Matemática II

Base Knowledge

Differential calculus in IR

Teaching Methodologies

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.

Learning Results

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, assess the appropriate method for solving each one and apply it correctly. 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 numerical methods of derivation and integration .

 

Program

1. Integration and applications

2. Differential equations

3. Functions of several variables and optimization

4. Introduction to Numerical Methods

Curricular Unit Teachers

Carla David Reis

Grading Methods

Periodic Evaluation
  • - Mini Tests - 10.0%
  • - Frequency - 90.0%
Normal / Resource Assessment
  • - Exam - 100.0%

Internship(s)

NAO

Bibliography

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.