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IPLUSO 3561

Computational Mathematics

Automation and Computer Systems
  • ApresentaçãoPresentation
    Mathematics
  • ProgramaProgramme
    S1. Arithmetic in finite precision. Representation of integers and real numbers. Errors in floating point arithmetic. Error propagation. S2. Nonlinear equations. Bisection, false position and secant, Newton and fixed point methods. Zeros of polynomials. S3. Systems of linear equations. Gaussian elimination. Calculation of the inverse and determinant. Iterative methods. S4. Polynomial interpolation. Polynomial forms. Lagrange interpolators. Equidistant nodes. Interpolation formulas. Cubic splines. S5. Numerical differentiation and numerical integration. First and second order derivatives. Newton-Cotes rules. S6. Use of software (Octave) to solve computational mathematics problems.
  • ObjectivosObjectives
    LO1. Understand the fundamentals of the numerical methods studied as well as their framing in the engineering context; LO2. Develop in students the ability to implement the algorithms necessary for the numerical solution of problems in various areas (interpolation, integration, differentiation, non-linear equations, differential equations, systems of equations); LO3. Introduce students to the use of specific software (Octave) to solve computational mathematics problems.
  • BibliografiaBibliography
    Atkinson, K. Numerical Analysis, John Wiley and Sons, New York; Chapra, S. e Canale, R. Numerical methods for Engineers, McGraw-Hill Book Company-New York Conte, S. e Boor, C. Elementary Numerical Analysis, McGraw-Hill Ledermann, W. Handbook of Applicable Mathematics Numerical Methods (vol.III), Jonh Wiley and Sons- New York Pina, Heitor. Métodos Numéricos, McGraw-Hill-Lisboa Ruggiero, M. e Lopes, V. C_alculo Numérico - Aspectos Teóricos e Computacionais, McGraw-Hill do Brasil Lta-S:Paulo  
  • MetodologiaMethodology
    The teaching of this curricular unit includes: Theoretical classes (expository); Theoretical-practical classes (exercise solving); Practical classes (to help solve projects that require computational methods, in which Octave is used).
  • LínguaLanguage
    Português
  • TipoType
    Semestral
  • ECTS
    6
  • NaturezaNature
    Mandatory
  • EstágioInternship
    Não