| Code |
15967
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| Year |
2
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
PL(30H)/TP(30H)
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| Scientific area |
Mathematics
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Entry requirements |
The student should already be able to:
- calculate derivatives of an actual function;
- operate with matrices;
- use the concept of linear combination in polynomial vector spaces;
- efficiently use the calculator as an auxiliary calculation tool.
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Learning outcomes |
With this curricular unit it is intended that the student obtain numerical tools to solve the most varied problems in chemistry and related areas.
At the end of this curricular unit the student should be able to:
a) perform simple mathematical operations on Matlab with scalars, vectors or matrices;
b) solve simple problems by exploiting the symbolic and graphic capabilities of the computer;
c) program small routines;
d) analyze the errors and determine their propagation;
e) numerically determine function zeros;
f) numerically solve systems of equations;
g) interpolate and approximate functions;
h) integrate functions numerically;
i) implement the numerical methods studied in problem solving;
j) apply the acquired knowledge to practical problems, namely in the area of Chemistry.
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Syllabus |
1. Matlab programming:
1.1. Matlab initiation;
1.2. symbolic calculation;
1.3. introduction to programming.
2. Error theory.
3. Nonlinear equations:
3.1. bisection method;
3.2. fixed point method;
3.3. Newton's method.
4. Systems of equations:
4.1. direct methods and numerical instability;
4.2. iterative Jacobi and Gauss-Seidel methods;
4.3. Newton's method.
5 Interpolation and polynomial approximation:
5.1. Lagrange’s formula;
5.2. Newton's formula;
5.3. interpolation by segmented polynomials;
5.4. least squares method.
6. Numerical Integration:
6.1. Newton-Cotes rules;
6.2. Gauss quadrature.
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Main Bibliography |
- V. Morais & C. Vieira, “MATLAB - Curso Completo”, FCA, 2003
- Amos Gilat, “MATLAB: An Introduction with Applications, 6 edition”, John Wiley & Sons, Inc., 2017
- 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.
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Teaching Methodologies and Assessment Criteria |
The curricular unit works with theoretical-practical classes and laboratory practices. The teacher exposes the concepts, enunciates and demonstrates fundamental results, presents examples and applications in theoretical-practical classes. The lab classes work in a computer-equipped lab where the student is encouraged to participate in classes, interact with the teacher and colleagues, and work autonomously in the form of exercises, formulation and problem solving.
Continuous assessment will be done by performing two written tests of 8 values each and four mini tests to be performed on the computer during laboratory classes, worth 1 each. The student may 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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