15-03-26_MateE (3)
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Matematica E
Juan Pablo Pascual
Departamento de Ciencias BasicasFacultad de Ingenierıa
Universidad Nacional de La Plata
La Plata, 26-03-2015
J.P. Pascual (FI-UNLP) Matematica E La Plata, 26-03-2015 1 / 5
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Ajuste
Ajuste discreto.Mınimos cuadrados lineales.
Caso polinomial.
Transformacion de parametros.
Ajuste continuo.Mınimos cuadrados lineales.
Caso polinomial.
Serie de Fourier Generalizada.
Convergencia.
Serie de Fourier.
J.P. Pascual (FI-UNLP) Matematica E La Plata, 26-03-2015 2 / 5
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Ajuste
Ajuste continuo.Mınimos cuadrados lineales.
Caso polinomial.
Serie de Fourier Generalizada.
Bibliografıa
R.L. Burden y J.D. Faires, Numerical Analysis, 9th ed., Brooks/Cole, 2011.
Capıtulo 8, extendido al caso complejo.
D.G. Zill y M.R. Cullen, Differential Equations, with Boundary-Value
Problems, 7th ed., Brooks/Cole, 2009.
Capıtulo 11, extendido al caso complejo.
J.P. Pascual (FI-UNLP) Matematica E La Plata, 26-03-2015 3 / 5
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Ajuste continuoEjemplo
0 0.2 0.4 0.6 0.8 1−0.2
0
0.2
0.4
0.6
0.8
1
1.2
x
sen(πx)
P2(x)
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Serie generalizada de FourierEjemplo: polinomios de Legendre
−1 −0.5 0 0.5 1−0.2
0
0.2
0.4
0.6
0.8
1
1.2
x
sen(0.5π(x+1))
P(x)
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