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.
Intermediate Tests (50%) or final written exam (100%). It is approved any student who obtains as final classification, not greater than or equal to 9,5 values. When the final grade is greater than or equal to 18 the students will be subject to further proof.
Additionally students can submit a supplementary work (3 values), held in groups or individually, to address important issues related to the syllabus of the Course

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 learner 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
Compreention:To solve practical problems with an increasing autonomy, using the subjects treated in the classroom and other related topics;
Aplication: To find and select relevant information from different sources such as monographs textbooks and the web.

Real functions of one real variable:
1.Limit and continuity; Basic theorems; Trigonometric and inverse trigonometric functions; Basic properties of the Logarithm and the Exponential.
2. Primitives:definition; immediate primitives
3.Integral calculus:Applications of integration to the calculation of area, volume and length; Indefinite integrals and improper integrals.
4.An introduction to ordinary differential equations:Terminology; First-order differential equations: First-order linear differential equation and separable equation.
5.Numerical Séries:Definition of convergence. Necessary condition for convergence. particular series
6.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.

NAO