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
Objectives
An introduction to Numerical Linear Algebra
An introduction to numerical methods to solve ordinary and partial differential equations.
Prerequisites
Background in Analysis (I A, II A and III A) and Algebra (Linear Algebra I and II).
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.
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.
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 three tests (T1, T2, T3).
2. The tests will all have the same weight. Each test will be graded 0-20 values.
3. To pass, students must obtain a final classification equal to, or higher than 10. The final classification (CF) is obtained by rounding the following value (V), to the units
V = (C1 + C2 + C3) / 3,
where C1, C2 and C3 represent the grades of tests T1, T2, T3, respectively.
Example: if V = 12.4 then CF = 12; if V = 12.5 is then CF = 13.
4. An exam will take place after the end of the course for those who did not succeed. The classification will be an integer from 0 to 20. The student will pass if the classification is 10 or higher, in a maximum of 20.