Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis.
Algebraic and order properties of R, the completeness property, cluster points, open and closed sets in R
Sequences, the limit of a function, limit theorems
Boundedness theorem, maximum-minimum theorem and the intermediate value theorem; uniform continuity
The mean value theorem
Taylor’s theorem, Limit and continuity of functions of two and three variables
Partial derivatives
Differentiable functions, regions in the x-y plane, iterated integrals, double integrals, change in the order of integration, transformation of double integrals
Jordan curve, regular region, line integral
Green’s theorem, independence of the path, surface integrals
Principles of Mathematical Analysis by 
