Numerical Calculus D
Objectives
Students 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.
Students must also be able to implement computational algorithms in order to solve the aforementioned problems.
General characterization
Code
12038
Credits
3.0
Responsible teacher
António Manuel Morais Fernandes de Oliveira
Hours
Weekly - 3
Total - 42
Teaching language
Português
Prerequisites
Available soon
Bibliography
- Atkinson K., An Introduction to Numerical Analysis, Wiley, Second Edition, 1989.
- Burden R. e Faires J. , Numerical Analysis, Brooks-Cole Publishing Company, 9th Edition, 2011.
- Conte S. e Boor C., Elementary Numerical Analysis: an algorithmic approach, Mc Graw Hill, 1981.
- Isaacson E. e Keller H., Analysis of Numerical Methods, Dover, 1994.
- Martins, M. F. e Rebelo M., Introdução à Análise Numérica, Casa das Folhas, 1997.
- Pina H., Métodos Numéricos, Mc Graw Hill, 1995.
- Valença M. R., Métodos Numéricos, Livraria Minho, Terceira Edição, 1993.
Teaching method
Available soon
Evaluation method
Available soon
Subject matter
1. Errors
Absolute error, relative error, significant digits. Condition number. Numerical algorithms stability.
2. Polynomial approximation and interpolation
Polynomial interpolation: Lagrange and Newton formulas, cubic Spline interpolation.
Least squares approximation.
3. Numerical integration
Newton-Cotes integration formulas, Gaussian integration.
4. Rootfinding for nonlinear equations
Bissection method, fixed-point iteration, Newton method, Secant method.
5. Linear systems
Vector norms and induced matrix norms.
Eigenvectors and eigenvalues. Gershgorin theorem.
Iterative methods: general procedure, Jacobi method, Gauss-Seidel method, SOR method.
6. Numerical solution of ODE
Euler methods, Taylor methods for higher orders, Runge-Kutta methods.