Numerical Analysis II
Code
10982
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Luís Manuel Trabucho de Campos
Weekly hours
5
Teaching language
Português
Subject matter
Numerical Analysis II
1-Numerical Matricial Analysis
-Matrix condition number
-Iterative methods for the solution of a system of equations: Jacobi, Gauss-Seidel, Relaxation, Gradient Methods.
-Iterative methods for the calculation of eigenvalues and eigenvectors; Power method, Jacobi.
2-Numerical solution of Ordinary Differential Equations
-Euler Method;
-Taylor method;
-Runge-Kutta methods;
-Multistep methods (implicit and explicit);
-Predictor–corrector methods;
-Higher-order equations and systems of differential equations.
-Finite Difference Methods
Bibliography
BURDEN, R.L.; FAIRES, J.D. (1993) -- Numerical Analysis (fifth edition), Prindle, Weber & Schmidt, Boston.
PINA, H. (1995) -- Métodos Numéricos, McGrawHill.
CIARLET, P.G. (1985) -- Introduction à l''''Analyse Numérique
Matricielle et à l''''Optimisation, Masson, Paris.
CROUZEIX, M. and A. MIGNOT (1984) -- Analyse
Numérique des Equations Differentielles, Masson, Paris.
RAVIART, P.A. and J.M. THOMAS (1983) -- Introduction
a l''''Analyse Numérique des Equations aux Derivées Partielles, Masson,
Paris.
BRAUN, M. (1993) -- Differential Equations and their applications (4th edition). Springer-Verlag.
ISAACSON, E. and H.B. KELLER (1994) -- Analysis of Numerical Methods, Dover.
Teaching method
The theory is explained and illustrated with examples. Main results are proved. The students are given the opportunity of working some problems, with the instructor´s support if needed, and the instructor´s comments on relevant results highlighted in the problems.
Evaluation method
1. The assessment will be done through two tests (T1, T2) and six homeworks (Tr1, Tr2, Tr3, Tr4, Tr5, Tr6) each one chosen from a different group of homeworks.
2. Each test will be will be graded 0-20 values and will be worth 7/20 of the final grade.
3. Each homework will be will be graded 0-20 values and will be worth 1/20 of the final grade.
4. To pass, students must obtain a final classification equal to, or higher than 10.