit of calculus, i'm in 11th grade
Then you'll need to start with understanding all of calculus. That is: differentiation, integration, series, sequences and multivariable stuff. This is very much essential to mathematics.
I recommend you start with the book of Keisler: https://www.math.wisc.edu/~keisler/calc.html It gives awesome intuition for calculus. It deals with two very different approach to calculus, both standard and nonstandard (but focuses on the latter). That is: it accepts infinitesimals and does most calculations with them. The benefit is that
1) This is how calculus was historically developed.
2) It is more intuitive than the standard epsilon-delta approach
3) It is easier to give rigorous proofs than in the standard approach (except for some easy-to-believe facts)
4) Infinitesimals are still used widely in a lot of math and physics
If you do not feel comfortable learning about infinitesimals, then I recommend Lang's First course in calculus. This is also a very decent book, but his treatment of limits and continuity is a bit too brief.
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