Two Questions on analysis and books 
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*What the difference between analysis and calculus? Is calculus a prerequisite for analysis? I would like to know what's the order in which subjects are meant to be learned, and what is the definition of each one.

*I'm trying to learn calculus deeply, but my goal is physics and applied math, I've been told that books like Spivak are for math majors, so the what the book for physics majors? Precisely, what books should I read in succession to obtain enough knowledge and skill to understand the math of physics?
 A: The ${\it difference}$ between analysis and calculus is rather tenuous, but in general, analysis is often seen as the RIGOROUS study of calculus. Many people find the basics of calculus challenging, and so a certain level of abstraction can be intimidating to beginning students. As such, in introductory calculus classes, many teachers will sacrifice more careful, precise definitions of certain concepts (like limits, Riemann sums, integration and differentiation, continuity, etc) in favor of a more concrete approach which makes these concepts more palatable. However, in order to truly master the ideas in calculus, one must put the general concepts introduced in calculus onto rock solid footing, with little imprecision and no inconsistency. This is among the primary goals of the study of analysis. 
For this reason, while it's not strictly necessary to know calculus before studying analysis, it is often a good idea for two reasons. One, an informal familiarity with calculus concepts helps to helps peel back certain abstractions which can be confusing when made formal. Two, having studied calculus makes it so that you can better understand the $\underline{point}$ of analysis. If you don't understand basic calculus concepts before studying analysis, it's hard to appreciate just how badly things can go if we're not absolutely precise in our definitions. The first section of Terry Tao's introductory analysis notes address this really well, and require little familiarity with calculus to understand. I encourage you to look at them to get a firmer understanding of what analysis is. They can be found here.
Regarding your second question, if you want to learn calculus deeply, Spivak is a fine choice. Apostol's "Calculus" is also often recommended. You'll find on MSE (and on the web) a number of debates on their various merits. In my mind, there is no book for "math majors" or "physics majors"; that kind of distinction is artificial. All that matters is how deeply you would like to learn the subject, and if you indeed desire a strong understanding of calculus, either book will do quite well. 
