Computational Methods in Engineering
Code
10437
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
3.0
Teacher in charge
António Manuel Morais Fernandes de Oliveira
Weekly hours
3
Total hours
42
Teaching language
Português
Objectives
The student must be able to apply numerical methods for mathematical problems, such as, non linear equations, approximation of functions, integration, systems of equations and ordinary differential equations.
The student must also be able to implement computational algorithms in order to solve the aforementioned problems.
Prerequisites
Students must have basic knowledge in mathematical analysis (AMI) and linear algebra (ALGA).
Subject matter
1. Introduction
- Floating point arithmetic. Error and error propagation. Conditioning of a problem and stability of a method.
2. Interpolation and approximation of functions.
- Polynomial interpolation: Lagrange polynomial.
- Discrete least squares approximation.
3. Numerical integration.
- Newton-Cotes formulas. Composite rules.
- Gaussian quadrature.
4. Nonlinear equations.
- Bissection method
- Fixed point and Newton methods.
- Order of convergence.
5. Numerical methods in linear algebra
- Vector norms and induced matrix norms.
- Eigenvalues and eigenvectors.
- Iterative methods for linear systems of equations
- Jacobi and Gauss-Seidel methods
6. Numerical methods for ordinary differential equations.
- Taylor and Runge-Kutta methods.
Bibliography
ATKINSON, K., An Introduction to Numerical Analysis, Wiley, 1989.
BURDEN, R.; FAIRES, D., Numerical Analysis (8th Edition) - Brooks-Cole Publishing, 2004.
KINCAID D., CHENEY W., Numerical Analysis: mathematics of scientific computing, Brooks-Cole, 2002.
MARTINS, M. F., Introdução à Análise Numérica, Casa das Folhas, 1997.
VALENÇA, M. R., Análise Numérica, Universidade Aberta, 1996.