Code: | M232 | Acronym: | M232 |
Keywords | |
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Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Responsible unit: | Department of Mathematics |
Course/CS Responsible: | Bachelor in Physics |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
L:AST | 2 | Plano de Estudos a partir de 2008 | 2 | - | 7,5 | - | |
L:B | 1 | Plano de estudos a partir de 2008 | 3 | - | 7,5 | - | |
L:F | 0 | Plano de estudos a partir de 2008 | 3 | - | 7,5 | - | |
L:G | 0 | P.E - estudantes com 1ª matricula anterior a 09/10 | 3 | - | 7,5 | - | |
P.E - estudantes com 1ª matricula em 09/10 | 3 | - | 7,5 | - | |||
L:Q | 0 | Plano de estudos Oficial | 3 | - | 7,5 | - |
Familiarize the students with robust numerical methods used in solving mathematical problems in science and engineering, including their conditions of applicability and their limitations, with a particular emphasis on applications and the development of algorithms in solving problems. It is intended that the students acquire the knowledge necessary to identify and use the most robust numerical methods in solving problems.
The student must show skills in solving numerically mathematical problems in the areas described.
Error theory:
Types of errors. Absolute and relative error. Rounding error and truncation error. Propagation of the error. Computation of the sum of a convergent series.
Nonlinear equation:
Root finding methods: bisection method, fixed point method , Newton method and variants. Systems of linear equations:
Direct methods. Gauss elimination. Pivoting.
Polynomial interpolation:
Lagrange method. Error in interpolation. Aitken-Neville method. Divided differences. Newton method. Inverse interpolation.
Approximation:
Least squares polynomial approximation of a set of points. Generalized least squares approximation. Least squares approximation of a function defined in an interval.
Numerical differentiation and integration:Newton-Cotes formulas. Simple and composite rules of rectangles, trapezium and Simpson. Truncation errors. Numerical differentiation formulas.
Lectures, problems and computational projects.
designation | Weight (%) |
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Participação presencial | 0,00 |
Teste | 60,00 |
Trabalho laboratorial | 40,00 |
Total: | 100,00 |
designation | Time (hours) |
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Estudo autónomo | 0,00 |
Frequência das aulas | 0,00 |
Total: | 0,00 |
A minimum of 3.5 points in the practical classification.
Theoretical classification (CT): Sum of the classifications of 4 tests ( 3 points each) or a final examination (12 points)
Practical classification (CP): sum of classifications obtained in 4 practical tests (2 points each)
Final classification (CF): CT+CP
One final examination (theoretical and practical).