Mathematics Elements II

Knowledge of Mathematics covered in secondary school and in the course unit Elements of Mathematics I.

The following teaching methodologies are used in this curricular unit
1) Verbal methods (say), making use of the following educational resources: Exposition, Explanation, Dialogue and questioning;
2) Intuitive Methodologies (show), making use of the following educational resources: Demo, Audiovisual, written texts;
3) Active Methodologies (doing), making use of pedagogical resources: problem solving; technology.

Provide students with the basic mathematical knowledge needed in the professional training of a professional superior technician

1. Primitives

– Notion of primitive: motivation, definition and properties.

– Immediate primitives.

– Primitive methods: primitives by parts, by substitution and by decomposition.

2. Integral Calculus in ℝ

– Riemann Integral and its geometric interpretation; properties.

– Indefinite integral and its properties. Fundamental theorem of integral calculus and Barrow’s formula.

– Integration by parts and by substitution.

– Applications of integral calculus. – Improper integrals of the 1st and 2nd kind.

NAO

Azenha, A. & Jerónimo, M. A. (2000). Cálculo Diferencial e Integral em IR e IRⁿ. McGraw-Hill.

James, G., & Dyke, P. (2020). Modern engineering mathematics. Pearson Education Limited.

Larson, R., Hostetler, R. P. &  Edwards, B. H. (2006). Cálculo, Volume II. McGraw-Hill.

Pinto, G. (2015). Primitivas e Integrais – Exercícios resolvidos. Edições Sílabo.

Sequeira, F. (1982). Análise Matemática, 3º Volume – Exercícios Resolvidos e Propostos. Litexa Editora.