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Difference between Calculus & Analysis

  1. Jan 13, 2009 #1
    Hi, I'm just asking this out of curiousity, but I have never really understood the difference between calculus and analysis. The only thing I can say is that calculus is basically applied analysis or analysis is the rigorous theory behind calculus. So, if the difference is just a matter of theory versus application, do pure math students really need to learn calculus as it usually taught in first year or can they just begin with analysis? For instance, I did a math major in undergrad and now I want to seriously re-learn mathematics on my own, but since I have forgotton most of my calculus, is it more helpful to just study books like Rudin's analysis instead of brushing up on my first year calculus text again?
  2. jcsd
  3. Jan 13, 2009 #2
    Analysis 1 is probably the theory behind Calc 1 and 2. But Analysis is so much more, when you get into measure theory you are still doing "calculus" but it's not anything you would learn in a Calculus class. I suppose you could skip straight to Analysis without taking Calculus 1 and 2 but most math students do not possess the math maturity needed. It's a lot easier to learn how to do a bunch of problems and then try to figure out the theory behind why the cogs turn the way they do.
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