ejercicio 2 - ujaen.esajlopez/asignat/ampliacion/... · ampliación de matemáticas - iti -...

Ampliación de Matemáticas - ITI - 2015/2016 Examen prácticas EDP para el número de serie: 1

� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<3, 0<t

uH0,tL=uH3,tL=0 0 £ t

uHx,0L=

7 x 0 £ x £ 1

13 - 6 x 1 £ x £ 2

3 - x 2 £ x £ 3

0 £ x £ 3

Calcular la temperatura que tendrá la barra en el punto x=1

en el instante t=1. mediante un desarrollo en serie de Fourier de orden 9.

1L uH1,1.L = 4.52452 ´ 10-12

2L uH1,1.L = -0.730427

3L uH1,1.L = -4.47049

4L uH1,1.L = 6.0442

5L uH1,1.L = -5.12904

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<Π, 0<t

¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-3 x

20 £ x £ 2

8 x - 19 2 £ x £ 3

-5 x

-3+Π+

15

-3+Π+ 5 3 £ x £ Π

0 £ x £ Π


en el instante t=0.1 mediante un desarrollo en serie de Fourier de orden 12.

1L uH2,0.1L = -0.478056

2L uH2,0.1L = 0.520959

3L uH2,0.1L = -2.67978

4L uH2,0.1L = -1.24838

5L uH2,0.1L = 1.66359

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=2 x 0 £ x £ 1

3 - x 1 £ x £ 30 £ x £ 3

¶

¶tuHx,0L=Hx - 3L2 Hx - 2L Hx - 1L x2 0. £ x £ 3

Calcular la posición de la cuerda en el punto x=2 en el instante t=

0.3 mediante un desarrollo en serie de Fourier de orden 12.

1L uH2,0.3L = -5.18028

2L uH2,0.3L = 6.47391

3L uH2,0.3L = 0.24684

4L uH2,0.3L = -6.33988

5L uH2,0.3L = 0.873203

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� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-2 x 0 £ x £ 2

4 x - 12 2 £ x £ 30 £ x £ 3



1L uH1,0.7L = 5.35949

2L uH1,0.7L = -0.00273303

3L uH1,0.7L = 5.34366

4L uH1,0.7L = 8.73541

5L uH1,0.7L = 5.03599

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=2 Hx - 3L x Hx - ΠL 0 £ x £ Π



1L uH2,0.3L = 2.02222

2L uH2,0.3L = -4.10136

3L uH2,0.3L = -3.7308

4L uH2,0.3L = 4.6926

5L uH2,0.3L = -4.53718

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� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u


uH0,tL=uHΠ,tL=0 0 £ t

uHx,0L=

-5 x 0 £ x £ 15 x

-1+Π-

5

-1+Π- 5 1 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=Hx - 3L x Hx - ΠL 0. £ x £ Π



1L uH1,0.1L = 1.24487

2L uH1,0.1L = -2.7485

3L uH1,0.1L = -4.00376

4L uH1,0.1L = -3.79842

5L uH1,0.1L = -8.66483

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� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=Hx - 4L2 Hx - 2L x2 0 £ x £ 4



1L uH2,0.4L = 3.47817

2L uH2,0.4L = 1.1243 ´ 10-39

3L uH2,0.4L = -3.55294

4L uH2,0.4L = 2.01531

5L uH2,0.4L = -7.18783

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=3 Hx - 3L x Hx - ΠL2 0 £ x £ Π



1L uH1,0.3L = 3.19659

2L uH1,0.3L = 0.98632

3L uH1,0.3L = 1.08677

4L uH1,0.3L = -13.9571

5L uH1,0.3L = -3.47456

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� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u



uHx,0L=

-3 x

20 £ x £ 2

9 x - 21 2 £ x £ 3

-6 x

-3+Π+

18

-3+Π+ 6 3 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

7 x

30 £ x £ 3

-7 x

-3+Π+

21

-3+Π+ 7 3 £ x £ Π

0. £ x £ Π



1L uH2,0.9L = -6.10467

2L uH2,0.9L = 8.28021

3L uH2,0.9L = 2.76493

4L uH2,0.9L = 0.990838

5L uH2,0.9L = 7.2235

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� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u



uHx,0L=

4 x 0 £ x £ 2

-8 x

-2+Π+

16

-2+Π+ 8 2 £ x £ Π

0 £ x £ Π



1L uH2,0.7L = -5.20939

2L uH2,0.7L = 1.33141

3L uH2,0.7L = 0.0000792305

4L uH2,0.7L = -6.90352

5L uH2,0.7L = 5.14464

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t

uHx,0L=6 x 0 £ x £ 1

8 - 2 x 1 £ x £ 40 £ x £ 4



1L uH3,0.6L = -3.00732

2L uH3,0.6L = 3.5807

3L uH3,0.6L = -4.6087

4L uH3,0.6L = 4.73185

5L uH3,0.6L = 2.78392

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� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u



uHx,0L=2 Hx - 3L Hx - 2L x Hx - ΠL 0 £ x £ Π

¶

¶tuHx,0L=Hx - 2L Hx - 1L x2 Hx - ΠL2 0. £ x £ Π



1L uH1,0.3L = -5.4992

2L uH1,0.3L = 1.2568

3L uH1,0.3L = -5.01301

4L uH1,0.3L = 3.82171

5L uH1,0.3L = -7.97185

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� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=

5 x 0 £ x £ 1

2 x + 3 1 £ x £ 235

3-

7 x

32 £ x £ 5

0 £ x £ 5



1L uH4,0.7L = 1.14467

2L uH4,0.7L = 3.98318

3L uH4,0.7L = 4.39238

4L uH4,0.7L = 5.5429

5L uH4,0.7L = -7.53722

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t

uHx,0L=-2 Hx - 4L2 Hx - 2L Hx - 1L x 0 £ x £ 4



1L uH2,0.4L = -4.26667

2L uH2,0.4L = 2.01792

3L uH2,0.4L = 0.765524

4L uH2,0.4L = -0.346748

5L uH2,0.4L = 4.83632

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� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=-8 x 0 £ x £ 1

2 x - 10 1 £ x £ 50 £ x £ 5

¶

¶tuHx,0L=

5 x 0 £ x £ 122

3-

7 x

31 £ x £ 4

2 x - 10 4 £ x £ 5

0. £ x £ 5



1L uH3,0.7L = -2.82484

2L uH3,0.7L = 4.82113

3L uH3,0.7L = -5.22357

4L uH3,0.7L = 8.25332

5L uH3,0.7L = 0.0135431

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� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u



uHx,0L=

-3 x 0 £ x £ 39 x

-3+Π-

27

-3+Π- 9 3 £ x £ Π

0 £ x £ Π



1L uH1,0.8L = -7.17413

2L uH1,0.8L = -7.73987

3L uH1,0.8L = -0.0037568

4L uH1,0.8L = -3.40567

5L uH1,0.8L = -6.45444

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

3 x

20 £ x £ 2

7 - 2 x 2 £ x £ 3

-x

-3+Π+

3

-3+Π+ 1 3 £ x £ Π

0 £ x £ Π



1L uH2,0.6L = 1.61408

2L uH2,0.6L = -1.41983

3L uH2,0.6L = -4.85075

4L uH2,0.6L = -0.0027552

5L uH2,0.6L = -0.24815

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� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-2 Hx - 2L2 Hx - 1L x2 0 £ x £ 2

¶

¶tuHx,0L=

3 x 0 £ x £ 1

6 - 3 x 1 £ x £ 20. £ x £ 2

Calcular la posición de la cuerda en el punto x=1

5


1L uH15,1.L = -0.547449

2L uH15,1.L = -2.71096

3L uH15,1.L = -8.4623

4L uH15,1.L = -1.38202

5L uH15,1.L = 7.5687

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� Ejercicio 1

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=2 Hx - 4L2 Hx - 3L Hx - 2L x2 0 £ x £ 4



1L uH2,0.4L = -1.33218

2L uH2,0.4L = -4.29521

3L uH2,0.4L = 4.94206

4L uH2,0.4L = 0.221639

5L uH2,0.4L = 8.31109

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<5, 0<t

¶u

¶xH0,tL=

¶u

¶xH5,tL=0 0 £ t

uHx,0L=-Hx - 5L2 Hx - 3L Hx - 1L x 0 £ x £ 5



1L uH2,0.5L = -1.67532

2L uH2,0.5L = 0.212689

3L uH2,0.5L = -0.847851

4L uH2,0.5L = 2.74392

5L uH2,0.5L = -3.0358

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� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u




¶

¶tuHx,0L=-2 Hx - 3L Hx - 2L x2 Hx - ΠL2 0. £ x £ Π



1L uH2,0.6L = -4.58731

2L uH2,0.6L = -6.1558

3L uH2,0.6L = 0.233206

4L uH2,0.6L = -8.43837

5L uH2,0.6L = -3.10571

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� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=3 Hx - 3L Hx - 2L x Hx - ΠL2 0 £ x £ Π



1L uH2,0.5L = -0.97402

2L uH2,0.5L = 7.84046

3L uH2,0.5L = -6.324

4L uH2,0.5L = 0.0000548608

5L uH2,0.5L = -3.5469

� Ejercicio 2

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=-8 x 0 £ x £ 1

8 x - 16 1 £ x £ 20 £ x £ 2


10


1L uH1110

,0.2L = 1.39507

2L uH1110

,0.2L = 2.65746

3L uH1110

,0.2L = -4.42834

4L uH1110

,0.2L = 0.377136

5L uH1110

,0.2L = 1.7011

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� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=-3 Hx - 4L Hx - 1L x 0 £ x £ 4

¶

¶tuHx,0L=

x 0 £ x £ 14

3-

x

31 £ x £ 4

0. £ x £ 4



1L uH1,0.9L = 10.1985

2L uH1,0.9L = -2.0788

3L uH1,0.9L = 2.79379

4L uH1,0.9L = -6.31034

5L uH1,0.9L = -3.69655

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� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=

-2 x 0 £ x £ 1

2 - 4 x 1 £ x £ 2

6 x - 18 2 £ x £ 3

0 £ x £ 3



1L uH1,0.1L = -1.33308

2L uH1,0.1L = 5.99713

3L uH1,0.1L = 7.77057

4L uH1,0.1L = 6.02466

5L uH1,0.1L = -4.71323

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t

uHx,0L=-5 x

30 £ x £ 3

5 x - 20 3 £ x £ 40 £ x £ 4



1L uH1,0.3L = 4.50662

2L uH1,0.3L = 4.88906

3L uH1,0.3L = 3.93507

4L uH1,0.3L = -0.447492

5L uH1,0.3L = -2.35035

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� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-2 Hx - 2L Hx - 1L x 0 £ x £ 2

¶

¶tuHx,0L=

8 x 0 £ x £ 1

16 - 8 x 1 £ x £ 20. £ x £ 2


5


1L uH45,1.L = -4.59749

2L uH45,1.L = 5.16213

3L uH45,1.L = 5.03884

4L uH45,1.L = -0.383104

5L uH45,1.L = -2.88108

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� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u



uHx,0L=

x

20 £ x £ 2

-x

-2+Π+

2

-2+Π+ 1 2 £ x £ Π

0 £ x £ Π



1L uH1,0.5L = -2.96956

2L uH1,0.5L = -6.3046

3L uH1,0.5L = 0.000224842

4L uH1,0.5L = -5.35386

5L uH1,0.5L = 6.29306

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=-3 Hx - 3L Hx - 1L x Hx - ΠL2 0 £ x £ Π



1L uH2,0.7L = 0.565654

2L uH2,0.7L = 2.54378

3L uH2,0.7L = -4.98995

4L uH2,0.7L = 1.75191

5L uH2,0.7L = 4.35737

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� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

45 x

20 £ x £

2

5

15 - 15 x 2

5£ x £ 1

0 £ x £ 1

¶

¶tuHx,0L=

-70 x 0 £ x £1

10

70 x

9-

70

9

1

10£ x £ 1

0. £ x £ 1


5


1L uH25,1.L = -1.08468

2L uH25,1.L = -6.0425

3L uH25,1.L = 5.03616

4L uH25,1.L = 5.66325

5L uH25,1.L = 3.10544

20 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

-40 x 0 £ x £1

5

30 x - 14 1

5£ x £

3

10

50 x

7-

50

7

3

10£ x £ 1

0 £ x £ 1


10


1L uH 7

10,0.2L = -4.28076

2L uH 7

10,0.2L = -5.64126

3L uH 7

10,0.2L = -1.37481 ´ 10-21

4L uH 7

10,0.2L = -6.77292

5L uH 7

10,0.2L = 7.80865

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-5 x

20 £ x £ 2

5 x

-2+Π-

10

-2+Π- 5 2 £ x £ Π

0 £ x £ Π



1L uH1,0.4L = -3.83178

2L uH1,0.4L = -2.49944

3L uH1,0.4L = 0.7564

4L uH1,0.4L = 4.11633

5L uH1,0.4L = -0.54739

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� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u



uHx,0L=

5 x 0 £ x £ 1

17 - 12 x 1 £ x £ 27 x

-2+Π-

14

-2+Π- 7 2 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

3 x 0 £ x £ 2

12 - 3 x 2 £ x £ 3

-3 x

-3+Π+

9

-3+Π+ 3 3 £ x £ Π

0. £ x £ Π



1L uH2,0.2L = -2.29426

2L uH2,0.2L = 4.03555

3L uH2,0.2L = -0.382366

4L uH2,0.2L = 7.03391

5L uH2,0.2L = -3.00545

22 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

90 x 0 £ x £1

10

11 - 20 x 1

10£ x £

3

10

50

7-

50 x

7

3

10£ x £ 1

0 £ x £ 1


2en el instante t=0.6 mediante un desarrollo en serie de Fourier de orden 8.

1L uH12,0.6L = 2.59242

2L uH12,0.6L = -7.52835

3L uH12,0.6L = 5.15769

4L uH12,0.6L = 2.42517 ´ 10-64

5L uH12,0.6L = -4.87957

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=-2 Hx - 2L Hx - 1L x 0 £ x £ 2


10


1L uH1310

,1.L = -3.02046

2L uH1310

,1.L = 0.000016434

3L uH1310

,1.L = 2.86852

4L uH1310

,1.L = -3.7076

5L uH1310

,1.L = -1.79468

� Ejercicio 3

Untitled-2 23

�

Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u



uHx,0L=3 Hx - 3L Hx - 2L x2 Hx - ΠL 0 £ x £ Π

¶

¶tuHx,0L=

3 x 0 £ x £ 2

-6 x

-2+Π+

12

-2+Π+ 6 2 £ x £ Π

0. £ x £ Π



1L uH2,0.5L = 3.54536

2L uH2,0.5L = 0.433697

3L uH2,0.5L = 8.81795

4L uH2,0.5L = 6.69563

5L uH2,0.5L = -4.39974

24 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u



uHx,0L=-Hx - 2L x2 Hx - ΠL2 0 £ x £ Π



1L uH2,0.5L = -6.88263

2L uH2,0.5L = 0.000710254

3L uH2,0.5L = -1.28932

4L uH2,0.5L = 3.09719

5L uH2,0.5L = -4.19744

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<3, 0<t

¶u

¶xH0,tL=

¶u

¶xH3,tL=0 0 £ t

uHx,0L=-2 Hx - 3L2 Hx - 1L x2 0 £ x £ 3



1L uH1,1.L = 1.22108

2L uH1,1.L = 2.95209

3L uH1,1.L = 1.35226

4L uH1,1.L = 2.07282

5L uH1,1.L = -2.7

Untitled-2 25

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=-x 0 £ x £ 2

x - 4 2 £ x £ 40 £ x £ 4

¶

¶tuHx,0L=-3 Hx - 4L Hx - 2L Hx - 1L x 0. £ x £ 4



1L uH3,0.1L = -5.17403

2L uH3,0.1L = 4.86654

3L uH3,0.1L = 0.778802

4L uH3,0.1L = 8.11087

5L uH3,0.1L = -3.43434

26 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u



uHx,0L=

x

20 £ x £ 2

-x

-2+Π+

2

-2+Π+ 1 2 £ x £ Π

0 £ x £ Π



1L uH1,0.3L = -0.54698

2L uH1,0.3L = -3.42607

3L uH1,0.3L = -6.89581

4L uH1,0.3L = 6.38146

5L uH1,0.3L = 0.450555

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-2 x

30 £ x £ 3

2 x

-3+Π-

6

-3+Π- 2 3 £ x £ Π

0 £ x £ Π



1L uH1,0.3L = 1.83205

2L uH1,0.3L = -0.999775

3L uH1,0.3L = -4.11619

4L uH1,0.3L = -4.3364

5L uH1,0.3L = 4.08596

Untitled-2 27

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=-3 Hx - 3L Hx - 1L x2 Hx - ΠL2 0 £ x £ Π

¶

¶tuHx,0L=-3 Hx - 3L Hx - 2L x Hx - ΠL2 0. £ x £ Π



1L uH1,0.6L = -3.49633

2L uH1,0.6L = -6.11971

3L uH1,0.6L = 0.809592

4L uH1,0.6L = -4.28168

5L uH1,0.6L = -3.77565

28 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=Hx - 3L2 Hx - 2L Hx - 1L x 0 £ x £ 3



1L uH2,0.5L = 0.0000267728

2L uH2,0.5L = -2.1754

3L uH2,0.5L = 6.63624

4L uH2,0.5L = 1.68432

5L uH2,0.5L = 5.27905

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t

uHx,0L=-Hx - 4L Hx - 3L Hx - 2L x 0 £ x £ 4



1L uH2,1.L = 3.78356

2L uH2,1.L = 3.62608

3L uH2,1.L = -0.83981

4L uH2,1.L = 2.13333

5L uH2,1.L = 2.8699

Untitled-2 29

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u




¶

¶tuHx,0L=

-8 x 0 £ x £ 18 x

-1+Π-

8

-1+Π- 8 1 £ x £ Π

0. £ x £ Π



1L uH1,0.1L = 2.17038

2L uH1,0.1L = -0.239443

3L uH1,0.1L = 3.27624

4L uH1,0.1L = -5.00251

5L uH1,0.1L = 3.13135

30 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=Hx - 5L2 Hx - 1L x2 0 £ x £ 5



1L uH4,0.1L = -5.05838

2L uH4,0.1L = -0.528003

3L uH4,0.1L = 18.2841

4L uH4,0.1L = -7.15882

5L uH4,0.1L = 1.06645

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=2 Hx - 3L Hx - 1L x2 Hx - ΠL2 0 £ x £ Π



1L uH2,1.L = 0.0151513

2L uH2,1.L = -3.00881

3L uH2,1.L = -4.39661

4L uH2,1.L = -2.33505

5L uH2,1.L = -0.819339

Untitled-2 31

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=-2 Hx - 3L Hx - 2L x Hx - ΠL 0 £ x £ Π

¶

¶tuHx,0L=

8 x

30 £ x £ 3

-8 x

-3+Π+

24

-3+Π+ 8 3 £ x £ Π

0. £ x £ Π



1L uH1,0.6L = 3.3527

2L uH1,0.6L = -3.06462

3L uH1,0.6L = 6.23769

4L uH1,0.6L = 2.63953

5L uH1,0.6L = -1.15085

32 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-5 x 0 £ x £ 1

5 x - 10 1 £ x £ 20 £ x £ 2


10


1L uH 9

10,0.2L = -3.09882

2L uH 9

10,0.2L = -2.44852

3L uH 9

10,0.2L = 8.01239

4L uH 9

10,0.2L = 3.47498

5L uH 9

10,0.2L = -7.6721

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<5, 0<t

¶u

¶xH0,tL=

¶u

¶xH5,tL=0 0 £ t

uHx,0L=

7 x

20 £ x £ 2

35

3-

7 x

32 £ x £ 5

0 £ x £ 5



1L uH3,0.6L = -1.17078

2L uH3,0.6L = -3.19356

3L uH3,0.6L = 0.908917

4L uH3,0.6L = -0.255357

5L uH3,0.6L = 3.49947

Untitled-2 33

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=

7 x

20 £ x £ 2

-7 x

-2+Π+

14

-2+Π+ 7 2 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

x

20 £ x £ 2

19 - 9 x 2 £ x £ 38 x

-3+Π-

24

-3+Π- 8 3 £ x £ Π

0. £ x £ Π



1L uH2,0.2L = 4.46115

2L uH2,0.2L = -8.19511

3L uH2,0.2L = 2.99247

4L uH2,0.2L = -4.67156

5L uH2,0.2L = 0.478837

34 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=2 Hx - 3L Hx - 2L x2 0 £ x £ 3



1L uH1,0.4L = -7.53664

2L uH1,0.4L = -1.61603

3L uH1,0.4L = 0.31001

4L uH1,0.4L = -0.517031

5L uH1,0.4L = 1.2779

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t




1L uH2,0.2L = 0.840225

2L uH2,0.2L = -0.468089

3L uH2,0.2L = 4.3914

4L uH2,0.2L = 4.29638

5L uH2,0.2L = -2.49321

Untitled-2 35

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=3 Hx - 2L Hx - 1L x2 0 £ x £ 2¶

¶tuHx,0L=-3 Hx - 2L2 Hx - 1L x2 0. £ x £ 2



1L uH32,0.3L = 1.20024

2L uH32,0.3L = 6.08115

3L uH32,0.3L = -7.63243

4L uH32,0.3L = 8.86057

5L uH32,0.3L = 8.47336

36 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u






1L uH2,0.5L = -7.2824

2L uH2,0.5L = 2.37209

3L uH2,0.5L = -0.000214428

4L uH2,0.5L = 7.78369

5L uH2,0.5L = -7.7392

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=Hx - 2L Hx - 1L x2 0 £ x £ 2


10


1L uH 9

10,0.8L = -3.05886

2L uH 9

10,0.8L = -1.71435

3L uH 9

10,0.8L = -1.97672

4L uH 9

10,0.8L = -4.0375

5L uH 9

10,0.8L = -0.133313

Untitled-2 37

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=2 Hx - 2L x2 Hx - ΠL 0 £ x £ Π

¶

¶tuHx,0L=2 Hx - 2L x Hx - ΠL 0. £ x £ Π



1L uH1,0.6L = 3.11805

2L uH1,0.6L = -3.1224

3L uH1,0.6L = 3.62604

4L uH1,0.6L = -0.157384

5L uH1,0.6L = 1.72986

38 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u



uHx,0L=

-5 x 0 £ x £ 15 x

-1+Π-

5

-1+Π- 5 1 £ x £ Π

0 £ x £ Π



1L uH1,1.L = 5.26519

2L uH1,1.L = 6.11187

3L uH1,1.L = -0.000408029

4L uH1,1.L = 8.67419

5L uH1,1.L = 7.85841

� Ejercicio 2

¶u

¶tHx,tL=

¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=-Hx - 1L x Hx - ΠL2 0 £ x £ Π



1L uH1,0.7L = 2.00551

2L uH1,0.7L = 4.25672

3L uH1,0.7L = 1.90775

4L uH1,0.7L = -3.19724

5L uH1,0.7L = -0.33429

Untitled-2 39

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

-80 x

30 £ x £

3

10

-5 x

3-

15

2

3

10£ x £

9

10

90 x - 90 9

10£ x £ 1

0 £ x £ 1

¶

¶tuHx,0L=

10 x

30 £ x £

3

5

5 - 5 x 3

5£ x £ 1

0. £ x £ 1


5en el instante t=


1L uH15,0.9L = -2.88881

2L uH15,0.9L = 5.25698

3L uH15,0.9L = -0.562377

4L uH15,0.9L = -8.28703

5L uH15,0.9L = 8.55094

40 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u



uHx,0L=

-4 x 0 £ x £ 1x

2-

9

21 £ x £ 3

3 x

-3+Π-

9

-3+Π- 3 3 £ x £ Π

0 £ x £ Π



1L uH1,0.3L = 3.47352

2L uH1,0.3L = -0.241425

3L uH1,0.3L = 8.68325

4L uH1,0.3L = 2.6447

5L uH1,0.3L = -7.60475

� Ejercicio 2

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=-2 Hx - 2L2 Hx - 1L x 0 £ x £ 2



1L uH1,0.4L = 0.775924

2L uH1,0.4L = 1.1749

3L uH1,0.4L = -4.41306

4L uH1,0.4L = 0.26329

5L uH1,0.4L = -0.453352

Untitled-2 41

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=-2 Hx - 1L Ix -7

10M x 0 £ x £ 1

¶

¶tuHx,0L=

40 x

30 £ x £

3

5

44 - 60 x 3

5£ x £

7

10

20

3-

20 x

3

7

10£ x £ 1

0. £ x £ 1


5


1L uH45,0.8L = 0.609665

2L uH45,0.8L = -7.01308

3L uH45,0.8L = 7.04172

4L uH45,0.8L = -0.769121

5L uH45,0.8L = -7.61191

42 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=Hx - 2L Hx - 1L x2 0 £ x £ 2


10


1L uH1710

,0.2L = -4.43129

2L uH1710

,0.2L = -0.000753887

3L uH1710

,0.2L = 5.9463

4L uH1710

,0.2L = 8.08536

5L uH1710

,0.2L = 6.9754

� Ejercicio 2

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=-Hx - 1L2 Ix -1

2M x 0 £ x £ 1


10


1L uH 3

10,1.L = 3.75087

2L uH 3

10,1.L = 0.008334

3L uH 3

10,1.L = 4.03051

4L uH 3

10,1.L = -3.16548

5L uH 3

10,1.L = -0.944756

Untitled-2 43

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u



uHx,0L=

4 x 0 £ x £ 2

-8 x

-2+Π+

16

-2+Π+ 8 2 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=Hx - 2L x Hx - ΠL 0. £ x £ Π



1L uH1,0.3L = 4.49283

2L uH1,0.3L = 3.2591

3L uH1,0.3L = -3.72514

4L uH1,0.3L = 1.61383

5L uH1,0.3L = 2.74322

44 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u



uHx,0L=Hx - 1L x2 Hx - ΠL2 0 £ x £ Π



1L uH1,1.L = 0.915845

2L uH1,1.L = 8.83461

3L uH1,1.L = -6.29861

4L uH1,1.L = 6.38144

5L uH1,1.L = -6.89184

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=-3 Hx - 1L2 Ix -3

5M Ix -

3

10M x 0 £ x £ 1


5


1L uH25,0.3L = -0.005

2L uH25,0.3L = 4.40788

3L uH25,0.3L = 1.93496

4L uH25,0.3L = -2.53438

5L uH25,0.3L = -2.63365

Untitled-2 45

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=2 Hx - 1L2 Ix -1

2M x 0 £ x £ 1

¶

¶tuHx,0L=

40 x

70 £ x £

7

10

40

3-

40 x

3

7

10£ x £ 1

0. £ x £ 1


5


1L uH25,0.2L = 6.73692

2L uH25,0.2L = -4.90354

3L uH25,0.2L = 4.63999

4L uH25,0.2L = 0.442604

5L uH25,0.2L = 1.22269

46 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u



uHx,0L=

-3 x 0 £ x £ 13 x

-1+Π-

3

-1+Π- 3 1 £ x £ Π

0 £ x £ Π



1L uH1,1.L = 5.66952

2L uH1,1.L = -0.000244817

3L uH1,1.L = 0.828446

4L uH1,1.L = 6.5567

5L uH1,1.L = 2.19998

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t




1L uH2,0.7L = -2.23717

2L uH2,0.7L = 2.97373

3L uH2,0.7L = 1.89646

4L uH2,0.7L = -2.56248

5L uH2,0.7L = -3.64153

Untitled-2 47

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=

5 x 0 £ x £ 1

-5 x

-1+Π+

5

-1+Π+ 5 1 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

-7 x

30 £ x £ 3

7 x

-3+Π-

21

-3+Π- 7 3 £ x £ Π

0. £ x £ Π



1L uH1,0.1L = -2.23354

2L uH1,0.1L = -7.64115

3L uH1,0.1L = 3.28542

4L uH1,0.1L = 3.87538

5L uH1,0.1L = -2.74791

48 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

-20 x 0 £ x £3

10

60 x

7-

60

7

3

10£ x £ 1

0 £ x £ 1


10


1L uH 3

10,0.9L = 8.90901

2L uH 3

10,0.9L = -1.41504

3L uH 3

10,0.9L = -1.40554 ´ 10-15

4L uH 3

10,0.9L = -8.95998

5L uH 3

10,0.9L = 2.73289

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=-3 Hx - 1L Ix -1

10M x2 0 £ x £ 1


10


1L uH 3

10,1.L = -1.84691

2L uH 3

10,1.L = -1.8605

3L uH 3

10,1.L = 0.125

4L uH 3

10,1.L = 2.59648

5L uH 3

10,1.L = 1.12276

Untitled-2 49

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u



uHx,0L=

-6 x 0 £ x £ 16 x

-1+Π-

6

-1+Π- 6 1 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

-8 x 0 £ x £ 1

6 x - 14 1 £ x £ 22 x

-2+Π-

4

-2+Π- 2 2 £ x £ Π

0. £ x £ Π



1L uH1,0.9L = 4.90214

2L uH1,0.9L = 1.83257

3L uH1,0.9L = 1.58784

4L uH1,0.9L = 2.52104

5L uH1,0.9L = -5.81208

50 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=Hx - 3L Hx - 1L x2 Hx - ΠL2 0 £ x £ Π



1L uH1,1.L = -1.19203

2L uH1,1.L = -8.85027

3L uH1,1.L = -3.49859 ´ 10-11

4L uH1,1.L = 2.76315

5L uH1,1.L = -8.94398

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=-3 Hx - 1L2 Ix -2

5M Ix -

1

10M x 0 £ x £ 1


5


1L uH45,0.5L = 2.5233

2L uH45,0.5L = -0.01

3L uH45,0.5L = -2.0263

4L uH45,0.5L = -4.46946

5L uH45,0.5L = 3.46278

Untitled-2 51

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=-Hx - 5L Hx - 3L Hx - 2L x2 0 £ x £ 5¶

¶tuHx,0L=-2 Hx - 5L Hx - 1L x2 0. £ x £ 5



1L uH3,0.2L = -1.671

2L uH3,0.2L = 6.46295

3L uH3,0.2L = 4.24612

4L uH3,0.2L = 21.1344

5L uH3,0.2L = 7.9156

52 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-Hx - 2L2 Hx - 1L x 0 £ x £ 2


10


1L uH 3

10,0.9L = -0.83171

2L uH 3

10,0.9L = 2.37362 ´ 10-17

3L uH 3

10,0.9L = 4.31569

4L uH 3

10,0.9L = -5.54525

5L uH 3

10,0.9L = -6.39286

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=

-60 x 0 £ x £1

10

20 x

3-

20

3

1

10£ x £ 1

0 £ x £ 1


10


1L uH 3

10,0.1L = 3.32776

2L uH 3

10,0.1L = -3.00017

3L uH 3

10,0.1L = -0.966251

4L uH 3

10,0.1L = 4.21462

5L uH 3

10,0.1L = 1.85541

Untitled-2 53

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=2 x 0 £ x £ 2

12 - 4 x 2 £ x £ 30 £ x £ 3

¶

¶tuHx,0L=

6 x 0 £ x £ 1

15 - 9 x 1 £ x £ 2

3 x - 9 2 £ x £ 3

0. £ x £ 3



1L uH2,0.8L = -2.43913

2L uH2,0.8L = 1.49006

3L uH2,0.8L = 5.77565

4L uH2,0.8L = -0.0365747

5L uH2,0.8L = -7.91557

54 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u



uHx,0L=

x

20 £ x £ 2

-x

-2+Π+

2

-2+Π+ 1 2 £ x £ Π

0 £ x £ Π



1L uH1,0.7L = -8.95176

2L uH1,0.7L = -1.79305

3L uH1,0.7L = 0.00123078

4L uH1,0.7L = -8.21706

5L uH1,0.7L = 4.00271

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<5, 0<t

¶u

¶xH0,tL=

¶u

¶xH5,tL=0 0 £ t

uHx,0L=

-5 x 0 £ x £ 12 x

3-

17

31 £ x £ 4

3 x - 15 4 £ x £ 5

0 £ x £ 5



1L uH1,1.L = -3.21635

2L uH1,1.L = 1.12479

3L uH1,1.L = -3.78671

4L uH1,1.L = 1.09884

5L uH1,1.L = -1.17265

Untitled-2 55

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=

4 x 0 £ x £ 1

5 x - 1 1 £ x £ 2

27 - 9 x 2 £ x £ 3

0 £ x £ 3

¶

¶tuHx,0L=

6 x 0 £ x £ 1

3 x + 3 1 £ x £ 2

27 - 9 x 2 £ x £ 3

0. £ x £ 3



1L uH2,0.3L = -3.67482

2L uH2,0.3L = 6.35843

3L uH2,0.3L = 3.39734

4L uH2,0.3L = -7.07642

5L uH2,0.3L = 9.43143

56 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u



uHx,0L=

-7 x 0 £ x £ 17 x

-1+Π-

7

-1+Π- 7 1 £ x £ Π

0 £ x £ Π



1L uH1,0.3L = -7.22144

2L uH1,0.3L = -8.06925

3L uH1,0.3L = -6.51706

4L uH1,0.3L = -3.83913

5L uH1,0.3L = -7.13005

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

8 x

30 £ x £ 3

-8 x

-3+Π+

24

-3+Π+ 8 3 £ x £ Π

0 £ x £ Π



1L uH2,0.7L = 4.00231

2L uH2,0.7L = -2.78078

3L uH2,0.7L = -1.97274

4L uH2,0.7L = -4.32654

5L uH2,0.7L = -4.4991

Untitled-2 57

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u




¶

¶tuHx,0L=

4 x 0 £ x £ 1

8 - 4 x 1 £ x £ 34 x

-3+Π-

12

-3+Π- 4 3 £ x £ Π

0. £ x £ Π



1L uH1,0.6L = -3.10847

2L uH1,0.6L = 8.55997

3L uH1,0.6L = 0.480603

4L uH1,0.6L = -1.58476

5L uH1,0.6L = 3.50415

58 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=-3 Hx - 4L2 Hx - 3L Hx - 1L x 0 £ x £ 4



1L uH3,0.8L = 0.0936036

2L uH3,0.8L = -5.87573

3L uH3,0.8L = -7.22837

4L uH3,0.8L = -1.53067

5L uH3,0.8L = 2.0071

� Ejercicio 2

¶u

¶tHx,tL=

¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=-3 Hx - 2L x2 Hx - ΠL2 0 £ x £ Π



1L uH2,0.8L = 2.6322

2L uH2,0.8L = -1.56829

3L uH2,0.8L = 3.1626

4L uH2,0.8L = 0.606434

5L uH2,0.8L = -2.12878

Untitled-2 59

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u



uHx,0L=

-7 x 0 £ x £ 1

8 x - 15 1 £ x £ 2

-x

-2+Π+

2

-2+Π+ 1 2 £ x £ Π

0 £ x £ Π

¶




1L uH2,0.4L = -2.08305

2L uH2,0.4L = 8.17555

3L uH2,0.4L = 5.41267

4L uH2,0.4L = -3.94465

5L uH2,0.4L = -3.31385

60 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

-35 x

30 £ x £

3

5

35 x

2-

35

2

3

5£ x £ 1

0 £ x £ 1


10


1L uH 3

10,0.7L = -7.51517

2L uH 3

10,0.7L = -6.0874

3L uH 3

10,0.7L = -4.47771 ´ 10-48

4L uH 3

10,0.7L = -5.79928

5L uH 3

10,0.7L = 2.12082

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t




1L uH1,1.L = 4.58846

2L uH1,1.L = 0.460317

3L uH1,1.L = 2.14318

4L uH1,1.L = -2.49936

5L uH1,1.L = -2.66868

Untitled-2 61

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u



uHx,0L=Hx - 3L x Hx - ΠL2 0 £ x £ Π

¶

¶tuHx,0L=

8 x

30 £ x £ 3

-8 x

-3+Π+

24

-3+Π+ 8 3 £ x £ Π

0. £ x £ Π



1L uH1,0.9L = -0.905171

2L uH1,0.9L = -6.79225

3L uH1,0.9L = 1.23257

4L uH1,0.9L = -6.31391

5L uH1,0.9L = 3.84717

62 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

-10 x 0 £ x £1

5

10 x - 4 1

5£ x £

1

2

2 - 2 x 1

2£ x £ 1

0 £ x £ 1


10


1L uH 9

10,0.2L = 4.63723

2L uH 9

10,0.2L = 2.94619 ´ 10-10

3L uH 9

10,0.2L = 5.49509

4L uH 9

10,0.2L = 5.20064

5L uH 9

10,0.2L = 8.04108

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<3, 0<t

¶u

¶xH0,tL=

¶u

¶xH3,tL=0 0 £ t

uHx,0L=-2 x 0 £ x £ 2

4 x - 12 2 £ x £ 30 £ x £ 3



1L uH1,0.4L = 4.80278

2L uH1,0.4L = -1.99413

3L uH1,0.4L = 3.53332

4L uH1,0.4L = 1.4699

5L uH1,0.4L = -2.92743

Untitled-2 63

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-Hx - 2L Hx - 1L x 0 £ x £ 2¶

¶tuHx,0L=3 Hx - 2L2 Hx - 1L x2 0. £ x £ 2



1L uH32,0.8L = 6.26779

2L uH32,0.8L = 7.41732

3L uH32,0.8L = 8.30172

4L uH32,0.8L = -2.25452

5L uH32,0.8L = -0.162165

64 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=-2 Hx - 2L x Hx - ΠL 0 £ x £ Π



1L uH2,0.2L = -7.54164

2L uH2,0.2L = -0.0133927

3L uH2,0.2L = -2.35293

4L uH2,0.2L = -8.67663

5L uH2,0.2L = 2.34328

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t




1L uH2,0.7L = 4.68798

2L uH2,0.7L = 4.85251

3L uH2,0.7L = -4.46785

4L uH2,0.7L = -1.04713

5L uH2,0.7L = 2.58766

Untitled-2 65

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=-2 x 0 £ x £ 2

2 x - 8 2 £ x £ 40 £ x £ 4

¶

¶tuHx,0L=

-4 x 0 £ x £ 1

12 x - 16 1 £ x £ 2

16 - 4 x 2 £ x £ 4

0. £ x £ 4



1L uH1,0.7L = -2.35144

2L uH1,0.7L = 5.05848

3L uH1,0.7L = -8.5558

4L uH1,0.7L = 2.7067

5L uH1,0.7L = -2.87883

66 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u



uHx,0L=

7 x

30 £ x £ 3

-7 x

-3+Π+

21

-3+Π+ 7 3 £ x £ Π

0 £ x £ Π



1L uH2,0.3L = 8.52126

2L uH2,0.3L = 3.62029

3L uH2,0.3L = 1.99583

4L uH2,0.3L = 6.98462

5L uH2,0.3L = -8.58317

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=-3 Hx - 2L Hx - 1L x2 0 £ x £ 2


10


1L uH 9

10,0.4L = 0.396831

2L uH 9

10,0.4L = 4.98207

3L uH 9

10,0.4L = -3.04543

4L uH 9

10,0.4L = -2.74041

5L uH 9

10,0.4L = -1.58348

Untitled-2 67

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=Hx - 2L2 Hx - 1L x2 0 £ x £ 2¶

¶tuHx,0L=Hx - 2L Hx - 1L x2 0. £ x £ 2


5


1L uH75,0.1L = -4.30034

2L uH75,0.1L = 3.75607

3L uH75,0.1L = -1.77366

4L uH75,0.1L = -8.27541

5L uH75,0.1L = 0.2185

68 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u



uHx,0L=

x 0 £ x £ 1

2 x - 1 1 £ x £ 2

-3 x

-2+Π+

6

-2+Π+ 3 2 £ x £ Π

0 £ x £ Π



1L uH2,1.L = -0.872158

2L uH2,1.L = 7.88482

3L uH2,1.L = 3.67614

4L uH2,1.L = -3.15281

5L uH2,1.L = 0.726692

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t




1L uH2,0.6L = -1.30658

2L uH2,0.6L = 0.346707

3L uH2,0.6L = 3.83794

4L uH2,0.6L = 1.04715

5L uH2,0.6L = 4.89443

Untitled-2 69

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-2 Hx - 3L2 Hx - 2L Hx - 1L x2 0 £ x £ 3

¶

¶tuHx,0L=

-8 x 0 £ x £ 1

15 x - 23 1 £ x £ 2

21 - 7 x 2 £ x £ 3

0. £ x £ 3



1L uH2,0.6L = 6.02228

2L uH2,0.6L = 8.34817

3L uH2,0.6L = 8.16116

4L uH2,0.6L = -0.884699

5L uH2,0.6L = -7.51272

70 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-Hx - 2L2 Hx - 1L x 0 £ x £ 2


5


1L uH15,0.4L = -1.32943

2L uH15,0.4L = 6.04501 ´ 10-6

3L uH15,0.4L = -4.17337

4L uH15,0.4L = 0.827836

5L uH15,0.4L = 6.94208

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<3, 0<t

¶u

¶xH0,tL=

¶u

¶xH3,tL=0 0 £ t

uHx,0L=

9 x 0 £ x £ 1

16 - 7 x 1 £ x £ 2

6 - 2 x 2 £ x £ 3

0 £ x £ 3



1L uH2,0.7L = 0.662108

2L uH2,0.7L = 3.66667

3L uH2,0.7L = -3.06648

4L uH2,0.7L = 0.219084

5L uH2,0.7L = -1.2639

Untitled-2 71

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u




¶

¶tuHx,0L=-Hx - 3L Hx - 1L x2 Hx - ΠL 0. £ x £ Π


1. mediante un desarrollo en serie de Fourier de orden 11.

1L uH1,1.L = -5.43469

2L uH1,1.L = 3.62216

3L uH1,1.L = -2.64636

4L uH1,1.L = -2.16571

5L uH1,1.L = 1.16543

72 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u






1L uH2,0.5L = -0.0733431

2L uH2,0.5L = -6.4477

3L uH2,0.5L = 4.90715

4L uH2,0.5L = 3.8672

5L uH2,0.5L = 2.52984

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t




1L uH1,0.1L = -1.21957

2L uH1,0.1L = -4.81683

3L uH1,0.1L = -1.90118

4L uH1,0.1L = -3.07394

5L uH1,0.1L = 10.6237

Untitled-2 73

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=Hx - 5L Hx - 2L Hx - 1L x 0 £ x £ 5

¶

¶tuHx,0L=

5 x

20 £ x £ 2

25

3-

5 x

32 £ x £ 5

0. £ x £ 5



1L uH2,0.4L = 5.05449

2L uH2,0.4L = -2.35945

3L uH2,0.4L = 4.24094

4L uH2,0.4L = -4.40812

5L uH2,0.4L = 0.612684

74 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=-Hx - 1L x2 Hx - ΠL 0 £ x £ Π



1L uH1,0.1L = -6.13731

2L uH1,0.1L = -7.11576

3L uH1,0.1L = -0.680294

4L uH1,0.1L = 0.216848

5L uH1,0.1L = 6.22433

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-5 x

30 £ x £ 3

5 x

-3+Π-

15

-3+Π- 5 3 £ x £ Π

0 £ x £ Π



1L uH2,0.7L = -3.38233

2L uH2,0.7L = -4.57427

3L uH2,0.7L = -2.5

4L uH2,0.7L = -0.223753

5L uH2,0.7L = -4.29425

Untitled-2 75

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u




¶

¶tuHx,0L=

-3 x 0 £ x £ 1

2 x - 5 1 £ x £ 2x

-2+Π-

2

-2+Π- 1 2 £ x £ Π

0. £ x £ Π



1L uH1,0.4L = 3.64935

2L uH1,0.4L = 3.10567

3L uH1,0.4L = -8.78715

4L uH1,0.4L = -7.2065

5L uH1,0.4L = 3.93478

76 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=3 Hx - 5L2 Hx - 4L x 0 £ x £ 5



1L uH2,0.6L = 4.58705

2L uH2,0.6L = -8.65021

3L uH2,0.6L = -81.6184

4L uH2,0.6L = -2.78408

5L uH2,0.6L = 2.85944

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-9 x

20 £ x £ 2

9 x

-2+Π-

18

-2+Π- 9 2 £ x £ Π

0 £ x £ Π



1L uH2,0.1L = -3.12637

2L uH2,0.1L = 0.374303

3L uH2,0.1L = -4.74914

4L uH2,0.1L = -0.407596

5L uH2,0.1L = -4.20401

Untitled-2 77

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u



uHx,0L=-2 Hx - 3L Hx - 1L x2 Hx - ΠL 0 £ x £ Π

¶

¶tuHx,0L=

-2 x 0 £ x £ 24 x

-2+Π-

8

-2+Π- 4 2 £ x £ Π

0. £ x £ Π



1L uH1,0.5L = -0.468852

2L uH1,0.5L = -1.84139

3L uH1,0.5L = -4.73178

4L uH1,0.5L = 7.17987

5L uH1,0.5L = 2.58752

78 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u



uHx,0L=

5 x 0 £ x £ 1

7 - 2 x 1 £ x £ 2

-3 x

-2+Π+

6

-2+Π+ 3 2 £ x £ Π

0 £ x £ Π



1L uH2,0.7L = -2.5334

2L uH2,0.7L = 1.87501

3L uH2,0.7L = -8.87574

4L uH2,0.7L = -0.386521

5L uH2,0.7L = 0.227436

� Ejercicio 2

¶u

¶tHx,tL=

¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-4 x 0 £ x £ 1

-x - 3 1 £ x £ 25 x

-2+Π-

10

-2+Π- 5 2 £ x £ Π

0 £ x £ Π



1L uH1,1.L = -2.96327

2L uH1,1.L = -4.70886

3L uH1,1.L = -4.31856

4L uH1,1.L = -0.69425

5L uH1,1.L = 2.39926

Untitled-2 79

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=3 Hx - 1L x2 Hx - ΠL2 0 £ x £ Π

¶

¶tuHx,0L=-3 Hx - 3L Hx - 1L x Hx - ΠL2 0. £ x £ Π



1L uH1,0.1L = -0.127768

2L uH1,0.1L = -2.8543

3L uH1,0.1L = 2.1068

4L uH1,0.1L = 6.64818

5L uH1,0.1L = 5.06611

80 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

-45 x

20 £ x £

2

5

70 x - 37 2

5£ x £

3

5

25

2-

25 x

2

3

5£ x £ 1

0 £ x £ 1


10


1L uH 3

10,0.9L = -5.92355

2L uH 3

10,0.9L = -8.99749

3L uH 3

10,0.9L = -4.359

4L uH 3

10,0.9L = -5.78311 ´ 10-16

5L uH 3

10,0.9L = 7.42515

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=-3 Hx - 2L x2 Hx - ΠL 0 £ x £ Π



1L uH1,0.8L = -1.98951

2L uH1,0.8L = 3.03168

3L uH1,0.8L = -0.994077

4L uH1,0.8L = -2.69301

5L uH1,0.8L = -3.08839

Untitled-2 81

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=

9 x

20 £ x £ 2

39 - 15 x 2 £ x £ 3

6 x - 24 3 £ x £ 4

0 £ x £ 4

¶

¶tuHx,0L=

7 x

20 £ x £ 2

33 - 13 x 2 £ x £ 3

6 x - 24 3 £ x £ 4

0. £ x £ 4



1L uH2,0.7L = 3.75534

2L uH2,0.7L = 8.5464

3L uH2,0.7L = -3.6695

4L uH2,0.7L = 4.6738

5L uH2,0.7L = 3.80899

82 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=-3 Hx - 3L x2 Hx - ΠL2 0 £ x £ Π



1L uH2,0.1L = -6.38388

2L uH2,0.1L = 3.7627

3L uH2,0.1L = 1.73588

4L uH2,0.1L = -8.68703

5L uH2,0.1L = 7.40264

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=2 Hx - 2L Hx - 1L x 0 £ x £ 2


10


1L uH1910

,0.3L = -4.62613

2L uH1910

,0.3L = 2.49533

3L uH1910

,0.3L = -3.5421

4L uH1910

,0.3L = -3.05561

5L uH1910

,0.3L = -0.0357879

Untitled-2 83

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=-2 Hx - 5L Hx - 2L x2 0 £ x £ 5¶

¶tuHx,0L=-2 Hx - 5L Hx - 3L Hx - 1L x2 0. £ x £ 5



1L uH4,0.3L = 5.61929

2L uH4,0.3L = 4.8486

3L uH4,0.3L = 88.1593

4L uH4,0.3L = -2.94427

5L uH4,0.3L = -5.71381

84 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-3 Hx - 3L Hx - 2L Hx - 1L x 0 £ x £ 3



1L uH1,0.7L = -2.77189

2L uH1,0.7L = -5.39292

3L uH1,0.7L = 8.45947

4L uH1,0.7L = -6.50691

5L uH1,0.7L = 0.160473

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=2 Hx - 2L Hx - 1L x2 0 £ x £ 2



1L uH12,0.1L = 1.69606

2L uH12,0.1L = 2.50986

3L uH12,0.1L = -0.257117

4L uH12,0.1L = 1.21866

5L uH12,0.1L = 2.75327

Untitled-2 85

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=-Hx - 2L Hx - 1L x2 Hx - ΠL 0 £ x £ Π

¶

¶tuHx,0L=2 Hx - 3L Hx - 2L x2 Hx - ΠL2 0. £ x £ Π



1L uH2,0.8L = -5.08286

2L uH2,0.8L = 7.35403

3L uH2,0.8L = 3.90991

4L uH2,0.8L = 6.22139

5L uH2,0.8L = 0.0860651

86 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=-2 Hx - 4L2 Hx - 2L x2 0 £ x £ 4



1L uH3,0.4L = 2.4593

2L uH3,0.4L = -7.58616

3L uH3,0.4L = -0.843466

4L uH3,0.4L = -2.32563

5L uH3,0.4L = -0.00238242

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

7 x 0 £ x £ 1

-7 x

-1+Π+

7

-1+Π+ 7 1 £ x £ Π

0 £ x £ Π



1L uH1,0.5L = 4.2204

2L uH1,0.5L = -2.52445

3L uH1,0.5L = -0.17649

4L uH1,0.5L = -2.40091

5L uH1,0.5L = 3.50694

Untitled-2 87

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=Hx - 3L2 Hx - 2L Hx - 1L x2 0 £ x £ 3

¶

¶tuHx,0L=

-2 x 0 £ x £ 1

4 - 6 x 1 £ x £ 2

8 x - 24 2 £ x £ 3

0. £ x £ 3



1L uH2,0.2L = -0.907217

2L uH2,0.2L = 2.26285

3L uH2,0.2L = 2.58907

4L uH2,0.2L = 6.10713

5L uH2,0.2L = -4.7361

88 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u



uHx,0L=

-7 x 0 £ x £ 1

16 x - 23 1 £ x £ 2

-9 x

-2+Π+

18

-2+Π+ 9 2 £ x £ Π

0 £ x £ Π



1L uH2,0.2L = 3.3278

2L uH2,0.2L = -0.302308

3L uH2,0.2L = 6.4134

4L uH2,0.2L = 1.87076

5L uH2,0.2L = -7.88003

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<5, 0<t

¶u

¶xH0,tL=

¶u

¶xH5,tL=0 0 £ t




1L uH3,0.3L = -4.86671

2L uH3,0.3L = -2.62119

3L uH3,0.3L = 24.4502

4L uH3,0.3L = 2.22623

5L uH3,0.3L = 0.104583

Untitled-2 89

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u



uHx,0L=

4 x 0 £ x £ 2

30 - 11 x 2 £ x £ 33 x

-3+Π-

9

-3+Π- 3 3 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=Hx - 2L Hx - 1L x2 Hx - ΠL 0. £ x £ Π



1L uH1,1.L = -6.27894

2L uH1,1.L = 5.71072

3L uH1,1.L = -7.95056

4L uH1,1.L = -2.31943

5L uH1,1.L = -2.05635

90 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=-3 Hx - 5L Hx - 3L x 0 £ x £ 5



1L uH2,0.4L = 0.894191

2L uH2,0.4L = -5.86171

3L uH2,0.4L = -4.02742

4L uH2,0.4L = 7.22153

5L uH2,0.4L = -0.735933

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

6 x 0 £ x £ 1

-6 x

-1+Π+

6

-1+Π+ 6 1 £ x £ Π

0 £ x £ Π



1L uH1,1.L = -3.99212

2L uH1,1.L = 0.13855

3L uH1,1.L = 3.00007

4L uH1,1.L = -1.6609

5L uH1,1.L = 0.147895

Untitled-2 91

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u



uHx,0L=

9 x 0 £ x £ 1

9 1 £ x £ 2

-9 x

-2+Π+

18

-2+Π+ 9 2 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

-7 x 0 £ x £ 17 x

-1+Π-

7

-1+Π- 7 1 £ x £ Π

0. £ x £ Π



1L uH2,0.4L = 1.95181

2L uH2,0.4L = -5.74499

3L uH2,0.4L = -6.61547

4L uH2,0.4L = -2.24139

5L uH2,0.4L = 7.19259

92 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u






1L uH2,0.3L = -8.38917

2L uH2,0.3L = -2.35592

3L uH2,0.3L = 6.61255

4L uH2,0.3L = 5.11667

5L uH2,0.3L = 5.85228

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=

35 x 0 £ x £1

5

67

5- 32 x 1

5£ x £

7

10

30 x - 30 7

10£ x £ 1

0 £ x £ 1


10


1L uH 1

10,0.7L = -1.15

2L uH 1

10,0.7L = 0.313182

3L uH 1

10,0.7L = -0.524944

4L uH 1

10,0.7L = 2.97087

5L uH 1

10,0.7L = -3.96538

Untitled-2 93

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=Hx - 2L2 Hx - 1L x 0 £ x £ 2

¶

¶tuHx,0L=

-x 0 £ x £ 1

x - 2 1 £ x £ 20. £ x £ 2


5


1L uH95,0.1L = -3.97022

2L uH95,0.1L = -8.35389

3L uH95,0.1L = 8.48937

4L uH95,0.1L = 0.0630284

5L uH95,0.1L = 0.977583

94 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u



uHx,0L=Hx - 3L Hx - 2L x Hx - ΠL 0 £ x £ Π



1L uH2,0.8L = 7.81376

2L uH2,0.8L = 0.807054

3L uH2,0.8L = 8.33245

4L uH2,0.8L = -7.16352

5L uH2,0.8L = -0.902623

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t

uHx,0L=-Hx - 4L Hx - 2L x2 0 £ x £ 4



1L uH2,0.6L = 3.92601

2L uH2,0.6L = 2.13333

3L uH2,0.6L = -3.76904

4L uH2,0.6L = -3.53883

5L uH2,0.6L = 0.431548

Untitled-2 95

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u



uHx,0L=

3 x 0 £ x £ 2

32 - 13 x 2 £ x £ 37 x

-3+Π-

21

-3+Π- 7 3 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

-6 x 0 £ x £ 17 x

2-

19

21 £ x £ 3

-x

-3+Π+

3

-3+Π+ 1 3 £ x £ Π

0. £ x £ Π



1L uH2,0.1L = 2.03831

2L uH2,0.1L = 0.544507

3L uH2,0.1L = -6.4425

4L uH2,0.1L = -4.80306

5L uH2,0.1L = 5.12379

96 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=Hx - 1L2 Ix -7

10M x 0 £ x £ 1


10


1L uH 3

10,0.7L = -0.620743

2L uH 3

10,0.7L = -2.75708 ´ 10-50

3L uH 3

10,0.7L = 7.13242

4L uH 3

10,0.7L = 6.14517

5L uH 3

10,0.7L = -8.52443

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

9 x

20 £ x £ 2

-9 x

-2+Π+

18

-2+Π+ 9 2 £ x £ Π

0 £ x £ Π



1L uH1,0.5L = -0.196407

2L uH1,0.5L = 4.4998

3L uH1,0.5L = 0.201841

4L uH1,0.5L = -0.871894

5L uH1,0.5L = -1.16423

Untitled-2 97

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=

-5 x 0 £ x £ 110 x

3-

25

31 £ x £ 4

25 - 5 x 4 £ x £ 5

0 £ x £ 5

¶

¶tuHx,0L=3 Hx - 5L Hx - 2L Hx - 1L x2 0. £ x £ 5



1L uH2,0.5L = -28.0812

2L uH2,0.5L = 8.35591

3L uH2,0.5L = -6.97588

4L uH2,0.5L = -5.54158

5L uH2,0.5L = 3.98013

98 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u



uHx,0L=-3 Hx - 1L x Hx - ΠL2 0 £ x £ Π



1L uH1,0.7L = 5.35503

2L uH1,0.7L = -4.14758

3L uH1,0.7L = -0.0000491903

4L uH1,0.7L = -6.71862

5L uH1,0.7L = -7.34585

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=-Hx - 3L Hx - 2L x2 Hx - ΠL 0 £ x £ Π



1L uH2,1.L = -2.83428

2L uH2,1.L = -4.11088

3L uH2,1.L = -3.33051

4L uH2,1.L = 0.137599

5L uH2,1.L = 1.35143

Untitled-2 99

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u



uHx,0L=2 Hx - 3L x Hx - ΠL2 0 £ x £ Π

¶

¶tuHx,0L=

2 x 0 £ x £ 2

-4 x

-2+Π+

8

-2+Π+ 4 2 £ x £ Π

0. £ x £ Π



1L uH1,0.3L = -3.65994

2L uH1,0.3L = 1.96255

3L uH1,0.3L = 8.74278

4L uH1,0.3L = -6.26471

5L uH1,0.3L = 3.4396

100 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-3 Hx - 3L Hx - 1L x2 0 £ x £ 3



1L uH1,0.5L = 6.1219

2L uH1,0.5L = 5.23716

3L uH1,0.5L = 0.000987826

4L uH1,0.5L = 7.41353

5L uH1,0.5L = -0.874666

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-9 x

20 £ x £ 2

17 x - 43 2 £ x £ 3

-8 x

-3+Π+

24

-3+Π+ 8 3 £ x £ Π

0 £ x £ Π



1L uH1,0.4L = -0.497097

2L uH1,0.4L = 2.61457

3L uH1,0.4L = -2.24754

4L uH1,0.4L = -1.12486

5L uH1,0.4L = -2.84527

Untitled-2 101

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=x 0 £ x £ 1

2 - x 1 £ x £ 20 £ x £ 2

¶

¶tuHx,0L=3 Hx - 2L Hx - 1L x2 0. £ x £ 2


10en el instante t=


1L uH 3

10,0.6L = 8.1229

2L uH 3

10,0.6L = 8.7615

3L uH 3

10,0.6L = 5.57589

4L uH 3

10,0.6L = 0.454403

5L uH 3

10,0.6L = 8.46199

102 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u



uHx,0L=3 Hx - 3L x2 Hx - ΠL 0 £ x £ Π



1L uH1,0.6L = -3.59678

2L uH1,0.6L = 0.0553968

3L uH1,0.6L = 6.29931

4L uH1,0.6L = 1.38085

5L uH1,0.6L = 1.78583

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=2 Hx - 1L x2 Hx - ΠL2 0 £ x £ Π



1L uH2,1.L = 3.70672

2L uH2,1.L = -1.08062

3L uH2,1.L = -1.90981

4L uH2,1.L = 1.31109

5L uH2,1.L = -4.41642

Untitled-2 103

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u



uHx,0L=

5 x

30 £ x £ 3

-5 x

-3+Π+

15

-3+Π+ 5 3 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

5 x

20 £ x £ 2

5 2 £ x £ 3

-5 x

-3+Π+

15

-3+Π+ 5 3 £ x £ Π

0. £ x £ Π



1L uH1,0.2L = 2.17233

2L uH1,0.2L = -5.34888

3L uH1,0.2L = 6.50881

4L uH1,0.2L = -8.01158

5L uH1,0.2L = 4.14368

104 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-4 x 0 £ x £ 1

2 x - 6 1 £ x £ 30 £ x £ 3



1L uH1,0.6L = -0.00733289

2L uH1,0.6L = -8.26306

3L uH1,0.6L = -1.46186

4L uH1,0.6L = 6.83218

5L uH1,0.6L = 2.03824

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-3 x 0 £ x £ 1

x - 4 1 £ x £ 22 x

-2+Π-

4

-2+Π- 2 2 £ x £ Π

0 £ x £ Π



1L uH2,0.9L = -2.89179

2L uH2,0.9L = -1.63662

3L uH2,0.9L = 4.30664

4L uH2,0.9L = 2.1389

5L uH2,0.9L = 0.485828

Untitled-2 105

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=

2 x 0 £ x £ 1

x + 1 1 £ x £ 2

-3 x

-2+Π+

6

-2+Π+ 3 2 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

-4 x 0 £ x £ 1

11 x - 15 1 £ x £ 2

-7 x

-2+Π+

14

-2+Π+ 7 2 £ x £ Π

0. £ x £ Π



1L uH1,0.4L = 0.527578

2L uH1,0.4L = -7.47151

3L uH1,0.4L = 4.28258

4L uH1,0.4L = 6.78516

5L uH1,0.4L = -3.91401

106 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u






1L uH1,0.6L = 5.7646

2L uH1,0.6L = -4.2438

3L uH1,0.6L = 3.52537

4L uH1,0.6L = 0.727263

5L uH1,0.6L = -2.32768

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t

uHx,0L=

x 0 £ x £ 1

2 x - 1 1 £ x £ 3

20 - 5 x 3 £ x £ 4

0 £ x £ 4



1L uH3,0.3L = 2.42957

2L uH3,0.3L = 4.74173

3L uH3,0.3L = -0.0273467

4L uH3,0.3L = -3.76634

5L uH3,0.3L = 0.000552025

Untitled-2 107

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u



uHx,0L=

3 x

20 £ x £ 2

-3 x

-2+Π+

6

-2+Π+ 3 2 £ x £ Π

0 £ x £ Π

¶




1L uH1,0.7L = -2.15423

2L uH1,0.7L = -2.95751

3L uH1,0.7L = -7.72496

4L uH1,0.7L = 3.38904

5L uH1,0.7L = 6.75267

108 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u



uHx,0L=-3 Hx - 1L x2 Hx - ΠL2 0 £ x £ Π



1L uH2,1.L = -7.9383

2L uH2,1.L = -4.45005

3L uH2,1.L = 3.19405

4L uH2,1.L = -0.154715

5L uH2,1.L = 5.88858

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=2 Hx - 1L2 Ix -9

10M x2 0 £ x £ 1


5


1L uH45,0.6L = 0.612288

2L uH45,0.6L = 4.63808

3L uH45,0.6L = -0.0266667

4L uH45,0.6L = -1.91215

5L uH45,0.6L = 2.41109

Untitled-2 109

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u



uHx,0L=

-9 x 0 £ x £ 19 x

-1+Π-

9

-1+Π- 9 1 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

8 x 0 £ x £ 127

2-

11 x

21 £ x £ 3

3 x

-3+Π-

9

-3+Π- 3 3 £ x £ Π

0. £ x £ Π



1L uH1,0.6L = 4.84177

2L uH1,0.6L = 5.38221

3L uH1,0.6L = 8.87452

4L uH1,0.6L = -1.39533

5L uH1,0.6L = 6.02965

110 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-3 Hx - 3L Hx - 2L Hx - 1L x2 0 £ x £ 3



1L uH1,0.4L = -5.96724

2L uH1,0.4L = 1.20761

3L uH1,0.4L = 3.82141

4L uH1,0.4L = 7.347

5L uH1,0.4L = 0.0773271

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

3 x

20 £ x £ 2

-3 x

-2+Π+

6

-2+Π+ 3 2 £ x £ Π

0 £ x £ Π



1L uH2,1.L = 4.55776

2L uH2,1.L = 1.5

3L uH2,1.L = -0.820773

4L uH2,1.L = -3.29303

5L uH2,1.L = 4.98823

Untitled-2 111

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-3 Hx - 2L2 Hx - 1L x2 0 £ x £ 2¶

¶tuHx,0L=-3 Hx - 2L Hx - 1L x 0. £ x £ 2


10en el instante t=


1L uH 7

10,0.9L = -7.28146

2L uH 7

10,0.9L = 1.83345

3L uH 7

10,0.9L = -5.53323

4L uH 7

10,0.9L = -0.186378

5L uH 7

10,0.9L = 0.517638

112 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=Hx - 2L x Hx - ΠL2 0 £ x £ Π



1L uH1,1.L = -3.00921 ´ 10-11

2L uH1,1.L = -8.54704

3L uH1,1.L = 6.34084

4L uH1,1.L = -1.25682

5L uH1,1.L = 6.88577

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

x 0 £ x £ 2

-2 x

-2+Π+

4

-2+Π+ 2 2 £ x £ Π

0 £ x £ Π



1L uH1,0.5L = 4.77937

2L uH1,0.5L = 4.1199

3L uH1,0.5L = -1.73044

4L uH1,0.5L = 0.998497

5L uH1,0.5L = 1.61795

Untitled-2 113

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=-Hx - 2L x Hx - ΠL2 0 £ x £ Π

¶

¶tuHx,0L=Hx - 3L x2 Hx - ΠL2 0. £ x £ Π



1L uH2,0.9L = -2.44173

2L uH2,0.9L = 2.13421

3L uH2,0.9L = -7.77456

4L uH2,0.9L = -5.27874

5L uH2,0.9L = 1.72653

114 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=

-5 x

30 £ x £ 3

5 x

-3+Π-

15

-3+Π- 5 3 £ x £ Π

0 £ x £ Π



1L uH1,0.2L = -1.34735

2L uH1,0.2L = -1.88075

3L uH1,0.2L = -4.18787

4L uH1,0.2L = -0.0188362

5L uH1,0.2L = 7.06112

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=-Hx - 3L Hx - 1L x Hx - ΠL 0 £ x £ Π



1L uH2,0.4L = -3.50383

2L uH2,0.4L = -2.81153

3L uH2,0.4L = 1.76803

4L uH2,0.4L = -1.36365

5L uH2,0.4L = -0.543407

Untitled-2 115

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u



uHx,0L=-Hx - 3L x2 Hx - ΠL 0 £ x £ Π

¶

¶tuHx,0L=-Hx - 3L Hx - 2L x2 Hx - ΠL 0. £ x £ Π



1L uH2,0.9L = -8.73679

2L uH2,0.9L = -6.81471

3L uH2,0.9L = 2.00722

4L uH2,0.9L = -0.91116

5L uH2,0.9L = -3.66957

116 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=3 Hx - 5L Hx - 2L Hx - 1L x2 0 £ x £ 5



1L uH2,0.2L = -8.71672

2L uH2,0.2L = 4.50076

3L uH2,0.2L = 7.74789

4L uH2,0.2L = -5.64978

5L uH2,0.2L = -46.8364

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<3, 0<t

¶u

¶xH0,tL=

¶u

¶xH3,tL=0 0 £ t




1L uH1,0.4L = -4.07295

2L uH1,0.4L = 0.384957

3L uH1,0.4L = -2.56999

4L uH1,0.4L = 3.27376

5L uH1,0.4L = -0.655193

Untitled-2 117

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u



uHx,0L=

4 x

30 £ x £ 3

-4 x

-3+Π+

12

-3+Π+ 4 3 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

-4 x

30 £ x £ 3

4 x

-3+Π-

12

-3+Π- 4 3 £ x £ Π

0. £ x £ Π



1L uH1,0.4L = 8.45357

2L uH1,0.4L = 0.802366

3L uH1,0.4L = -0.479523

4L uH1,0.4L = -8.4679

5L uH1,0.4L = -7.27854

118 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=-3 Hx - 4L2 Hx - 1L x2 0 £ x £ 4



1L uH2,0.5L = -0.307613

2L uH2,0.5L = 6.42154

3L uH2,0.5L = 4.59818

4L uH2,0.5L = 8.50319

5L uH2,0.5L = 3.98406

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

6 x 0 £ x £ 1

21 - 15 x 1 £ x £ 29 x

-2+Π-

18

-2+Π- 9 2 £ x £ Π

0 £ x £ Π



1L uH2,0.2L = -3.53543

2L uH2,0.2L = -1.97187

3L uH2,0.2L = -1.23319

4L uH2,0.2L = -1.84331

5L uH2,0.2L = -1.91873

Untitled-2 119

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u




¶

¶tuHx,0L=-3 Hx - 2L Hx - 1L x2 Hx - ΠL2 0. £ x £ Π



1L uH1,0.3L = 2.03854

2L uH1,0.3L = 8.76012

3L uH1,0.3L = -7.53076

4L uH1,0.3L = -3.17164

5L uH1,0.3L = 2.70317

120 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u



uHx,0L=3 Hx - 1L x2 Hx - ΠL 0 £ x £ Π



1L uH1,1.L = -8.75017

2L uH1,1.L = 5.8852

3L uH1,1.L = -0.000978652

4L uH1,1.L = 8.98076

5L uH1,1.L = 2.95271

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=-5 x 0 £ x £ 1

5 x - 10 1 £ x £ 20 £ x £ 2


5


1L uH65,0.9L = -2.5

2L uH65,0.9L = 0.531595

3L uH65,0.9L = -0.718945

4L uH65,0.9L = 0.885723

5L uH65,0.9L = 4.95218

Untitled-2 121

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=3 Hx - 2L Hx - 1L x2 0 £ x £ 2¶

¶tuHx,0L=-Hx - 2L2 Hx - 1L x2 0. £ x £ 2


5en el instante t=


1L uH85,0.5L = -7.99378

2L uH85,0.5L = -0.119786

3L uH85,0.5L = 4.68105

4L uH85,0.5L = 4.25403

5L uH85,0.5L = 6.83163

122 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=-Hx - 1L Ix -4

5M x 0 £ x £ 1


10


1L uH 3

10,0.9L = -1.18519 ´ 10-63

2L uH 3

10,0.9L = -2.36409

3L uH 3

10,0.9L = 0.684984

4L uH 3

10,0.9L = -4.6122

5L uH 3

10,0.9L = -8.11232

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-3 x 0 £ x £ 1

4 x - 7 1 £ x £ 3

-5 x

-3+Π+

15

-3+Π+ 5 3 £ x £ Π

0 £ x £ Π



1L uH2,0.8L = -1.61279

2L uH2,0.8L = 1.15823

3L uH2,0.8L = 2.11611

4L uH2,0.8L = 1.2905

5L uH2,0.8L = 0.271831

Untitled-2 123

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=

8 x 0 £ x £ 1

-8 x

-1+Π+

8

-1+Π+ 8 1 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

8 x 0 £ x £ 1

8 1 £ x £ 3

-8 x

-3+Π+

24

-3+Π+ 8 3 £ x £ Π

0. £ x £ Π



1L uH1,0.8L = -5.10102

2L uH1,0.8L = -8.42737

3L uH1,0.8L = -1.22019

4L uH1,0.8L = 7.96811

5L uH1,0.8L = -3.8454

124 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=-3 Hx - 1L2 Ix -7

10M Ix -

1

5M x 0 £ x £ 1


5


1L uH45,0.5L = 3.80855 ´ 10-37

2L uH45,0.5L = 4.42119

3L uH45,0.5L = -2.12691

4L uH45,0.5L = 8.74456

5L uH45,0.5L = -8.31584

� Ejercicio 2

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=-Hx - 1L Ix -2

5M Ix -

1

10M x 0 £ x £ 1


10


1L uH 9

10,0.6L = 0.0150558

2L uH 9

10,0.6L = 4.4197

3L uH 9

10,0.6L = -1.39227

4L uH 9

10,0.6L = 2.73578

5L uH 9

10,0.6L = 3.58468

Untitled-2 125

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u



uHx,0L=

2 x 0 £ x £ 1

8 - 6 x 1 £ x £ 24 x

-2+Π-

8

-2+Π- 4 2 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=-Hx - 3L Hx - 1L x2 Hx - ΠL2 0. £ x £ Π



1L uH2,0.3L = -7.6118

2L uH2,0.3L = -3.07288

3L uH2,0.3L = 2.45342

4L uH2,0.3L = 1.64712

5L uH2,0.3L = -7.72049

126 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u



uHx,0L=-Hx - 2L x Hx - ΠL2 0 £ x £ Π



1L uH2,0.3L = 6.13916

2L uH2,0.3L = 3.42064

3L uH2,0.3L = -5.80104

4L uH2,0.3L = 1.03304

5L uH2,0.3L = -3.3841

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-7 x 0 £ x £ 1

x - 8 1 £ x £ 35 x

-3+Π-

15

-3+Π- 5 3 £ x £ Π

0 £ x £ Π



1L uH2,0.7L = -5.04713

2L uH2,0.7L = -1.75982

3L uH2,0.7L = 4.90359

4L uH2,0.7L = -1.99203

5L uH2,0.7L = 0.170842

Untitled-2 127

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u



uHx,0L=

-2 x 0 £ x £ 12 x

-1+Π-

2

-1+Π- 2 1 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=-Hx - 2L x Hx - ΠL2 0. £ x £ Π



1L uH2,0.3L = -8.10088

2L uH2,0.3L = 0.508919

3L uH2,0.3L = -4.42494

4L uH2,0.3L = -4.08151

5L uH2,0.3L = -0.952112

128 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=3 Hx - 3L x2 Hx - ΠL 0 £ x £ Π



1L uH1,1.L = 0.643356

2L uH1,1.L = -4.96089

3L uH1,1.L = -2.95085

4L uH1,1.L = 1.16989

5L uH1,1.L = 1.70339 ´ 10-10

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t




1L uH2,0.5L = -1.94526

2L uH2,0.5L = 9.75234

3L uH2,0.5L = -1.34463

4L uH2,0.5L = 0.163868

5L uH2,0.5L = 1.20785

Untitled-2 129

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u



uHx,0L=

-5 x 0 £ x £ 17 x

2-

17

21 £ x £ 3

-2 x

-3+Π+

6

-3+Π+ 2 3 £ x £ Π

0 £ x £ Π

¶




1L uH2,0.9L = 2.94277

2L uH2,0.9L = 0.863541

3L uH2,0.9L = 8.3136

4L uH2,0.9L = 0.139843

5L uH2,0.9L = 3.54835

130 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=Hx - 2L2 Hx - 1L x2 0 £ x £ 2


10


1L uH1110

,0.3L = 0.00429167

2L uH1110

,0.3L = 3.48345

3L uH1110

,0.3L = -3.91467

4L uH1110

,0.3L = -7.83233

5L uH1110

,0.3L = 8.84536

� Ejercicio 2

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t

uHx,0L=

-4 x 0 £ x £ 14 x

3-

16

31 £ x £ 4

0 £ x £ 4



1L uH1,0.2L = 3.7419

2L uH1,0.2L = 2.9438

3L uH1,0.2L = 1.98529

4L uH1,0.2L = -2.77654

5L uH1,0.2L = 0.154237

Untitled-2 131

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u



uHx,0L=Hx - 3L Hx - 2L x Hx - ΠL2 0 £ x £ Π

¶

¶tuHx,0L=2 Hx - 1L x2 Hx - ΠL 0. £ x £ Π



1L uH1,0.8L = -8.20829

2L uH1,0.8L = 1.10398

3L uH1,0.8L = -1.29545

4L uH1,0.8L = -7.9269

5L uH1,0.8L = 3.7959

132 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u






1L uH2,0.3L = 6.99736

2L uH2,0.3L = 5.35779

3L uH2,0.3L = -1.57276

4L uH2,0.3L = -0.295714

5L uH2,0.3L = -8.54757

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

6 x 0 £ x £ 123

2-

11 x

21 £ x £ 3

5 x

-3+Π-

15

-3+Π- 5 3 £ x £ Π

0 £ x £ Π



1L uH1,0.4L = 1.16065

2L uH1,0.4L = 3.07399

3L uH1,0.4L = 3.75998

4L uH1,0.4L = -3.30133

5L uH1,0.4L = 3.76146

Untitled-2 133

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u



uHx,0L=

-2 x 0 £ x £ 1

2 - 4 x 1 £ x £ 26 x

-2+Π-

12

-2+Π- 6 2 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

-7 x

20 £ x £ 2

7 x

-2+Π-

14

-2+Π- 7 2 £ x £ Π

0. £ x £ Π



1L uH2,0.6L = -2.92547

2L uH2,0.6L = 6.01962

3L uH2,0.6L = 2.48956

4L uH2,0.6L = -2.64627

5L uH2,0.6L = -5.96225

134 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-3 Hx - 3L Hx - 2L Hx - 1L x2 0 £ x £ 3



1L uH2,0.3L = 0.578549

2L uH2,0.3L = 6.97263

3L uH2,0.3L = 4.70297

4L uH2,0.3L = 8.82399

5L uH2,0.3L = 0.000138977

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<3, 0<t

¶u

¶xH0,tL=

¶u

¶xH3,tL=0 0 £ t

uHx,0L=

-3 x 0 £ x £ 1

12 x - 15 1 £ x £ 2

27 - 9 x 2 £ x £ 3

0 £ x £ 3



1L uH2,1.L = 2.00009

2L uH2,1.L = -3.3927

3L uH2,1.L = -4.22181

4L uH2,1.L = 2.54035

5L uH2,1.L = -0.359145

Untitled-2 135

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=

2 x 0 £ x £ 1

-2 x

-1+Π+

2

-1+Π+ 2 1 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=3 Hx - 2L Hx - 1L x Hx - ΠL2 0. £ x £ Π



1L uH2,0.1L = -5.13824

2L uH2,0.1L = 1.05394

3L uH2,0.1L = 5.60414

4L uH2,0.1L = -8.11795

5L uH2,0.1L = 3.86405

136 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=x 0 £ x £ 2

6 - 2 x 2 £ x £ 30 £ x £ 3



1L uH2,0.5L = 0.828667

2L uH2,0.5L = -7.02768

3L uH2,0.5L = -7.74348

4L uH2,0.5L = -7.21997

5L uH2,0.5L = -7.60044

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<3, 0<t

¶u

¶xH0,tL=

¶u

¶xH3,tL=0 0 £ t

uHx,0L=

5 x

20 £ x £ 2

15 - 5 x 2 £ x £ 30 £ x £ 3



1L uH2,0.2L = 2.5531

2L uH2,0.2L = -2.19397

3L uH2,0.2L = -2.32841

4L uH2,0.2L = 4.51396

5L uH2,0.2L = -4.73667

Untitled-2 137

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=5 x 0 £ x £ 1

10 - 5 x 1 £ x £ 20 £ x £ 2

¶

¶tuHx,0L=Hx - 2L Hx - 1L x2 0. £ x £ 2


10


1L uH 7

10,0.2L = -0.0161439

2L uH 7

10,0.2L = -2.61764

3L uH 7

10,0.2L = -4.30918

4L uH 7

10,0.2L = 8.28959

5L uH 7

10,0.2L = 6.80608

138 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-9 x 0 £ x £ 1

9 x - 18 1 £ x £ 20 £ x £ 2


10


1L uH 7

10,0.4L = -6.53497

2L uH 7

10,0.4L = -1.22859

3L uH 7

10,0.4L = 5.09556

4L uH 7

10,0.4L = -2.33019

5L uH 7

10,0.4L = -9.01177 ´ 10-7

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=Hx - 3L Hx - 1L x Hx - ΠL2 0 £ x £ Π



1L uH1,0.3L = -3.852

2L uH1,0.3L = -0.135361

3L uH1,0.3L = -4.00029

4L uH1,0.3L = -4.21202

5L uH1,0.3L = -4.50132

Untitled-2 139

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

-20 x 0 £ x £3

10

15 x -21

2

3

10£ x £

1

2

6 x - 6 1

2£ x £ 1

0 £ x £ 1

¶

¶tuHx,0L=

10 x 0 £ x £1

10

10

9-

10 x

9

1

10£ x £ 1

0. £ x £ 1


5


1L uH35,0.4L = -2.57995

2L uH35,0.4L = 1.79323

3L uH35,0.4L = 3.20922

4L uH35,0.4L = 7.38586

5L uH35,0.4L = 3.76913

140 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u



uHx,0L=-Hx - 2L x2 Hx - ΠL2 0 £ x £ Π



1L uH1,0.2L = 6.75362

2L uH1,0.2L = 3.05641

3L uH1,0.2L = 1.65303

4L uH1,0.2L = 0.0798722

5L uH1,0.2L = 3.10137

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=-3 Hx - 1L x2 Hx - ΠL 0 £ x £ Π



1L uH1,1.L = 2.8194

2L uH1,1.L = 6.85979

3L uH1,1.L = 3.29529

4L uH1,1.L = -1.0664

5L uH1,1.L = -1.30187

Untitled-2 141

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=2 x 0 £ x £ 1

4 - 2 x 1 £ x £ 20 £ x £ 2

¶

¶tuHx,0L=

-x 0 £ x £ 1

x - 2 1 £ x £ 20. £ x £ 2


10en el instante t=


1L uH1910

,0.6L = -5.30089

2L uH1910

,0.6L = 0.134792

3L uH1910

,0.6L = 4.79132

4L uH1910

,0.6L = -3.75151

5L uH1910

,0.6L = 8.51257

142 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u






1L uH2,0.3L = -2.85473

2L uH2,0.3L = 0.153034

3L uH2,0.3L = -7.67681

4L uH2,0.3L = 2.50092

5L uH2,0.3L = -7.02054

� Ejercicio 2

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<3, 0<t

¶u

¶xH0,tL=

¶u

¶xH3,tL=0 0 £ t

uHx,0L=-3 x 0 £ x £ 2

6 x - 18 2 £ x £ 30 £ x £ 3



1L uH1,0.9L = 3.46227

2L uH1,0.9L = 3.77934

3L uH1,0.9L = -2.84975

4L uH1,0.9L = 1.48692

5L uH1,0.9L = -0.524002

Untitled-2 143

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u



uHx,0L=

2 x 0 £ x £ 1

3 x - 1 1 £ x £ 2

-5 x

-2+Π+

10

-2+Π+ 5 2 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=-3 Hx - 2L x2 Hx - ΠL2 0. £ x £ Π



1L uH1,0.1L = -8.04959

2L uH1,0.1L = -8.98605

3L uH1,0.1L = -4.24145

4L uH1,0.1L = -2.90985

5L uH1,0.1L = 3.42779

144 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=

-9 x 0 £ x £ 1

12 x - 21 1 £ x £ 2

9 - 3 x 2 £ x £ 3

0 £ x £ 3



1L uH2,0.8L = -3.82554

2L uH2,0.8L = -0.0818509

3L uH2,0.8L = 2.38912

4L uH2,0.8L = -5.26124

5L uH2,0.8L = -7.14239

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t

uHx,0L=2 Hx - 4L2 Hx - 2L x 0 £ x £ 4



1L uH3,0.8L = -4.17339

2L uH3,0.8L = 1.65336

3L uH3,0.8L = 3.23088

4L uH3,0.8L = 2.98606

5L uH3,0.8L = 2.73839

Untitled-2 145

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=

-x 0 £ x £ 1

6 - 7 x 1 £ x £ 2

4 x - 16 2 £ x £ 4

0 £ x £ 4

¶

¶tuHx,0L=

4 x 0 £ x £ 2

16 - 4 x 2 £ x £ 40. £ x £ 4



1L uH2,0.6L = -2.32973

2L uH2,0.6L = 3.10818

3L uH2,0.6L = -0.573192

4L uH2,0.6L = -1.41429

5L uH2,0.6L = 0.0578286

146 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=Hx - 1L2 Ix -1

10M x2 0 £ x £ 1


5


1L uH35,0.9L = 4.04499 ´ 10-37

2L uH35,0.9L = 5.92616

3L uH35,0.9L = 7.05067

4L uH35,0.9L = -4.14053

5L uH35,0.9L = 7.2208

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t

uHx,0L=-3 Hx - 4L2 Hx - 2L x2 0 £ x £ 4



1L uH1,0.9L = 3.115

2L uH1,0.9L = 0.0956234

3L uH1,0.9L = 1.95553

4L uH1,0.9L = 2.03462

5L uH1,0.9L = 3.39496

Untitled-2 147

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=

-2 x 0 £ x £ 2

8 x - 20 2 £ x £ 3

16 - 4 x 3 £ x £ 4

0 £ x £ 4

¶

¶tuHx,0L=-Hx - 4L2 Hx - 3L x 0. £ x £ 4



1L uH2,0.3L = -5.06727

2L uH2,0.3L = 0.316429

3L uH2,0.3L = 4.40156

4L uH2,0.3L = 5.25843

5L uH2,0.3L = -0.258318

148 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-4 x 0 £ x £ 1

2 x - 6 1 £ x £ 2 ê 2 £ x £ 30 £ x £ 3



1L uH1,0.7L = -6.82246

2L uH1,0.7L = -7.49514

3L uH1,0.7L = -0.000012676

4L uH1,0.7L = 3.35135

5L uH1,0.7L = -5.81987

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-3 x 0 £ x £ 2

7 x - 20 2 £ x £ 3

-x

-3+Π+

3

-3+Π+ 1 3 £ x £ Π

0 £ x £ Π



1L uH2,0.9L = -4.99657

2L uH2,0.9L = -2.04679

3L uH2,0.9L = -2.6831

4L uH2,0.9L = -3.56361

5L uH2,0.9L = 3.79

Untitled-2 149

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=

4 x 0 £ x £ 240

3-

8 x

32 £ x £ 5

0 £ x £ 5

¶

¶tuHx,0L=

-x

20 £ x £ 4

2 x - 10 4 £ x £ 50. £ x £ 5



1L uH2,0.9L = 3.91501

2L uH2,0.9L = 6.69762

3L uH2,0.9L = -4.51463

4L uH2,0.9L = 5.83505

5L uH2,0.9L = -6.80555

150 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u



uHx,0L=-Hx - 3L Hx - 2L x Hx - ΠL 0 £ x £ Π



1L uH2,0.2L = 7.92863

2L uH2,0.2L = -0.00344346

3L uH2,0.2L = -3.68991

4L uH2,0.2L = 0.816337

5L uH2,0.2L = -1.67528

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t




1L uH1,1.L = 4.79773

2L uH1,1.L = -0.692502

3L uH1,1.L = 4.34462

4L uH1,1.L = 4.52061

5L uH1,1.L = -4.38363

Untitled-2 151

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=-2 Hx - 4L Hx - 2L x2 0 £ x £ 4

¶

¶tuHx,0L=

3 x

20 £ x £ 2

6 -3 x

22 £ x £ 4

0. £ x £ 4



1L uH1,0.9L = -6.29479

2L uH1,0.9L = 4.04622

3L uH1,0.9L = 11.1853

4L uH1,0.9L = 5.11889

5L uH1,0.9L = 2.76125

152 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=-3 Hx - 5L Hx - 4L x2 0 £ x £ 5



1L uH3,0.6L = -4.44206

2L uH3,0.6L = -1.20452

3L uH3,0.6L = 6.97063

4L uH3,0.6L = -2.46299

5L uH3,0.6L = 6.45644

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-x

30 £ x £ 3

x

-3+Π-

3

-3+Π- 1 3 £ x £ Π

0 £ x £ Π



1L uH1,0.1L = -0.417653

2L uH1,0.1L = -3.03676

3L uH1,0.1L = -2.9685

4L uH1,0.1L = 3.8866

5L uH1,0.1L = 1.81179

Untitled-2 153

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=

-x 0 £ x £ 1x

3-

4

31 £ x £ 4

0 £ x £ 4

¶

¶tuHx,0L=

6 x 0 £ x £ 1

8 - 2 x 1 £ x £ 40. £ x £ 4



1L uH1,0.6L = -6.25514

2L uH1,0.6L = 2.90696

3L uH1,0.6L = 0.736331

4L uH1,0.6L = 4.56079

5L uH1,0.6L = 8.86221

154 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-Hx - 3L2 Hx - 2L Hx - 1L x2 0 £ x £ 3



1L uH2,0.4L = 8.33024

2L uH2,0.4L = 1.19822

3L uH2,0.4L = 8.61825

4L uH2,0.4L = 0.0000325788

5L uH2,0.4L = -2.58948

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=

-60 x

70 £ x £

7

10

20 x - 20 7

10£ x £ 1

0 £ x £ 1


10


1L uH 3

10,1.L = -3.

2L uH 3

10,1.L = -0.325842

3L uH 3

10,1.L = 4.79292

4L uH 3

10,1.L = -3.99008

5L uH 3

10,1.L = 4.02783

Untitled-2 155

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-3 Hx - 2L2 Hx - 1L x2 0 £ x £ 2

¶

¶tuHx,0L=

4 x 0 £ x £ 1

8 - 4 x 1 £ x £ 20. £ x £ 2


5


1L uH95,0.7L = 0.33429

2L uH95,0.7L = -8.69389

3L uH95,0.7L = -1.7576

4L uH95,0.7L = -8.5334

5L uH95,0.7L = 8.13013

156 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=Hx - 2L x2 Hx - ΠL2 0 £ x £ Π



1L uH1,0.6L = 8.9953

2L uH1,0.6L = -5.99357 ´ 10-7

3L uH1,0.6L = 8.57374

4L uH1,0.6L = -7.76321

5L uH1,0.6L = -7.41548

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=-2 x 0 £ x £ 1

2 x - 4 1 £ x £ 20 £ x £ 2


10


1L uH 1

10,0.2L = 1.24806

2L uH 1

10,0.2L = -4.60112

3L uH 1

10,0.2L = 0.9318

4L uH 1

10,0.2L = 3.70117

5L uH 1

10,0.2L = -1.

Untitled-2 157

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u



uHx,0L=

7 x

20 £ x £ 2

-7 x

-2+Π+

14

-2+Π+ 7 2 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

-x

30 £ x £ 3

x

-3+Π-

3

-3+Π- 1 3 £ x £ Π

0. £ x £ Π



1L uH2,0.5L = -0.454281

2L uH2,0.5L = -5.83309

3L uH2,0.5L = 4.67986

4L uH2,0.5L = 5.23591

5L uH2,0.5L = 7.79108

158 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

-35 x

30 £ x £

3

5

5 - 20 x 3

5£ x £

7

10

30 x - 30 7

10£ x £ 1

0 £ x £ 1



1L uH12,0.3L = -0.000047356

2L uH12,0.3L = 1.49795

3L uH12,0.3L = 7.01535

4L uH12,0.3L = -8.99381

5L uH12,0.3L = 3.22253

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=-Hx - 1L2 Ix -9

10M Ix -

7

10M x2 0 £ x £ 1


10


1L uH 3

10,0.2L = -0.574811

2L uH 3

10,0.2L = 3.5515

3L uH 3

10,0.2L = -1.46098

4L uH 3

10,0.2L = -0.00385714

5L uH 3

10,0.2L = 1.97224

� Ejercicio 3

Untitled-2 159

�

Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-Hx - 2L Hx - 1L x2 0 £ x £ 2¶

¶tuHx,0L=-Hx - 2L Hx - 1L x 0. £ x £ 2


10en el instante t=


1L uH1110

,0.5L = 7.73128

2L uH1110

,0.5L = -0.169579

3L uH1110

,0.5L = 2.13119

4L uH1110

,0.5L = -3.52358

5L uH1110

,0.5L = -5.79337

160 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=3 Hx - 3L Hx - 1L x 0 £ x £ 3



1L uH2,0.7L = -1.39638 ´ 10-8

2L uH2,0.7L = -2.9368

3L uH2,0.7L = 8.87262

4L uH2,0.7L = -3.30187

5L uH2,0.7L = 1.5139

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=-3 Hx - 2L x2 Hx - ΠL2 0 £ x £ Π



1L uH1,0.2L = -3.18456

2L uH1,0.2L = -0.0801207

3L uH1,0.2L = 2.7455

4L uH1,0.2L = 4.71584

5L uH1,0.2L = 2.07554

Untitled-2 161

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=3 Hx - 1L x2 Hx - ΠL2 0 £ x £ Π

¶

¶tuHx,0L=

9 x 0 £ x £ 1

-9 x

-1+Π+

9

-1+Π+ 9 1 £ x £ Π

0. £ x £ Π



1L uH2,0.5L = -0.855016

2L uH2,0.5L = -3.42236

3L uH2,0.5L = -7.38841

4L uH2,0.5L = -5.78842

5L uH2,0.5L = 8.82917

162 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u



uHx,0L=

7 x 0 £ x £ 1

-7 x

-1+Π+

7

-1+Π+ 7 1 £ x £ Π

0 £ x £ Π



1L uH1,0.1L = -7.20397

2L uH1,0.1L = 0.936786

3L uH1,0.1L = 2.12137

4L uH1,0.1L = 7.21127

5L uH1,0.1L = 5.19695

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=3 Hx - 3L x Hx - ΠL2 0 £ x £ Π



1L uH1,0.2L = 1.0581

2L uH1,0.2L = -16.5683

3L uH1,0.2L = -0.840399

4L uH1,0.2L = -4.78389

5L uH1,0.2L = 1.27601

Untitled-2 163

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u



uHx,0L=

-5 x

20 £ x £ 2

5 x

-2+Π-

10

-2+Π- 5 2 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

4 x 0 £ x £ 2

10 - x 2 £ x £ 3

-7 x

-3+Π+

21

-3+Π+ 7 3 £ x £ Π

0. £ x £ Π



1L uH2,0.5L = -8.43677

2L uH2,0.5L = -7.03684

3L uH2,0.5L = 0.127063

4L uH2,0.5L = 0.0182913

5L uH2,0.5L = 3.50158

164 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=-3 Hx - 4L2 Hx - 3L x 0 £ x £ 4



1L uH1,0.8L = -6.0531

2L uH1,0.8L = -5.02804

3L uH1,0.8L = -1.02023

4L uH1,0.8L = 0.262688

5L uH1,0.8L = 8.65857

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<5, 0<t

¶u

¶xH0,tL=

¶u

¶xH5,tL=0 0 £ t

uHx,0L=

-x

30 £ x £ 3

4 x - 13 3 £ x £ 4

15 - 3 x 4 £ x £ 5

0 £ x £ 5



1L uH2,0.9L = 0.199957

2L uH2,0.9L = -2.45666

3L uH2,0.9L = 1.14202

4L uH2,0.9L = 0.902874

5L uH2,0.9L = -4.57344

Untitled-2 165

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=2 Hx - 4L2 Hx - 2L x2 0 £ x £ 4

¶

¶tuHx,0L=

-7 x 0 £ x £ 1

3 x - 10 1 £ x £ 2

2 x - 8 2 £ x £ 4

0. £ x £ 4



1L uH3,0.7L = -6.22863

2L uH3,0.7L = -1.02151

3L uH3,0.7L = -6.94436

4L uH3,0.7L = 5.21277

5L uH3,0.7L = 4.34714

166 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=

-x 0 £ x £ 1 ê 1 £ x £ 33 x

-3+Π-

9

-3+Π- 3 3 £ x £ Π

0 £ x £ Π



1L uH1,0.3L = -6.98939

2L uH1,0.3L = -2.93306

3L uH1,0.3L = 4.41092

4L uH1,0.3L = -7.0424

5L uH1,0.3L = -0.000927702

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=8 x 0 £ x £ 1

16 - 8 x 1 £ x £ 20 £ x £ 2


10


1L uH1910

,0.2L = -3.92894

2L uH1910

,0.2L = -1.47593

3L uH1910

,0.2L = 2.96828

4L uH1910

,0.2L = 3.99885

5L uH1910

,0.2L = 0.728971

Untitled-2 167

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u



uHx,0L=-2 Hx - 2L x2 Hx - ΠL2 0 £ x £ Π

¶

¶tuHx,0L=-Hx - 1L x2 Hx - ΠL2 0. £ x £ Π



1L uH1,0.2L = -3.91885

2L uH1,0.2L = 2.33186

3L uH1,0.2L = -5.31142

4L uH1,0.2L = 3.38091

5L uH1,0.2L = 6.78932

168 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u






1L uH2,0.7L = -0.000782514

2L uH2,0.7L = 5.07813

3L uH2,0.7L = -1.87601

4L uH2,0.7L = -7.06423

5L uH2,0.7L = 4.22485

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-2 x 0 £ x £ 36 x

-3+Π-

18

-3+Π- 6 3 £ x £ Π

0 £ x £ Π



1L uH1,0.3L = 3.59935

2L uH1,0.3L = -0.662696

3L uH1,0.3L = 4.93585

4L uH1,0.3L = 2.92413

5L uH1,0.3L = -2.63257

Untitled-2 169

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u




¶

¶tuHx,0L=Hx - 2L x Hx - ΠL2 0. £ x £ Π



1L uH2,0.4L = 3.09816

2L uH2,0.4L = -2.01838

3L uH2,0.4L = -2.79556

4L uH2,0.4L = 7.251

5L uH2,0.4L = 18.3343

170 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=3 x 0 £ x £ 1

6 - 3 x 1 £ x £ 20 £ x £ 2


10


1L uH 7

10,0.1L = -8.24111

2L uH 7

10,0.1L = -2.55143

3L uH 7

10,0.1L = 5.78997

4L uH 7

10,0.1L = 4.66045

5L uH 7

10,0.1L = 0.235164

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u

¶x2Hx,tL 0<x<5, 0<t

¶u

¶xH0,tL=

¶u

¶xH5,tL=0 0 £ t

uHx,0L=

-2 x 0 £ x £ 1x

2-

5

21 £ x £ 5

0 £ x £ 5



1L uH4,0.7L = -1.97214

2L uH4,0.7L = 0.434469

3L uH4,0.7L = 2.21473

4L uH4,0.7L = -0.999572

5L uH4,0.7L = -0.361156

Untitled-2 171

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u



uHx,0L=

4 x 0 £ x £ 1

2 x + 2 1 £ x £ 3

-8 x

-3+Π+

24

-3+Π+ 8 3 £ x £ Π

0 £ x £ Π

¶

¶tuHx,0L=

-x

30 £ x £ 3

x

-3+Π-

3

-3+Π- 1 3 £ x £ Π

0. £ x £ Π



1L uH1,0.9L = -8.61038

2L uH1,0.9L = 1.38561

3L uH1,0.9L = 7.50567

4L uH1,0.9L = -6.26538

5L uH1,0.9L = 4.70275

172 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<3, 0<t





1L uH2,0.6L = -2.92438 ´ 10-6

2L uH2,0.6L = -1.93647

3L uH2,0.6L = 7.82778

4L uH2,0.6L = 4.09269

5L uH2,0.6L = -7.72843

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

x 0 £ x £ 2

12 - 5 x 2 £ x £ 33 x

-3+Π-

9

-3+Π- 3 3 £ x £ Π

0 £ x £ Π



1L uH1,0.1L = -3.00996

2L uH1,0.1L = 2.80122

3L uH1,0.1L = 4.22718

4L uH1,0.1L = 0.444926

5L uH1,0.1L = 3.71204

Untitled-2 173

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-Hx - 3L2 Hx - 2L Hx - 1L x 0 £ x £ 3¶

¶tuHx,0L=-3 Hx - 3L Hx - 2L Hx - 1L x2 0. £ x £ 3



1L uH1,0.2L = 0.489856

2L uH1,0.2L = -8.92192

3L uH1,0.2L = -5.03295

4L uH1,0.2L = -0.527902

5L uH1,0.2L = -8.31001

174 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u



uHx,0L=

8 x 0 £ x £ 1

22 - 14 x 1 £ x £ 26 x

-2+Π-

12

-2+Π- 6 2 £ x £ Π

0 £ x £ Π



1L uH1,1.L = -8.02378

2L uH1,1.L = -1.19901

3L uH1,1.L = 0.0000663151

4L uH1,1.L = 3.90601

5L uH1,1.L = -6.35455

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=-5 x 0 £ x £ 1

5 x - 10 1 £ x £ 20 £ x £ 2


10


1L uH1110

,0.5L = -2.5

2L uH1110

,0.5L = -3.46094

3L uH1110

,0.5L = 2.97403

4L uH1110

,0.5L = 2.47303

5L uH1110

,0.5L = 2.54255

Untitled-2 175

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=

2 x 0 £ x £ 18

3-

2 x

31 £ x £ 4

0 £ x £ 4

¶

¶tuHx,0L=

-3 x 0 £ x £ 1

x - 4 1 £ x £ 40. £ x £ 4



1L uH2,0.4L = 1.88776

2L uH2,0.4L = -4.34276

3L uH2,0.4L = -2.08377

4L uH2,0.4L = 0.518169

5L uH2,0.4L = -0.416297

176 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u



uHx,0L=

-6 x 0 £ x £ 1

-2 x - 4 1 £ x £ 28 x

-2+Π-

16

-2+Π- 8 2 £ x £ Π

0 £ x £ Π



1L uH2,0.5L = -2.7466

2L uH2,0.5L = 8.11166

3L uH2,0.5L = -0.905502

4L uH2,0.5L = -6.19618

5L uH2,0.5L = -4.75653

� Ejercicio 2

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<5, 0<t

¶u

¶xH0,tL=

¶u

¶xH5,tL=0 0 £ t

uHx,0L=

-x 0 £ x £ 1

4 - 5 x 1 £ x £ 2

2 x - 10 2 £ x £ 5

0 £ x £ 5



1L uH1,0.9L = 1.35065

2L uH1,0.9L = -2.37541

3L uH1,0.9L = 1.96003

4L uH1,0.9L = -1.51302

5L uH1,0.9L = -1.34462

Untitled-2 177

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

-80 x

90 £ x £

9

10

80 x - 80 9

10£ x £ 1

0 £ x £ 1

¶

¶tuHx,0L=

-80 x

70 £ x £

7

10

80 x

3-

80

3

7

10£ x £ 1

0. £ x £ 1


5


1L uH35,1.L = 0.974956

2L uH35,1.L = 3.51491

3L uH35,1.L = -0.887193

4L uH35,1.L = -5.36793

5L uH35,1.L = -7.23406

178 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=

¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-2 Hx - 2L Hx - 1L x 0 £ x £ 2


5


1L uH75,0.8L = 0.937771

2L uH75,0.8L = 1.98695

3L uH75,0.8L = 4.34045

4L uH75,0.8L = 1.95687

5L uH75,0.8L = 0.000274104

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=8 x 0 £ x £ 1

16 - 8 x 1 £ x £ 20 £ x £ 2


5


1L uH25,0.2L = -1.38278

2L uH25,0.2L = 2.46785

3L uH25,0.2L = -0.166537

4L uH25,0.2L = 3.99963

5L uH25,0.2L = 2.75982

Untitled-2 179

� Ejercicio 3

¶2u

¶t2Hx,tL=4 ¶2u



uHx,0L=-2 Hx - 3L x2 Hx - ΠL2 0 £ x £ Π

¶

¶tuHx,0L=

5 x 0 £ x £ 1

2 x + 3 1 £ x £ 3

-9 x

-3+Π+

27

-3+Π+ 9 3 £ x £ Π

0. £ x £ Π



1L uH2,0.1L = 6.28973

2L uH2,0.1L = 11.1227

3L uH2,0.1L = 5.58905

4L uH2,0.1L = -3.9704

5L uH2,0.1L = -2.61013

180 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=

6 x 0 £ x £ 1

20 - 14 x 1 £ x £ 2

8 x - 24 2 £ x £ 3

0 £ x £ 3



1L uH1,0.2L = -3.73493

2L uH1,0.2L = -1.14674

3L uH1,0.2L = -1.19273

4L uH1,0.2L = -5.08745

5L uH1,0.2L = -0.124889

� Ejercicio 2

¶u

¶tHx,tL=25 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=-Hx - 2L x2 Hx - ΠL2 0 £ x £ Π



1L uH2,0.6L = -0.588618

2L uH2,0.6L = 3.55922

3L uH2,0.6L = -4.81627

4L uH2,0.6L = 1.39361

5L uH2,0.6L = 0.775629

Untitled-2 181

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=

3 x 0 £ x £ 1

2 x + 1 1 £ x £ 2

15 - 5 x 2 £ x £ 3

0 £ x £ 3

¶

¶tuHx,0L=

-8 x 0 £ x £ 1

13 x - 21 1 £ x £ 2

15 - 5 x 2 £ x £ 3

0. £ x £ 3



1L uH2,0.8L = 6.02172

2L uH2,0.8L = -1.83026

3L uH2,0.8L = -3.63767

4L uH2,0.8L = 1.99606

5L uH2,0.8L = 0.723931

182 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=-Hx - 4L2 Hx - 1L x 0 £ x £ 4



1L uH1,0.1L = -4.89628

2L uH1,0.1L = 0.16092

3L uH1,0.1L = 8.23526

4L uH1,0.1L = 5.58096

5L uH1,0.1L = -2.08797

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<4, 0<t

¶u

¶xH0,tL=

¶u

¶xH4,tL=0 0 £ t

uHx,0L=

-9 x 0 £ x £ 1

7 x - 16 1 £ x £ 2

x - 4 2 £ x £ 4

0 £ x £ 4



1L uH1,0.2L = 4.60476

2L uH1,0.2L = -4.1746

3L uH1,0.2L = -1.6549

4L uH1,0.2L = -1.35194

5L uH1,0.2L = -2.65953

Untitled-2 183

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u



uHx,0L=2 Hx - 3L x Hx - ΠL 0 £ x £ Π

¶

¶tuHx,0L=

3 x 0 £ x £ 1

2 x + 1 1 £ x £ 3

-7 x

-3+Π+

21

-3+Π+ 7 3 £ x £ Π

0. £ x £ Π



1L uH1,0.7L = -3.94583

2L uH1,0.7L = -3.64853

3L uH1,0.7L = 7.4632

4L uH1,0.7L = 4.93402

5L uH1,0.7L = 6.10478

184 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=25 ¶2u



uHx,0L=

-3 x 0 £ x £ 26 x

-2+Π-

12

-2+Π- 6 2 £ x £ Π

0 £ x £ Π



1L uH1,0.8L = -8.28887 ´ 10-9

2L uH1,0.8L = -7.93394

3L uH1,0.8L = -7.69168

4L uH1,0.8L = 3.26946

5L uH1,0.8L = 2.59197

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<3, 0<t

¶u

¶xH0,tL=

¶u

¶xH3,tL=0 0 £ t

uHx,0L=2 Hx - 3L Hx - 2L Hx - 1L x 0 £ x £ 3



1L uH2,0.4L = 4.12393

2L uH2,0.4L = -1.14716

3L uH2,0.4L = -3.53019

4L uH2,0.4L = -2.77528

5L uH2,0.4L = -0.6

Untitled-2 185

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u

¶x2Hx,tL 0<x<3, 0<t


uHx,0L=-3 Hx - 3L2 Hx - 1L x2 0 £ x £ 3¶

¶tuHx,0L=Hx - 3L2 Hx - 2L Hx - 1L x2 0. £ x £ 3



1L uH1,0.1L = 2.39512

2L uH1,0.1L = -8.78825

3L uH1,0.1L = -2.95372

4L uH1,0.1L = 0.736241

5L uH1,0.1L = -1.03464

186 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u



uHx,0L=2 Hx - 3L x2 Hx - ΠL2 0 £ x £ Π



1L uH1,0.9L = -7.67911

2L uH1,0.9L = -4.38882

3L uH1,0.9L = 2.31467

4L uH1,0.9L = 7.93049

5L uH1,0.9L = -0.00396076

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-2 x 0 £ x £ 1

6 x - 8 1 £ x £ 2

-4 x

-2+Π+

8

-2+Π+ 4 2 £ x £ Π

0 £ x £ Π



1L uH1,0.1L = 2.25875

2L uH1,0.1L = -2.64362

3L uH1,0.1L = 3.40939

4L uH1,0.1L = 3.63783

5L uH1,0.1L = 0.534631

Untitled-2 187

� Ejercicio 3

¶2u

¶t2Hx,tL=

¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=3 Hx - 1L Ix -1

5M x2 0 £ x £ 1

¶

¶tuHx,0L=

-20 x

30 £ x £

3

10

20 x

7-

20

7

3

10£ x £ 1

0. £ x £ 1


5en el instante t=


1L uH45,0.5L = -8.65843

2L uH45,0.5L = -4.7505

3L uH45,0.5L = -0.185204

4L uH45,0.5L = -7.13902

5L uH45,0.5L = -3.12557

188 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-3 Hx - 2L Hx - 1L x 0 £ x £ 2


5


1L uH75,0.4L = 5.36526

2L uH75,0.4L = 4.33579

3L uH75,0.4L = -6.75911

4L uH75,0.4L = 3.76051

5L uH75,0.4L = 4.09568 ´ 10-16

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=

-7 x

30 £ x £ 3

7 x

-3+Π-

21

-3+Π- 7 3 £ x £ Π

0 £ x £ Π



1L uH2,0.6L = -1.13103

2L uH2,0.6L = -1.51176

3L uH2,0.6L = -4.37076

4L uH2,0.6L = -3.50007

5L uH2,0.6L = -2.17026

Untitled-2 189

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u




¶




1L uH2,0.3L = -4.5313

2L uH2,0.3L = -5.9127

3L uH2,0.3L = -1.04006

4L uH2,0.3L = 5.1739

5L uH2,0.3L = -7.59022

190 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u



uHx,0L=

-6 x 0 £ x £ 16 x

-1+Π-

6

-1+Π- 6 1 £ x £ Π

0 £ x £ Π



1L uH2,0.4L = 1.6565

2L uH2,0.4L = -5.15037

3L uH2,0.4L = -0.864

4L uH2,0.4L = 0.868914

5L uH2,0.4L = -4.68146

� Ejercicio 2

¶u

¶tHx,tL=9 ¶2u

¶x2Hx,tL 0<x<1, 0<t

¶u

¶xH0,tL=

¶u

¶xH1,tL=0 0 £ t

uHx,0L=

-15 x 0 £ x £2

5

-10 x - 2 2

5£ x £

1

2

14 x - 14 1

2£ x £ 1

0 £ x £ 1


5


1L uH15,0.8L = 2.73123

2L uH15,0.8L = 0.508362

3L uH15,0.8L = 3.51094

4L uH15,0.8L = -3.6

5L uH15,0.8L = 4.10048

Untitled-2 191

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=-2 Hx - 1L2 Ix -4

5M Ix -

3

10M x2 0 £ x £ 1

¶

¶tuHx,0L=

-20 x

70 £ x £

7

10

-2 7

10£ x £

4

5

10 x - 10 4

5£ x £ 1

0. £ x £ 1



1L uH12,0.7L = -0.923957

2L uH12,0.7L = 0.109931

3L uH12,0.7L = -7.40825

4L uH12,0.7L = -3.90472

5L uH12,0.7L = -4.97523

192 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<5, 0<t


uHx,0L=

-x 0 £ x £ 22 x

3-

10

32 £ x £ 5

0 £ x £ 5



1L uH3,0.1L = -1.83036

2L uH3,0.1L = 1.44787

3L uH3,0.1L = 1.75196

4L uH3,0.1L = -0.511999

5L uH3,0.1L = -1.23464

� Ejercicio 2

¶u

¶tHx,tL=

¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=Hx - 1L x2 Hx - ΠL 0 £ x £ Π



1L uH1,0.2L = -3.39198

2L uH1,0.2L = -0.876351

3L uH1,0.2L = 3.45209

4L uH1,0.2L = 4.18757

5L uH1,0.2L = 4.97881

Untitled-2 193

� Ejercicio 3

¶2u

¶t2Hx,tL=9 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=-9 x 0 £ x £ 1

3 x - 12 1 £ x £ 40 £ x £ 4

¶

¶tuHx,0L=3 Hx - 4L2 Hx - 1L x2 0. £ x £ 4



1L uH2,0.1L = -1.26562

2L uH2,0.1L = -4.16147

3L uH2,0.1L = 6.31946

4L uH2,0.1L = -3.77468

5L uH2,0.1L = -2.1848

194 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u



uHx,0L=Hx - 2L Hx - 1L x Hx - ΠL 0 £ x £ Π



1L uH1,0.7L = 6.47223

2L uH1,0.7L = 3.54417

3L uH1,0.7L = -0.0119875

4L uH1,0.7L = 3.60835

5L uH1,0.7L = 3.30546

� Ejercicio 2

¶u

¶tHx,tL=4 ¶2u


¶u

¶xH0,tL=

¶u

¶xHΠ,tL=0 0 £ t

uHx,0L=-3 Hx - 3L Hx - 2L x2 Hx - ΠL 0 £ x £ Π



1L uH1,0.3L = -3.95351

2L uH1,0.3L = -3.9938

3L uH1,0.3L = 2.72332

4L uH1,0.3L = 0.128951

5L uH1,0.3L = 4.93176

Untitled-2 195

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u

¶x2Hx,tL 0<x<4, 0<t


uHx,0L=2 Hx - 4L Hx - 2L Hx - 1L x 0 £ x £ 4

¶

¶tuHx,0L=

5 x

20 £ x £ 2

10 -5 x

22 £ x £ 4

0. £ x £ 4



1L uH1,0.1L = 5.36678

2L uH1,0.1L = 0.686625

3L uH1,0.1L = -5.4134

4L uH1,0.1L = 1.55892

5L uH1,0.1L = -0.166823

196 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=9 ¶2u



uHx,0L=2 Hx - 2L x Hx - ΠL2 0 £ x £ Π



1L uH1,1.L = -7.32172

2L uH1,1.L = -0.000534804

3L uH1,1.L = 4.81745

4L uH1,1.L = 2.24144

5L uH1,1.L = 2.30026

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<5, 0<t

¶u

¶xH0,tL=

¶u

¶xH5,tL=0 0 £ t

uHx,0L=-Hx - 5L2 Hx - 4L Hx - 3L x2 0 £ x £ 5



1L uH4,0.5L = -4.49358

2L uH4,0.5L = -32.8272

3L uH4,0.5L = 0.1607

4L uH4,0.5L = -0.725999

5L uH4,0.5L = -2.02974

Untitled-2 197

� Ejercicio 3

¶2u

¶t2Hx,tL=25 ¶2u

¶x2Hx,tL 0<x<2, 0<t


uHx,0L=-7 x 0 £ x £ 1

7 x - 14 1 £ x £ 20 £ x £ 2

¶

¶tuHx,0L=-3 Hx - 2L2 Hx - 1L x 0. £ x £ 2


5en el instante t=


1L uH15,0.3L = -1.01771

2L uH15,0.3L = 1.36811

3L uH15,0.3L = 4.53209

4L uH15,0.3L = -1.0117

5L uH15,0.3L = -8.81691

198 Untitled-2


� Ejercicio 1

¶u

¶tHx,tL=4 ¶2u

¶x2Hx,tL 0<x<1, 0<t


uHx,0L=

-10 x

30 £ x £

3

5

5 x - 5 3

5£ x £ 1

0 £ x £ 1


5


1L uH45,0.8L = 2.27511

2L uH45,0.8L = -3.16905

3L uH45,0.8L = -1.81454 ´ 10-14

4L uH45,0.8L = -4.54292

5L uH45,0.8L = -5.48751

� Ejercicio 2

¶u

¶tHx,tL=16 ¶2u

¶x2Hx,tL 0<x<2, 0<t

¶u

¶xH0,tL=

¶u

¶xH2,tL=0 0 £ t

uHx,0L=Hx - 2L2 Hx - 1L x2 0 £ x £ 2


5


1L uH95,0.4L = 3.49175

2L uH95,0.4L = 2.74699 ´ 10-8

3L uH95,0.4L = 3.41062

4L uH95,0.4L = -4.58873

5L uH95,0.4L = -4.3869

Untitled-2 199

� Ejercicio 3

¶2u

¶t2Hx,tL=16 ¶2u



uHx,0L=-Hx - 2L x Hx - ΠL2 0 £ x £ Π

¶

¶tuHx,0L=

9 x 0 £ x £ 1

18 - 9 x 1 £ x £ 39 x

-3+Π-

27

-3+Π- 9 3 £ x £ Π

0. £ x £ Π



1L uH2,0.8L = -4.0628

2L uH2,0.8L = 7.05441

3L uH2,0.8L = -7.18712

4L uH2,0.8L = 2.40845

5L uH2,0.8L = 0.458228

200 Untitled-2

ejercicio 2 - ujaen.esajlopez/asignat/ampliacion/... · ampliación de matemáticas - iti -...

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