Métodos Numéricos

Theoretical classes present the theoretical foundations of each topic, complemented by practical examples and exercises. In laboratory classes, students use Matlab software to implement the numerical methods studied, solving practical problems and analyzing results. The Moodle platform is used to provide supporting materials, such as lecture notes, exercises, and challenges, promoting autonomous and collaborative learning. The teaching methodology encourages the practical application of knowledge, the development of programming skills, and critical analysis capabilities.

The objectives of this curricular unit include equipping students with numerical tools to obtain approximate solutions for problems where exact analytical solutions are not feasible. Students are expected to develop skills in applying numerical methods, analyzing errors, and using computational software (Matlab) to implement algorithms and solve practical problems. The curricular unit fosters judgment, decisionmaking, communication, and self-learning skills, preparing students to tackle practical and theoretical challenges in the field of Industrial Engineering and Management.

1. Error theory: introduction and error analysis.
2. Nonlinear equations: bisection and Newton’s methods; stopping criteria; computational aspects.
3. Polynomial interpolation: Lagrange and Newton polynomials; divided and finite differences; inverse interpolation; interpolation error.
4. Numerical integration: Newton-Cotes rules (trapezoidal and Simpson’s); error analysis; computational aspects.
5. Numerical integration of first-order initial value problems: Euler and Runge-Kutta methods (2nd and 4th order); error analysis; computational aspects.
6. Solving linear systems: Jacobi and Gauss-Seidel iterative methods.

• - Test - 60.0%
• - Practical activity - 20.0%
• - Practical project - 20.0%

NAO