Difference between Calculus & Analysis

[dmuthuk]

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?

 

[NoMoreExams]

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 possesses 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.