Numerical Calculus - Universidade Presbiteriana Mackenzie

UNIVERSIDADE PRESBITERIANA MACKENZIE
Academic Dean’s Office
University Unit:
School of Engineering
Program:
Electrical Engineering
Course:
Numerical Calculus
Workload:
4
Syllabus:
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Area:
Mathematics
Code:
ENEC00191
(4) Theory
(0) Practical
Numerical solution of linear systems and determinants.
Numerical inversion of matrix.
Solutions of equations.
Interpolation, regression and series for real functions.
Numerical integration.
Numerical solution of differential equation.
Program Content:
1.
2.
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6.
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8.
Matrices and Determinants: Definition. Notations. Operations. Properties. Practical
applications.
Linear System of Equations: Definition. Notation. Gaussian Elimination with total pivoting.
Practical applications.
Roots of Equations: Classification of functions. Zeros of a function. Geometric
interpretation. Graphic separation of roots. Bolzano theorem. Bisection Method, NewtonRaphson Method and Iterative Method. Practical applications.
Polynomial Interpolation: Definition. Approximation by polynomial interpolation. Error.
Newton-Gregory Interpolation. Practical applications.
Series: Taylor’s Formula. McLaurin’s Formula. Practical applications: limits, derivatives
and integrals.
Regression: Curve fitting. Method of Least Squares. Linear, polynomial, exponential and
potential regression. Practical applications.
Numerical Integration: Rectangular, Trapezoidal and Simpson’s rule. Practical
applications.
Differential Equations. Runge-Kutta Method.
Basic Bibliography:
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ZAMBONI, L. C.; MONEZI JR; O.; PAMBOUKIAN; S. V. D. Métodos Quantitativos e
Computacionais. São Paulo: Páginas & Letras, 2009. 523 p.
BURDEN, R. L.; FAIRES, J.D. Análise Numérica. 1.ed. São Paulo: Cengage Learning,
2008.721 p.
MATSUMOTO, Élia Yathie. Matlab 6.5: Fundamentos de Programação. São Paulo:
Érica, 2002. 342 p.
Complementary Bibliography:
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CLAUDIO, D. M.; MARINS, J. M. Cálculo Numérico Computacional: teoria e prática. 3.
ed. São Paulo: Atlas, 2000. 464 p.
Campus Higienópolis: Rua da Consolação, 896  Edifício João Calvino – 7º andar – Sala 715  Consolação  São Paulo – SP  CEP 01302-907
Tel. (11) 2114-8165  www.mackenzie.br - e-mail: [email protected]
UNIVERSIDADE PRESBITERIANA MACKENZIE
Academic Dean’s Office
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GARCIA, A. L. Numerical Methodos for Physics. 2. ed. Upper Saddle River, N.J.:
Prentice-Hall, 2000. 423 p.
GREENSPAN, D.; CASULLI, V. Numerical Analysis for Applied Mathematics, Science
and Engineering. Redwood City: Addison-Wesley, 1988. 341 p.
HARMAN, T. L.; DABNEY, J. B.; RICHERT, N. J. Advanced Engineering Mathematics
with Matlab. 2. ed. Brooks: Cole Publishing, 2000. 750 p.
SCHEID, Francis. Análise Numérica. 2. ed. Lisboa: McGraw-Hill, 2000. 617 p.
Campus Higienópolis: Rua da Consolação, 896  Edifício João Calvino – 7º andar – Sala 715  Consolação  São Paulo – SP  CEP 01302-907
Tel. (11) 2114-8165  www.mackenzie.br - e-mail: [email protected]