Computational Methods in Physics and Engineering

Code: FIS10346M

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Physics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

Regime de Frequência: Presencial

Sustainable Development Goals

4. Educação de qualidade - Assegurar a educação inclusiva, e equitativa e de qualidade, e promover oportunidades de aprendizagem ao longo da vida para todos.

Learning Goals

The student must acquire competences on fundamentals of numerical methods and must be able to use those methods to solve practical application problems in physics and engineering.

1. Introduction - The actual paradigm in computation, computational algorithms and languages, computational arithmetic
2. Basic numerical methods - operation with matrix, differentiation and integration, interpolation, nonlinear equations, systems of linear equations, systems of nonlinear equations, approximation of functions
3. Differential equations - Ordinary differential equations and partial differential equations
4. Modelling of continuous systems - diffusion equation, wave equation and hydrodynamic equations
5. Spectral analysis - continuous Fourier transform, discrete Fourier transform, FFT, determination of spectral energy density
6. Optimization and inversion - Linear programming, quadratic, nonlinear and integer; linear and nonlinear inverse problem, least square method, Baysian formulation of inverse problem, a priori information, analysis of resolution and errors.

Teaching Methods

- Theoretical classes
- Practical classes for resolution of problems proposed in the classes

Students will be assessed by:
N1 - resolution of a set of problems (30%)
N2 - 1 main report (40%)
N3 - Exam (30%)