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IPLUSO 3561

Computational Mathematics

Computer Engineering and Applications
  • ApresentaçãoPresentation
    In many engineering applications the need arises to solve mathematical problems that either do not have an analytical solution, or the analytical solution is too computationally expensive to determine. In those situations, an approximate solution can often be obtained using numerical analysis algorithms. In this curricular unit we study a set of algorithms that solve some of the most common classes of problems, ranging from determining the zeros of non-linear equations to solving ordinary differential equations. This knowledge plays a central role in an engineering course, given the complexity of many real life mathematical models.
  • ProgramaProgramme
    1. Floating point Arithmetics. Representation of integer and real numbers. Errors in floating point arithmetics. Error propagation. 2. Non-linear equations. Bissection method, false position and secant. Newton and fixed point methods. 3. Systems of linear equations. Iterative methods. 4. Systems of non-linear equations. Newton's method. 5. Polynomial interpolation. Polynomial forms. Interpolation formulas. 6. Numerical differentiation. First and second order derivatives. 7. Numerical integration. Simple and composite rules. 8. Ordinary differential equations. Euler's and Runge-Kutta's methods. Convergence. Errors
  • ObjectivosObjectives
    The main outcome is to teach the students the techniques used in the solution of mathematical problems which do not have any analytical solution, thus familiarizing them with the numerical solution of common problems (function interpolation, numerical integration and differentiation, non-linear equations, differential equations, systems of equations). In addition, students are intended to gain the capacity to implement the algorithms thaught in the theoretical classes, using them to solve problems proposed during the curricular unit.
  • BibliografiaBibliography
    Atkinson, K. - Numerical Analysis. John Wiley and Sons, New York; Chapra, S. and Canale, R. - Numerical methods for Engineers. McGraw-Hill Book Comp-New York Pina, Heitor - Métodos Numéricos. McGraw-Hill-Lisboa  
  • MetodologiaMethodology
    Using MATLAB / Octave in class to demonstrate in an interactive way some of the concepts of the curricular unit.
  • LínguaLanguage
    Português
  • TipoType
    Semestral
  • ECTS
    6
  • NaturezaNature
    Mandatory
  • EstágioInternship
    Não