Why study calculus in real analysis when we can study it in elementary mathematics?



Real analysis is an area of analysis that studies concepts such as sequences and their limits, continuity, differentiation, integration and sequences of functions. By definition, real analysis focuses on the real numbers, often including positive and negative infinity to form the extended real line. In order to understand the analysis behind calculus, it is important to take a look at their real properties, these properties are what is translated into theorems that helps in combating problems related to calculus. To study calculus, it is important to have an understanding of functions and their limits defined on real line, since calculus has to do with functions too, then it is sufficient to study limits of functions and this is broadly analysed in real analysis. 
Calculus courses succeed in conveying an idea of what a derivative is and the students develop many
technical skills in computations of derivatives and their applications. To see a little deeper and to understand the basis on which the theories of calculus is built, real analysis provides an eye opener to this theories by providing more attention to details and less to the applications.