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Computational Mathematics

Code 10356
Year 2
Semester S2
ECTS Credits 6
Workload TP(60H)
Scientific area Mathematics
Entry requirements -
Mode of delivery Face to face.
Work placements There isn't.
Learning outcomes The general objective of this course is the study of efficient and stable numerical methods for solving certain mathematical problems. The study of each numerical method includes the analytic deduction of the formulae used, the description in algorithmic language and the presentation of techniques to estimate the solution error.

Syllabus 1. Errors and respective propagation.
2. Roots and extreme values of functions.
3. Solution of systems of linear and non-linear equations.
4. Interpolation, curve adjustment and function approximation.
5. Numerical differentiation and integration.
6. Numerical methods for differential equations and systems of differential equations; consistency, stability and convergence.
Main Bibliography I. Main references

• R.L. Burden & J.D. Faires , " Numerical Analysis 9e", 2011, Brooks/Cole, Cengage Learning.
• H. Pina, "Métodos Numéricos", Mc Graw-Hill, Alfragide, 1995.
• M.R. Valença , "Métodos Numéricos", INIC, Braga, 1988.

II. Secondary references

• J.C. Butcher , "The Numerical Analysis of Ordinary Differential Equations", John Wiley & Sons, Auckland, 1987.
• E. Hairer , S.P. Nørsett & G. Wanner , " Solving Ordinary Differential Equations I ", Springer Series in Comput. Mathematics, Vol. 8, Springer-Verlag, Heidelberg, 1987.
• E. Hairer & G. Wanner , " Solving Ordinary Differential Equations II ", Springer Series in Comput. Mathematics, Vol. 8, Springer-Verlag, Heidelberg, 1987.
Teaching Methodologies and Assessment Criteria The curricular unit works with classes on a non-classroom basis through the Zoom platform, and with the completion of proposed tasks. In addition, the student is encouraged to interact with the teacher and colleagues, and to work autonomously, in the form of exercises, formulation and problem solving. The teacher is available at predetermined times on the Zoom platform or via email to answer questions.
The continuous evaluation will be done through the accomplishment of small tasks during the classes, quoted in a total of 4 values and two frequencies with a quotation of 8 values each. The student may also take a final exam quoted for 20 values.
Language Portuguese. Tutorial support is available in English.
Last updated on: 2024-04-05

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