Calculus I

Base Knowledge

Trigonometry and elementary geometry Study of Functions and their inverse Trigonometric Functions Differential Calculus

Teaching Methodologies

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 software.

Learning Results

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

Program

Real functions of one real variable: Limit and continuity; Basic theorems; Trigonometric and inverse trigonometric functions; Basic properties of the Logarithm and the Exponential.

Integral calculus: Primitives, integration by parts, integration by substitution and integration of rational functions; Definite integral (Riemann’s integral) and the fundamental theorem of calculus; Applications of integration to the calculation of area, volume and length; Indefinite integrals and improper integrals.

Numerical Analysis: Root determination of non-linear equations: bisection method, Newton-Raphson method. Numerical integration: trapezoidal rule and Simpson’s rule.

An introduction to numerical series. Convergence criteria and power series.

Curricular Unit Teachers

Internship(s)

NAO

Bibliography

Main Bibliography

Notes and practical sheets made available, weekly, by the teacher on the MOODLE platform.

 

Secondary Bibliography

Available on the MOODLE platform

FAULHABER, C.- “Apontamentos teóricos e exercícios práticos de Análise Matemática I”-Curso de Electromecânica

CARREIRA, R.-“Notas teóricas de Análise Matemática”