The course studies theory of functions of one variable. In particular, we focus on the properties of monotonicity, continuity, derivability, and concavity/convexity of functions. As soon as the student understands these concepts, they are applied to the study of problems of interest in Economy, such as graphic representation, approximation by asymptotes, local approximation by polinomials and optimization.
The program is divided in four 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, both local and global.
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.