Computational Methods

Recommended Prerequisites

General Mathematics.

Teaching Methods

Classes are theoretical and theoretical-practical. Teaching methods are predominantly expository in theoretical components. In the practical components, problems are solved under the guidance of the teacher. In the exhibition, a strong interaction prevails between the concepts and their concrete application, giving a central role to the visualization and analysis of particular situations. The use of technologies in the classroom is promoted, namely specialized software (Matlab, Scilab, …), as it is understood that these tools facilitate the understanding of the various concepts.

Learning Outcomes

The aim of this curricular unit is to strengthen the mathematical bases of students with knowledge in the area of numerical methods, also introducing the fundamental concepts of differential equations, in an applied perspective. These concepts will be fundamental in subsequent courses of the course and it is essential to ensure that all students have an adequate level of knowledge in this area. It is also intended to develop critical thinking and the ability to interpret real problems, opting for an applied approach, considering the specific course in which it is inserted. The use of technological tools in the classroom is encouraged, namely symbolic, numerical and graphic computing software, promoting the ability to learn and explore independently.

Work Placement(s)

No

Syllabus

1. Introductory concepts

  a. Matrix concept and matrix operations

  b. Matrix representation of systems of linear equations and matrix inversion

  c. Methods for solving equation systems

 

2. Numerical methods

   a. Numerical solution of non-linear equations. Newton and fixed point methods.

   b. Systems of nonlinear equations.

   c. Polynomial interpolation and “Splines”.

   d. Numerical calculation of derivatives.

   e. Numerical integration.

 

3. Introduction to differential equations

  a. Differential equations and their applications

  b. Numerical solution of differential equations - Taylor and Runge Kutta methods.

Head Lecturer(s)

Anísio Alberto Martinho de Andrade

Assessment Methods

Assessment
Resolution Problems: 40.0%
Frequency: 60.0%

Bibliography

[1] Abreu, J.M., Carmo, J.S.A. (2015) - Métodos Numéricos em Engenharia, DEC-FCTUC.

[2] Chapra, S.C. (2017) - Applied Numerical Methods with MATLAB for Engineers and Scientists. McGraw-Hill, 4th Ed.

[3] Chapra, S.C., Canale, R.P. (2015) - Numerical methods for engineers. McGraw-Hill, 7th Ed.

[4] Young, T, Mohlenkamp, M.J. (2015) - Introduction to Numerical Methods and Matlab Programming for Engineers. Ohio State University.