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I want to study applied mathematics on my own

  1. Sep 15, 2015 #1
    i want to study applied mathematics on my own, but i don't know where to start
  2. jcsd
  3. Sep 15, 2015 #2


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    Staff: Mentor

    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?
  4. Sep 15, 2015 #3
    i know a little bit of calculus, i'm in 11th grade
  5. Sep 15, 2015 #4
    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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