Cálculo I

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 is also available with documents, discussion forums, learning tips. The assessment can be distributed using two intermediate tests (50%) or by exam (100%). The student obtains approval whenever the final classification is greater than or equal to 9.5 values ​​and is subject to a complementary test if the classification is greater than or equal to 18 values. Additionally, students can present a complementary work (3 points), carried out in groups or individually, addressing important related topics.

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.
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.

1. Differential Calculus in R: trigonometric functions, implicit functions, derivation
2. Primitives:definition; immediate primitives. Techniques 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 Séries:Definition of convergence. Necessary condition for convergence. Particular series. Infinite series: convergence criteria. Power series and Taylor Series.

NAO