Description

Theory
2

Theory/Practice
2

Instructors

Luis Augusto Roque

Contents

1.Differential calculus in IR(20%)
Derivative of a function at a point; derivative of a function and rules of derivation, the derivative of a composite and of an inverse, trigonometric functions and their inverses,
differential of a function
 

2.Integral calculus in IR(55%)
- Indefinite integral
Definition and Properties.
Primitive integral
Integration by substitution and parts.
-Improper Integrals
- Definite integral
Riemann sums
Geometric interpretation and properties.
The fundamental theorem of the Calculus.
Application of the definite integral to the calculation of plain areas.
 

3. Series (25%)
- Numerical Series
Definition. The necessary condition of convergence
Non-negative series. Tests for convergence: D'Alembert and Comparison Test
Alternating series. Absolute vs conditional convergence. The Leibniz's Test
-Power and functional series
Definition and convergence study
Power series representations of functions - MacLaurin and Taylor series.
MacLaurin and Taylor polynomials.

Learning Outcomes

This course aims to contribute for the student to:
- to develop its capacity of reasoning and abstraction;
- to acquire critical thinking and mathematical thought capabilities;
- to be apt to apply mathematics techniques very important for the Informatics Engineering programme.

The students will have to be able to:
- perform calculations of partial derivation;
- correct identification and application of the different techniques in the attainment of the primitive of a real function of real variable;
- apply analytic methods of integration to the calculation of plain areas;
- study the convergence of a series of powers;
- determine the development in series of a function - MacLaurin and and Taylor series;