Class Mathematics I

The course unit belongs to the compulsory group of curricular units and seeks to provide students with fundamental knowledge of mathematics, supplemented with Algebra and, in the second semester, with those of Mathematics II.

Not applicable

Revisions on fundamentals of mathematics (algebraic rules, logic, set theory, symbology). Analytical Geometry: Review of Essential Concepts on Plane Analytical Geometry: Straight and Circumferences; geometry in 3D space: points, vectors (definition, coordinates, operations with vectors), lines and planes. Study of real functions of real variable: review of the general study of functions; polynomial functions; rational functions; trigonometric functions and their inverses; exponentials and logarithmics; graphics. Derivation and differentiation. Geometric meaning of the derivative of a function at a point. Study of the variation of a function and ends of a function with recourse to derivatives. Multivariable functions: definitions; partial derivatives and their applications.

B-Learning teaching model, with a hybrid of synchronous remote classes (7 weeks) and face-to-face classes (8 weeks). Assessment model includes valuing class participation and weekly work outside of class (small homework assignments), to encourage continued dedication to the course. Support for students outside of class.

N. Piskounov. Cálculo Integral e Diferencial (Vol.I e II). Editora Lopes da Silva (there are other editions). B. Demidovitch. Problemas e Exercícios de Análise Matemática. Escolar Editora (there are other editions). Textos didáticos: Artur F. Costa (2018). Alguns elementos sobre teoria de conjuntos (5p.) Artur F. Costa (2020). Alguns elementos sobre geometria analítica (18p.) Artur F. Costa (2011). Conceitos de geometria analítica (manuscrito, 16p.) Artur F. Costa (2018). Alguns elementos sobre funções reais de variável real - Funções polinomiais e racionais (14p.) Artur F. Costa (2018). Alguns elementos sobre funções reais de variável real - Funções exponenciais e logarítmicas (4p.) Artur F. Costa (2018). Alguns elementos sobre funções reais de variável real - Funções trigonométricas (11p.) Artur F. Costa (2018). Alguns elementos sobre derivadas - Funções reais de variável real e funções multivariável (20p.) Outros fornecidos ao longo das aulas pelos docentes.