Teaching Methodologies
Classes are taught under theoretical and practical regime. An expository methodology is used for the presentation of the concepts of the course, supported by the resolution of proposed exercises of application of the concepts transmitted. Some of these exercises are based on real-life practical problems.
Learning Results
To give the students some numerical methods and techniques existent for the resolution of concrete problems, that occur in the most diverse areas, and that are not always solved in a direct (analytical) way.
To develop the capacity of selecting the methods that better adapt themselves to the resolution of several problems studying their efficiency, applicability and stability.
To introduce the discussion of the obtained numerical results.
Program
Chapter 1 – Errors theory
Basic definitions of the errors theory
Chapter 2 – Non-linear equations
2.1 Bisection method
2.2 Newton method
2.3 Secant method
Chapter 3 – Systems of linear equations
3.1 Jacobi method
3.2 Gauss-Seidel method
Chapter 4 – Polynomial Interpolation
4.1 Lagrange interpolation
4.2 Newton interpolation of the divided differences
4.3 Square minimums method
Chapter 5 – Numerical Differentiation and Integration
5.1 Numerical differentiation
5.2 Numerical integration
Chapter 6 – Ordinary differential problems
6.1 Euler methods
6.2 Runge-Kutta methods
Internship(s)
NAO
Bibliography
[1] Araújo, A., Sebenta de Análise Numérica, FCTUC, Coimbra, 2002.
[2] Atkinson, K. E., An Introduction to Numerical Analysis, John Wiley and sons, New York, 1989.
[3] Burden, R. I. e Faires, J. D., Numerical Analysis, PWSKent,
Boston, 1988.
[4] Neves, C., Métodos Numéricos, ISCAC, Coimbra, 2012.
[5] Pina, Heitor, Métodos Numéricos, McGrawHill,
Alfragide, 1995.
[6] Valença, M. R., Métodos Numéricos, INIC, Braga, 1988.