The goal is to carry on developing the mathematical reasoning initiated in highschool education, in order to be able to meet the demands of other curricular units. On completing this curricular unit, students should have acquired the necessary skills in differential calculus and integration of functions of one variable, including the fundamental theorems of calculus.

Limits and continuity: Basics on real valued functions. Exponential and logarithmic function. Trigonometric inverse functions. Continuity and limit. Mean Value and Weierstrass Theorems.
Differential calculus: Derivative concept, rules; differentiability and continuity; higher order derivatives, applications. Rolle’s, Lagrange’s, Cauchy’s and L’Hôpital’s Theorem. Taylor’s formula and its applications. Integral calculus: Antiderivatives by inspection, by parts, by substitution and integration of rational functions. Integral calculus of real functions. Integrability conditions; properties of integrable functions. Indefinite integral, derivative of an indefinite integral, Fundamental Theorem of Calculus, Barrow’s formula. Integration by parts and by substitution. Application of integral calculus to the computation of area, volume of revolution solids and curve length. Moments, center of mass and centroids.

Theoretical classes with lecturing periods with application examples followed by small tasks to be done by the students in order to consolidate the contents previously taught. Practical classes dedicated to problem solving, individually or in small groups.
The assessment will be done through a final written exam or, alternatively by student option, by four written tests each one contributing 25% to the final assessment.