Matemática II

Differential calculus in IR

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), using pedagogical resources: problem solving; technology.

It is intended that students:

1. Analyse and apply the rules and methods of primitivation in IR appropriately

2. Calculate indefinite integrals, definite integrals and improper integrals in IR.

3. Identify the different types of first order ordinary differential equations and evaluate which is the adequate method to solve each case. Solve second order linear differential equations with constant coefficients.

4. Calculate partial derivatives of a real function of vector variable and evaluate the extrema of such function.

5. Apply the principal numerical methods to approximate functions. Estimate the value of a derivative and an integral using derivation and numerical integration methods.

1. Integration and applications

2. Differential equations

3. Functions of several variables and optimization

4. Introduction to Numerical Methods

• - Exam - 100.0%

• - Frequency - 90.0%
• - Mini Tests - 10.0%

NAO

Campos Ferreira, J. (2014). Introdução à Análise Matemática (11ªEd). Fundação Calouste Gulbenkian.

Figueiredo, D. G., Neves, A.F. (2018). Equações Diferenciais Aplicadas (3ªEd). Instituto Nacional de Matemática Pura e Aplicada.

James, G. (2020). Modern Engineering Mathematics (6th Ed). Pearson.

Lima, E. L.(2016). Análise no Espaço lRⁿ (2.ª ed.). Instituto Nacional de Matemática Pura e Aplicada.

Lima, E.L. (2016). Análise Real – Vol. 2 (6.ª ed.).  Instituto Nacional de Matemática Pura e Aplicada.

Kreyszig, E. (2011).  Advanced Engineering Mathematics (10th Ed). John Wiley & Sons.

Stewart, J. (2017).  Cálculo, Vol. 2 (8ª Ed.). São Paulo: Cengage Learning.