The course studies theory of functions of one variable. In particular, we focus on the properties of continuity, derivability, and integration of functions. As soon as the student understands these concepts, they are applied to the study of problems of interest in Economy, such as monotony and convexity, graphic representation, polynomial approximation, optimization and calculus of areas.
The program is divided in five big lessons:
Lesson 1: elementary properties of functions. In particular, it is studied when a function is periodic, monotone, shows symmetries or has an inverse.
Lesson 2: continuity. In particular, it is studied when a function has limits and /or asymptotes, the calculus of intersection points of graphics and the existence of maxima and minima.
Lesson 3: differentiability, part one. We study the calculus of derivatives, stressing implicit differentiation. In the same way, we apply derivatives to study monotony and the calculus of maxima and minima.
Lesson 4: differentiability, part two. We use the concept of derivative to compute limits, to approximate locally a function by polynomials, to characterize concavity and convexity of a function and for an introductory study of the income, cost and profit functions.
Lesson 5: Integration. First of all, we introduce the concept of primitive of a function, and we study different methods of computing them. Secondly, we introduce the concepts of area and integral, and its relationship with the concept of primitive function. In a third step, we study the calculus of areas. Finally, we study improper integrals.