Calculus I

Trigonometry and elementary geometry.
Study of real functions and their inverse.
Trigonometric functions.
Differential calculus.

In the theoretical classes the expository method is applied, for introductory explanation of the subject with exemplification through solving exercises to acquire basic knowledge.

In the remaining classes, the shared resolution, individual and / or group, of exercises that leads to the understanding and application of the syllabus and specific activities of synthesis and analysis is used.

On the MOODLE platform, documents, discussion forums, learning suggestions are available.

Use of free mathematical software (Geogebra, Symbolab e Photomath).

The main objective of the Curricular Unit is to promote the learning of the concepts of mathematics so that the student acquires a reasoning ability and skills that allow him to understand and use mathematics as an aid tool in the different subjects of the course.

At the end of the academic semester, students must, in each of the following aspects, be able to:

Knowledge – Describe the main results in the area of ​​basic training in mathematical analysis, namely in the domain of differential and integral calculus, numerical series and differential equations. Identify the techniques to be used in problem solving;

Understanding – Build an appropriate attitude and thinking to solve Engineering problems;

Application – Develop a solid training base for later disciplines, which allows the correct use of techniques and the rigorous formulation of problems.

1. Real functions of one real variable.
Limit and continuity, basic theorems, trigonometric and inverse trigonometric functions, basic properties of the logarithm and the exponential.

2. Differential calculus on R.
Derivation: definitions and calculus rules. Linear interpolation (Taylor’s polynomial). 

3. Root determination of non-linear equations.
Bisection and Newton-Raphson methods. 

4. Antiderivative.
Antiderivative definition and basic rules.

5. Integral calculus on R.
Definite integral (Riemann’s integral) and the fundamental theorem of calculus. Applications of integration to the calculation of area, volume and length of planar curves. Numerical integration: trapezoidal rule and Simpson’s rule.

6. Indefinite integrals and improper integrals.
Definition and convergence analysis of improper integrals.

7. Integration techniques. 
Integration by parts, integration of rational functions, integration of trigonometric functions and integration by substitution. 

8. Series.
Numerical series: convergence definition and criteria. Power series.

NAO