### Análise e Computação Numérica - Matemática - Sem Ramos - Especialidades

7.5
ECTS / Credit Units
 Year: 2 / 2º Semestre Plan: 2015/16 Scientific Area: MAT Level: Intermédio

 Theorical: 48.00 Theorical-Pratical: 32.00 Pratical and Laboratorial: Fieldwork: Seminar: Internship: Tutorial:
 Assigned Internship Hours: Assigned Projects Hours: Assigned Fieldwork Hours: Assigned Study Hours: Assigned Evaluation Hours: Others:

### Degree having this Course

Degree - Branch Degree Plan Year
Matemática - Sem Ramos - Especialidades 2015/16

### Teaching Staff

Luís Filipe Silva Camacho

Responsibilities:
Ensino teórico-prático
Luiz Carlos Guerreiro Lopes

Responsibilities:
Regência
Responsável pelas Pautas
Ensino teórico

## Course Information

### Course Objectivs

This course aims to provide the students with basic knowledge on numerical methods for solving mathematical problems in science and engineering, emphasizing the analysis of the errors involved in the numerical approximations, the effects of finite-precision computer arithmetic, the construction and implementation of numerical algorithms, and the analysis of their theoretical properties.

### Evaluation Criteria

Classification Type: Quantitative (0-20)
Evaluation Model: A
Evaluation Methodology: The teaching methodology includes lectures and problem-solving classes, with the use of whiteboard, notebook, and video projector. The adopted evaluation methodology consists of three individual written tests: Test #1 ? weight 1/3 (topics 1 to 4 of the syllabus); Test #2 ? weight 1/3 (topics 5 to 7); Test #3 ? weight 1/3 (topics 8 and 9).

### Program Resume (get program detail)

1. Floating point systems and programming languages for numerical computation.
2. Numerical error theory, conditioning, and stability.
3. Direct and iterative methods for the solution of systems of linear equations.
4. Solution of nonlinear equations and polynomial zeros.
5. Numerical solution of systems of nonlinear equations.
6. Function interpolation and approximation.
7. Numerical integration and differentiation.
8. Numerical methods for the solution of initial-value problems in ordinary differential equations.
9. Introduction to finite difference methods for partial differential equations.

### Main Bibliography

R. L. Burden, J. D. Faires (2010). Numerical analysis. Brooks/Cole.
H. Pina (2010). Métodos numéricos (9789725922842). Escolar.
A. Quarteroni, R. Sacco, F. Saleri (2007). Numerical mathematics. Springer-Verlag.
M. R. Valença (1993). Métodos numéricos. Livraria Minho.
A. Quarteroni, F. Saleri, P. Gervasio (2014). Scientific computing with MATLAB and Octave. Springer-Verlag.
J.H. Mathews, K.D. Fink (2004). Numerical methods using MATLAB. Pearson Prentice Hall.
F.F. Campos Filho (2007). Algoritmos numéricos. LTC.
D.M. Claudio, J.M. Marins (2000). Cálculo numérico computacional: teoria e prática. Atlas.
N.J. Higham (2002). Accuracy and stability of numerical algorithms. SIAM.
M. Ruggiero, V. Lopes (1996). Cálculo numérico: aspectos teóricos e computacionais. Makron Books.
S.R. Otto, J.P. Denier (2005). An introduction to programming and numerical methods in MATLAB. Springer-Verlag.
J. Stoer, R. Bulirsch (2010). Introduction to numerical analysis. Springer.