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Computational Mathematics

Code 14904
Year 2
Semester S2
ECTS Credits 6
Workload TP(60H)
Scientific area Mathematics
Entry requirements None
Learning outcomes With this curricular unit it is intended that the student obtain numerical tools to solve the most varied problems in physics and related fields.
At the end of this curricular unit the student should be able to:
a) analyze the errors and determine their propagation
b) determine numerically zeros of functions
c) calculate numerically extremes of functions
d) solve numerically systems of linear equations
e) interpolate and approximate functions
f) derive and integrate functions numerically
g) solve equations and systems of differential equations by numerical methods
h) 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
Syllabus 1. Theory of errors
2. Non-linear equations
3. Extremes of functions
4. Systems of linear equations
5. Interpolation and polynomial approximation
6. Differentiation and numerical integration
7. Ordinary differential equations with initial values
Main Bibliography 1. Pina H (1995). Métodos Numéricos. Alfragide: McGraw-Hill
2. Valença MR (1988). Métodos Numéricos. Braga: INIC
3. Burden RI, Faires JD and Burden AM (2015). Numerical Analysis, 10th edition. Boston: PWS-Kent
Teaching Methodologies and Assessment Criteria The course 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 two written tests quoted for 8 values each and four mini tests to be carried out on the computer during the classes, quoted for 1 value each. The student can also take a final exam quoted for 20 values.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2020-07-14

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