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Cuestiones del Análisis Matemático e Ingenieriles

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Trabajo pr?ctico N?1 

Cuestiones del An?lisis Matem?tico e Ingenieriles 

 

 

Algebra Matricial 

Sea A= 

(1.1)
 

 

a) Hallar la inversa de A 

b) Su determinante 

 

>
 

(1.2)
 

>
 

true (1.3)
 

>
 

(1.4)
 

>
 

[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, cold...
(1.5)
 

>
 

`*`(`+`(1, `-`(x)), `*`(`+`(`-`(`*`(`^`(x, 2))), `-`(1), `-`(x)))) (1.6)
 

Ecuaciones 

Sea la ecuacion  

`+`(`*`(`^`(x, 3)), `-`(`*`(5, `*`(a, `*`(`^`(x, 2)))))) = 1 (2.1)
 

Halle sus ra?ces 

 

`+`(`*`(`^`(x, 3)), `-`(`*`(5, `*`(a, `*`(`^`(x, 2))))), `-`(1)) = 0 (2.2)
 

`+`(`*`(`^`(x, 3)), `-`(`*`(5, `*`(a, `*`(`^`(x, 2))))), `-`(1)) = 0 (2.3)
 

 

`+`(`*`(`/`(1, 6), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(50, 3), `*`(`^`(a, 2))), `*`(`^`(`+`(108, `*...
`+`(`*`(`/`(1, 6), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(50, 3), `*`(`^`(a, 2))), `*`(`^`(`+`(108, `*...
`+`(`*`(`/`(1, 6), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(50, 3), `*`(`^`(a, 2))), `*`(`^`(`+`(108, `*...
`+`(`*`(`/`(1, 6), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(50, 3), `*`(`^`(a, 2))), `*`(`^`(`+`(108, `*...
`+`(`*`(`/`(1, 6), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(50, 3), `*`(`^`(a, 2))), `*`(`^`(`+`(108, `*...
`+`(`*`(`/`(1, 6), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(50, 3), `*`(`^`(a, 2))), `*`(`^`(`+`(108, `*...
(2.4)
 

 

`*`(Primera, `*`(Raiz)) (2.5)
 

 

`+`(`*`(`/`(1, 6), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3)))), `/`(`*`(`/`(50, 3), `*`(`^`(a, 2))), `*`(`^`(`+`(108, `*... (2.6)
 

 

 

 

 

`*`(Segunda, `*`(Raiz)) (2.7)
 

 

`+`(`-`(`*`(`/`(1, 12), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3))))), `-`(`/`(`*`(`/`(25, 3), `*`(`^`(a, 2))), `*`(`^`(`...
`+`(`-`(`*`(`/`(1, 12), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3))))), `-`(`/`(`*`(`/`(25, 3), `*`(`^`(a, 2))), `*`(`^`(`...
`+`(`-`(`*`(`/`(1, 12), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3))))), `-`(`/`(`*`(`/`(25, 3), `*`(`^`(a, 2))), `*`(`^`(`...
(2.8)
 

 

 

`*`(Tercera, `*`(Raiz)) (2.9)
 

 

`+`(`-`(`*`(`/`(1, 12), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3))))), `-`(`/`(`*`(`/`(25, 3), `*`(`^`(a, 2))), `*`(`^`(`...
`+`(`-`(`*`(`/`(1, 12), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3))))), `-`(`/`(`*`(`/`(25, 3), `*`(`^`(a, 2))), `*`(`^`(`...
`+`(`-`(`*`(`/`(1, 12), `*`(`^`(`+`(108, `*`(1000, `*`(`^`(a, 3))), `*`(12, `*`(`^`(`+`(81, `*`(1500, `*`(`^`(a, 3)))), `/`(1, 2))))), `/`(1, 3))))), `-`(`/`(`*`(`/`(25, 3), `*`(`^`(a, 2))), `*`(`^`(`...
(2.10)
 

 

Integracion de ecuaciones diferenciales ordinarias 

 

Sea (x)     encuentre la solucion general y particaular para y(0)=1. 

 

Solucion General 

 

 

diff(y(x), x) = `*`(a, `*`(y(x))) (3.1)
 

 

y(x) = `*`(_C1, `*`(exp(`*`(a, `*`(x))))) (3.2)
 

Soluci?n particular para y(0)=1 

 

 

y(x) = exp(`*`(a, `*`(x))) (3.3)
 

 

Ecuaci?n de Bernoulli 

y?=y*(y+2x-1)/x+y Dibujar las soluciones para C1 

 

 

diff(y(x), x) = `/`(`*`(y(x), `*`(`+`(y(x), `*`(2, `*`(x)), `-`(1)))), `*`(`+`(x, y(x)))) (4.1)
 

 

y(x) = `+`(`-`(x), `*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(exp(x), 2), `*`(_C1))), `/`(1, 2)))), y(x) = `+`(`-`(x), `-`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(exp(x), 2), `*`(_C1))), `/`(1, 2))))) (4.2)
 

 

 

y[1] = (proc (_C1, x) options operator, arrow; `+`(`-`(x), `*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(exp(x), 2), `*`(_C1))), `/`(1, 2)))) end proc) (4.3)
 

 

 

y[1] = (proc (_C1, x) options operator, arrow; `+`(`-`(x), `-`(`*`(`^`(`+`(`*`(`^`(x, 2)), `*`(`^`(exp(x), 2), `*`(_C1))), `/`(1, 2))))) end proc) (4.4)
 




 

Warning, unable to evaluate 8 of the 11 functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct
Plot_2d  
 

 

 

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