| Code |
14809
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| Year |
3
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
NA
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Learning outcomes |
With this curricular unit it is intended that the student obtain numerical tools to solve the most varied mathematical problems.
At the end of this curricular unit the student should be able to:
a) calculate numerically approximations for the eigenvalues and eigenvectors of a matrix;
b) solve numerically systems of non-linear equations;
c) use computational methods to solve nonlinear programming problems;
d) approximate functions;
e) obtain numerically solutions of ordinary differential equations with values at the boundary;
f) solve differential equations with partial derivatives by numerical methods;
g) in face of a proposed problem, translate it mathematically, identify possible methods to solve it, choose the most appropriate, implement it and critically analyze the results.
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Syllabus |
1. Approximation of eigenvalues and eigenvectors
2. Numerical Solution of Nonlinear Systems of Equations
3. Nonlinear optimization
4. Approximation of functions
5. Boundary-Value Problems for Ordinary Differential Equations
6. Numerical Solutions to Partial Differential Equations
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Main Bibliography |
• H. Pina, "Métodos Numéricos", Mc GrawHill, Alfragide, 1995.
• M.R. Valença, "Métodos Numéricos", INIC, Braga, 1988.
• R.I. Burden & J.D. Faires & A.M. Burden, "Numerical Analysis 10e", PWSKent, Boston, 2015.
• J.C. Butcher, "The Numerical Analysis of Ordinary Differential Equations 2e", John Wiley & Sons, Auckland, 2
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Teaching Methodologies and Assessment Criteria |
The curricular unit is structured in theoretical-practical classes. The teacher introduces the concepts, states and proves the fundamental results, provides examples and applications. The combination of the theory with the practice in the classes allows the exercises to be performed immediately after each theoretical content, which improves the acquisition of knowledge and skills. In addition, the student is encouraged to participate in classes, to interact with the teacher and with colleagues, and to work autonomously, in the form of exercises, formulation and problem solving.
The evaluation carried out during the teaching-learning process consists of one written test quoted for 12 values and small projects of an analytical and computational nature that involve the application of the studied methods,quoted for 8 values in total. The student can also take a final exam quoted for 20 values.
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Language |
Portuguese. Tutorial support is available in English.
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