Numerical Analysis II
Keywords |
Classification |
Keyword |
OFICIAL |
Mathematics |
Instance: 2011/2012 - 1S
Cycles of Study/Courses
Teaching language
Portuguese
Objectives
The main aim of this subject is is given a mathematical problem, to study sufficient conditions for the existence and unicity of its solution, to establish a constructive method to solve it, to study and control the errors involved, to give an algoritmh for the solution and to implement it in a computer and to study and interpret the numerical results.
The following fundamental mathematical problems will be treated: the solution of systems of linear or nonlinear equations, computation of eigenelements of a matrix and the integration of ordinary differential equations.
Program
Systems of linear equations
Norms and limits of vectors and matrices. Direct methods. Gauss elimination. Pivoting. Inversion of regular matrices.
Sensibility to error in data. Iterative refinement of the solution of a system and of the inverse of a matrix.
Systems of nonlinear equations
Fixed point methods. Newton method.
Numerical integration of differential equations
Existence theorems. One-step methods: Euler, predictor-corrector, Taylor and Runge-Kutta methods. Consistence and convergence of one-step methods.
Numerical integration
Orthogonal polynomials. Gauss-Legendre Integration.
Eigenvalues
Gerschgorin theorems. Rayleigh coefficient.
Power method. Deflaction. Jacobi method. Triadiagonalization of matrices: Givens rotations and Householder reflections.
Mandatory literature
000071361. ISBN: 972-8298-04-8
000081959. ISBN: 2-7298-2246-1
000087488. ISBN: 978-2-7298-2887-5
000040213. ISBN: 0-8018-5414-8
Teaching methods and learning activities
Lectures, problems and computational projects.
Software
Python, Scilab or Maxima
Evaluation Type
Distributed evaluation without final exam
Assessment Components
Description |
Type |
Time (hours) |
Weight (%) |
End date |
Attendance (estimated) |
Participação presencial |
75,00 |
|
|
|
Total: |
- |
0,00 |
|
Eligibility for exams
A minimum of 3.5 points in the practical classification.
Calculation formula of final grade
Theoretical classification (CT): Sum of the classifications of 2 tests ( 5 points each)
Practical classification (CP): sum of classifications obtained in 4 practical tests (2.5points each)
Final classification (CF): CT+CP