Cuarta Practica Calificada Metodos Numericos.docx
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CUARTA PRACTICA CALIFICADA ALEXANDER RIVERA FERNANDEZ PREGUNTAS TEORICAS
RESOLUCION CON MATLAB
PREGUNTA 2 A) >>syms t positive >>f=t^4; >>F=laplace(f)
B) >>syms t positive >>f=t^0.5; >>F=laplace(f)
PREGUNTA 3 >>syms s >>Y=1/(s+1); >>y=ilaplace(Y)
para el grafico
>>syms t >>ezplot(t^2+4,[-1,1])
PREGUNTA 4 HALLANDO LA TRANSFORMADA INVERSA
>>syms s >>H=4*(s+10)/((s+5)*(s+15)) H= (4*s+40)/(s+5)/(s+15) >>h=ilaplace(H) h= 4*exp(-10*t)*cosh(s*t)
PREGUNTA 5 EJEMPLO
C) >>A=[2 4 7; 5 8 7; ....;]; >>b=[5 8 6; ...;]; >>m=lengt(b); >>d=det(A); >>x=zeros(n,1); >>for i=1:n Ab =[A(:,1:i-1),b,A(:,i+1:n)]; x(i)=det(Ab)/d; end >>disp('solucion'); >>disp(x)
E) >> A=[-4 4 0 0;2.25 -4 1.75 0;0 2.25 -4 1.75;0 0 2.25 -4]
A=
-4.0000 4.0000
0
0
2.2500 -4.0000 1.7500
0
0 2.2500 -4.0000 1.7500 0
0 2.2500 -4.0000
>> b=[1.1875;0.6960;0.7872;-7.8457]
b=
1.1875 0.6960 0.7872 -7.8457
>> Ab=[A b]
Ab =
-4.0000 4.0000
0
0 1.1875
2.2500 -4.0000 1.7500
0 0.6960
0 2.2500 -4.0000 1.7500 0.7872 0
0 2.2500 -4.0000 -7.8457
>> Ab(1,1:5)=Ab(1,1:5)/Ab(1,1)
Ab =
1.0000 -1.0000
0
2.2500 -4.0000 1.7500
0 -0.2969 0 0.6960
0 2.2500 -4.0000 1.7500 0.7872 0
0 2.2500 -4.0000 -7.8457
>> Ab(2,1:5)=Ab(2,1:5)-Ab(1,1:5)*Ab(2,1)
Ab =
1.0000 -1.0000
0
0 -0.2969
0 -1.7500 1.7500
0 1.3640
0 2.2500 -4.0000 1.7500 0.7872
0
0 2.2500 -4.0000 -7.8457
>> Ab(2,1:5)=Ab(2,1:5)/Ab(2,2)
Ab =
1.0000 -1.0000
0
0 -0.2969
0 1.0000 -1.0000
0 -0.7794
0 2.2500 -4.0000 1.7500 0.7872 0
0 2.2500 -4.0000 -7.8457
>> Ab(1,1:5)=Ab(1,1:5)-Ab(2,1:5)*Ab(1,2)
Ab =
1.0000
0 -1.0000
0 -1.0763
0 1.0000 -1.0000
0 -0.7794
0 2.2500 -4.0000 1.7500 0.7872 0
0 2.2500 -4.0000 -7.8457
>> Ab(3,1:5)=Ab(3,1:5)-Ab(2,1:5)*Ab(3,2)
Ab =
1.0000
0 -1.0000
0 -1.0763
0 1.0000 -1.0000
0 -0.7794
0
0 -1.7500 1.7500 2.5409
0
0 2.2500 -4.0000 -7.8457
>> Ab(3,1:5)=Ab(3,1:5)/Ab(3,3)
Ab =
1.0000
0 -1.0000
0 -1.0763
0 1.0000 -1.0000
0 -0.7794
0
0 1.0000 -1.0000 -1.4519
0
0 2.2500 -4.0000 -7.8457
>> Ab(1,1:5)=Ab(1,1:5)-Ab(3,1:5)*Ab(1,3)
Ab =
1.0000
0
0 -1.0000 -2.5282
0 1.0000 -1.0000
0 -0.7794
0
0 1.0000 -1.0000 -1.4519
0
0 2.2500 -4.0000 -7.8457
>> Ab(2,1:5)=Ab(2,1:5)-Ab(3,1:5)*Ab(2,3)
Ab =
1.0000
0
0 -1.0000 -2.5282
0 1.0000
0 -1.0000 -2.2313
0
0 1.0000 -1.0000 -1.4519
0
0 2.2500 -4.0000 -7.8457
>> Ab(4,1:5)=Ab(4,1:5)-Ab(3,1:5)*Ab(4,3)
Ab =
1.0000
0
0 -1.0000 -2.5282
0 1.0000
0 -1.0000 -2.2313
0
0 1.0000 -1.0000 -1.4519
0
0
0 -1.7500 -4.5789
>> Ab(4,1:5)=Ab(4,1:5)/Ab(4,4)
Ab =
1.0000
0
0 -1.0000 -2.5282
0 1.0000
0 -1.0000 -2.2313
0
0 1.0000 -1.0000 -1.4519
0
0
0 1.0000 2.6165
>> Ab(1,1:5)=Ab(1,1:5)-Ab(4,1:5)*Ab(1,4)
Ab =
1.0000
0
0 1.0000
0
0 0.0883
0 -1.0000 -2.2313
0
0 1.0000 -1.0000 -1.4519
0
0
0 1.0000 2.6165
>> Ab(2,1:5)=Ab(2,1:5)-Ab(4,1:5)*Ab(2,4)
Ab =
1.0000
0
0
0 0.0883
0 1.0000
0
0 0.3852
0
0 1.0000 -1.0000 -1.4519
0
0
0 1.0000 2.6165
>> Ab(3,1:5)=Ab(3,1:5)-Ab(4,1:5)*Ab(3,4)
Ab =
1.0000
0
0
0 0.0883
0 1.0000
0
0 0.3852
0
0 1.0000
0 1.1646
0
0
0 1.0000 2.6165
>> y=[Ab(17);Ab(18);Ab(19);Ab(20)]
y=
0.0883 0.3852 1.1646 2.6165
RESOLUCION CON MATLAB
PREGUNTA 2 A) >>syms t positive >>f=t^4; >>F=laplace(f)
B) >>syms t positive >>f=t^0.5; >>F=laplace(f)
PREGUNTA 3 >>syms s >>Y=1/(s+1); >>y=ilaplace(Y)
para el grafico
>>syms t >>ezplot(t^2+4,[-1,1])
PREGUNTA 4 HALLANDO LA TRANSFORMADA INVERSA
>>syms s >>H=4*(s+10)/((s+5)*(s+15)) H= (4*s+40)/(s+5)/(s+15) >>h=ilaplace(H) h= 4*exp(-10*t)*cosh(s*t)
PREGUNTA 5 EJEMPLO
C) >>A=[2 4 7; 5 8 7; ....;]; >>b=[5 8 6; ...;]; >>m=lengt(b); >>d=det(A); >>x=zeros(n,1); >>for i=1:n Ab =[A(:,1:i-1),b,A(:,i+1:n)]; x(i)=det(Ab)/d; end >>disp('solucion'); >>disp(x)
E) >> A=[-4 4 0 0;2.25 -4 1.75 0;0 2.25 -4 1.75;0 0 2.25 -4]
A=
-4.0000 4.0000
0
0
2.2500 -4.0000 1.7500
0
0 2.2500 -4.0000 1.7500 0
0 2.2500 -4.0000
>> b=[1.1875;0.6960;0.7872;-7.8457]
b=
1.1875 0.6960 0.7872 -7.8457
>> Ab=[A b]
Ab =
-4.0000 4.0000
0
0 1.1875
2.2500 -4.0000 1.7500
0 0.6960
0 2.2500 -4.0000 1.7500 0.7872 0
0 2.2500 -4.0000 -7.8457
>> Ab(1,1:5)=Ab(1,1:5)/Ab(1,1)
Ab =
1.0000 -1.0000
0
2.2500 -4.0000 1.7500
0 -0.2969 0 0.6960
0 2.2500 -4.0000 1.7500 0.7872 0
0 2.2500 -4.0000 -7.8457
>> Ab(2,1:5)=Ab(2,1:5)-Ab(1,1:5)*Ab(2,1)
Ab =
1.0000 -1.0000
0
0 -0.2969
0 -1.7500 1.7500
0 1.3640
0 2.2500 -4.0000 1.7500 0.7872
0
0 2.2500 -4.0000 -7.8457
>> Ab(2,1:5)=Ab(2,1:5)/Ab(2,2)
Ab =
1.0000 -1.0000
0
0 -0.2969
0 1.0000 -1.0000
0 -0.7794
0 2.2500 -4.0000 1.7500 0.7872 0
0 2.2500 -4.0000 -7.8457
>> Ab(1,1:5)=Ab(1,1:5)-Ab(2,1:5)*Ab(1,2)
Ab =
1.0000
0 -1.0000
0 -1.0763
0 1.0000 -1.0000
0 -0.7794
0 2.2500 -4.0000 1.7500 0.7872 0
0 2.2500 -4.0000 -7.8457
>> Ab(3,1:5)=Ab(3,1:5)-Ab(2,1:5)*Ab(3,2)
Ab =
1.0000
0 -1.0000
0 -1.0763
0 1.0000 -1.0000
0 -0.7794
0
0 -1.7500 1.7500 2.5409
0
0 2.2500 -4.0000 -7.8457
>> Ab(3,1:5)=Ab(3,1:5)/Ab(3,3)
Ab =
1.0000
0 -1.0000
0 -1.0763
0 1.0000 -1.0000
0 -0.7794
0
0 1.0000 -1.0000 -1.4519
0
0 2.2500 -4.0000 -7.8457
>> Ab(1,1:5)=Ab(1,1:5)-Ab(3,1:5)*Ab(1,3)
Ab =
1.0000
0
0 -1.0000 -2.5282
0 1.0000 -1.0000
0 -0.7794
0
0 1.0000 -1.0000 -1.4519
0
0 2.2500 -4.0000 -7.8457
>> Ab(2,1:5)=Ab(2,1:5)-Ab(3,1:5)*Ab(2,3)
Ab =
1.0000
0
0 -1.0000 -2.5282
0 1.0000
0 -1.0000 -2.2313
0
0 1.0000 -1.0000 -1.4519
0
0 2.2500 -4.0000 -7.8457
>> Ab(4,1:5)=Ab(4,1:5)-Ab(3,1:5)*Ab(4,3)
Ab =
1.0000
0
0 -1.0000 -2.5282
0 1.0000
0 -1.0000 -2.2313
0
0 1.0000 -1.0000 -1.4519
0
0
0 -1.7500 -4.5789
>> Ab(4,1:5)=Ab(4,1:5)/Ab(4,4)
Ab =
1.0000
0
0 -1.0000 -2.5282
0 1.0000
0 -1.0000 -2.2313
0
0 1.0000 -1.0000 -1.4519
0
0
0 1.0000 2.6165
>> Ab(1,1:5)=Ab(1,1:5)-Ab(4,1:5)*Ab(1,4)
Ab =
1.0000
0
0 1.0000
0
0 0.0883
0 -1.0000 -2.2313
0
0 1.0000 -1.0000 -1.4519
0
0
0 1.0000 2.6165
>> Ab(2,1:5)=Ab(2,1:5)-Ab(4,1:5)*Ab(2,4)
Ab =
1.0000
0
0
0 0.0883
0 1.0000
0
0 0.3852
0
0 1.0000 -1.0000 -1.4519
0
0
0 1.0000 2.6165
>> Ab(3,1:5)=Ab(3,1:5)-Ab(4,1:5)*Ab(3,4)
Ab =
1.0000
0
0
0 0.0883
0 1.0000
0
0 0.3852
0
0 1.0000
0 1.1646
0
0
0 1.0000 2.6165
>> y=[Ab(17);Ab(18);Ab(19);Ab(20)]
y=
0.0883 0.3852 1.1646 2.6165
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