Description

Theory
3

Theory/Practice
3

Instructors

Marisa Guerra Pereira

Contents

I - Complements on Differential Calculus in IR
-Complementation of the study of functions:
- absolute value, exponential and logarithmic functions - characterization, calculations and differentiation;
- direct and inverse trigonometric functions - characterization, calculations and differentiation;
-Implicit and parametric differentiation;
-Differential. Geometric interpretation.
II - The Indefinite Integral
-Definition. Properties.
-Integration by decomposition, substitution and parts.
III - The Definite Integral
-Geometric interpretation.
-Properties.
-The fundamental theorem of Calculus.
-Integration by substitution and parts.
-Applications.
IV - Infinite Series
-Introduction to series study.
-Analysis of positive-term series convergence - main tests.
-Analysis of alternating series. Absolute convergence.
V - Functional Series
-Power series.
-Convergence problem of power series.
-Power series representations of functions - MacLaurin and Taylor series.

Learning Outcomes

It is a propaedeutic discipline that aims to provide structuring knowledge, essential to the specific disciplines of the course, either through the integration and development of previously acquired knowledge, or by the acquisition of new fundamental knowledge.

Classes in this subject will aim to contribute to the development of students' reasoning and abstraction skills, in order to:
- facilitate them in acquiring basic knowledge (concepts and methods) of Mathematics, fundamental in the mathematical training of an Engineer;
- promote basic training in subjects of mathematical analysis essential to the understanding and interpretation of subjects covered in other subjects of the course, especially in the field of differential and integral calculus, numerical series and functional series.
- enable them to intuitively apply learned concepts to new situations;
- promote the acquisition of critical thinking in students.

Students should be able to:
A - Analyze real functions of a real variable, applying differential calculus.
B - Define and calculate the antiderivative of a real function of a real variable, distinguish the various types of integrals and choose the appropriate integration methods, applying them to calculate areas, volumes and arc lengths.
C - Study the convergence of Numerical and Functional Series.