Calculus I

Trigonometry and Elementary Geometry
Elementary Functions and Inverse Functions
Trigonometry Functions
Differential Calculus

In the classroom, is used the theoretical classes for introductory explanation of subjects, with exemplification
through problem solving for the acquisition of basic knowledge, while in the remaining classes other teaching
methods are applied and shared resolution of exercises led to the understanding and application of materials.
Specific activities are proposed to create in students the spirit of synthesis and analysis. A platform MOODLE /
LVM and Facebook groups are also available with documents, discussion forums, learning tips.

The main aim of this course unit is to promote the learning of math concepts for students to acquire a reasoning ability and powers to understand and use mathematics as a tool to aid in the various disciplines of
the course.
At the end of this course unit the student is expected to be able:
– Knowledge:To explain the concepts, discuss and present each problem solution in an appropriate way:basics
of mathematical analysis and real functions of one real variable;apply theoretical development of differential
and integral calculus; basic concepts of numerical series, ordinary differential equations and solve some
simple first order differential equations.
– Understanding:To solve practical problems with an increasing autonomy, using the subjects treated in the
classroom and other related topics.
– Application: To find and select relevant information from different sources such as monographs textbooks
and the web.

1. Differential Calculus in R: trigonometric functions, implicit functions, derivation
2. Primitives: definition; immediate primitives. Techiques of Primitivation: integration by parts, integration by
substitution and integration of rational functions; Definite integral (Riemann’s integral) and the fundamental
theorem of calculus.
3.Integral calculus:Applications of integration to the calculation of area, volume and length; Indefinite integrals
and improper integrals.
4.Numerical Series:Definition of convergence. Necessary condition for convergence. Particular series. Infinite
series: convergence criteria. Power series

NAO