Class Mathematical Analysis II

This curricular unit (UC) is part of the curricular plan of this degree, which will provide the necessary mathematics knowledge for successful learning in subsequent curricular units.

This UC aims to introduce the fundamental concepts about the propagation of uncertainties, the methodologies and applications of the integral calculus of functions with 1 variable and the techniques for solving 1st and 2nd order differential equations.

Part I – Uncertainties and propagation of uncertainties

1 – Concepts of absolute error, relative error, absolute uncertainty and relative uncertainty

2 – Rounding and truncating

3 – Propagation of uncertainties

PART II - Integral calculation

1 - Undefined Integral

1.1 - Definition and Properties

1.2 - Immediate primitives

1.3 - Integration methodologies (immediate primitiveness, by substitution and by parts)

1.4 - Integration of certain classes of functions: polynomial, rational, irrational and transcendent

2 - Defined integral

2.1 - Definition, properties and geometric meaning

2.2 - Calculation and applications

3 - Improper integrals

4 - Integration of functions with more than one variable

4.1 - Fundamental concepts, calculation and applications

Part III - Ordinary differential equations (EDO)

1 - Definitions

2 - Initial and boundary conditions

3 - Integration of the main 1st and 2nd order EDO

In this UC, some active methodologies will be used that promote greater student involvement in activities, such as learning through PBL and Formative assessments with feedback. In terms of digital technologies, Moodle will be used.

- Azenha, A., Jerónimo, M. E. (1995), Elementos de Cálculo Diferencial e Integral em IR e IRn, Editora MacGraw Hill.

- E.W. Swokowski (1995), Cálculo com Geometria Analítica (Vol.1 e II), Makron Books.

- B. Demidovitch, Problemas e Exercícios de Análise Matemática, McGraw-Hill.

- Textos de apoio e coleções de exercícios fornecidos ao longo das aulas pelos docentes