This course offers in-depth understanding of some common methods of calculus for single-variable real functions. The course puts emphasis on deducing new notions and theorems from earlier results but at the same time it leaves enough room for economic applications which are build upon knowledge obtained in the Mathematics for Business course. The following topics are covered: Limits, Continuity, Differentiation, Implicit Differentiation, Newton's Numerical Method, Taylor's Theorem with Approximations, Convex and Concave Functions, Simple Minimisation and Maximisation Problems and Indefinite Integration with Simplest Differential Equations. You will not only learn how to differentiate and integrate functions, but more importantly you will learn how to apply these skills; for example how to apply elasticity of a function in economy and how to maximise a general profit function.