The temperature u ( x , t ) when the left end of the rod is insulated using equation k ∂ 2 u ∂ x 2 = ∂ u ∂ t , 0 < x < 1 , t > 0 , where u ( 0 , t ) = 0 , ∂ u ∂ t | x = 1 = − h u ( 1 , t ) , h > 0 , t > 0 and u ( x , 0 ) = 1 , 0 < x < 1 .

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Answer 1

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Chapter 13.7, Problem 1E

To determine

The temperature u(x,t) when the left end of the rod is insulated using equation k∂2u∂x2=∂u∂t, 0<x<1, t>0, where u(0,t)=0, ∂u∂t|x=1=−hu(1,t), h>0, t>0 and u(x,0)=1, 0<x<1.

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)5. The operator T on a vector space V over Q has as its sequence of invariant factors the sequence (x-1)3(x-2)5(x-3)2, (x-1)(x-2)(x-3)2, (x-3). Find the Jordan normal form of T.

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Answer 2

Question

Chapter 13.7, Problem 1E

To determine

The temperature u(x,t) when the left end of the rod is insulated using equation k∂2u∂x2=∂u∂t, 0<x<1, t>0, where u(0,t)=0, ∂u∂t|x=1=−hu(1,t), h>0, t>0 and u(x,0)=1, 0<x<1.

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Answer 3

Question

Chapter 13.7, Problem 1E

To determine

The temperature u(x,t) when the left end of the rod is insulated using equation k∂2u∂x2=∂u∂t, 0<x<1, t>0, where u(0,t)=0, ∂u∂t|x=1=−hu(1,t), h>0, t>0 and u(x,0)=1, 0<x<1.

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Answer 4

Question

Chapter 13.7, Problem 1E

To determine

The temperature u(x,t) when the left end of the rod is insulated using equation k∂2u∂x2=∂u∂t, 0<x<1, t>0, where u(0,t)=0, ∂u∂t|x=1=−hu(1,t), h>0, t>0 and u(x,0)=1, 0<x<1.

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Answer 5

Chapter 13.7, Problem 1E

To determine

The temperature u(x,t) when the left end of the rod is insulated using equation k∂2u∂x2=∂u∂t, 0<x<1, t>0, where u(0,t)=0, ∂u∂t|x=1=−hu(1,t), h>0, t>0 and u(x,0)=1, 0<x<1.

Answer 6

Chapter 13.7, Problem 1E

To determine

The temperature u(x,t) when the left end of the rod is insulated using equation k∂2u∂x2=∂u∂t, 0<x<1, t>0, where u(0,t)=0, ∂u∂t|x=1=−hu(1,t), h>0, t>0 and u(x,0)=1, 0<x<1.

Answer 7

Chapter 13.7, Problem 1E

To determine

The temperature u(x,t) when the left end of the rod is insulated using equation k∂2u∂x2=∂u∂t, 0<x<1, t>0, where u(0,t)=0, ∂u∂t|x=1=−hu(1,t), h>0, t>0 and u(x,0)=1, 0<x<1.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

The temperature u ( x , t ) when the left end of the rod is insulated using equation k ∂ 2 u ∂ x 2 = ∂ u ∂ t , 0 < x < 1 , t > 0 , where u ( 0 , t ) = 0 , ∂ u ∂ t | x = 1 = − h u ( 1 , t ) , h > 0 , t > 0 and u ( x , 0 ) = 1 , 0 < x < 1 .

Solution Summary: The author calculates the temperature of the rod when the left end is insulated using the equation kpartial 2u

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The temperature u(x,t) when the left end of the rod is insulated using equation k∂2u∂x2=∂u∂t, 0<x<1, t>0, where u(0,t)=0, ∂u∂t|x=1=−hu(1,t), h>0, t>0 and u(x,0)=1, 0<x<1.

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Chapter 13 Solutions

The temperature u ( x , t ) when the left end of the rod is insulated using equation k ∂ 2 u ∂ x 2 = ∂ u ∂ t , 0 &lt; x &lt; 1 , t &gt; 0 , where u ( 0 , t ) = 0 , ∂ u ∂ t | x = 1 = − h u ( 1 , t ) , h &gt; 0 , t &gt; 0 and u ( x , 0 ) = 1 , 0 &lt; x &lt; 1 .

Solution Summary: The author calculates the temperature of the rod when the left end is insulated using the equation kpartial 2u

Concept explainers

Videos

The temperature u(x,t) when the left end of the rod is insulated using equation k∂2u∂x2=∂u∂t, 0<x<1, t>0, where u(0,t)=0, ∂u∂t|x=1=−hu(1,t), h>0, t>0 and u(x,0)=1, 0<x<1.

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Chapter 13 Solutions

The temperature u ( x , t ) when the left end of the rod is insulated using equation k ∂ 2 u ∂ x 2 = ∂ u ∂ t , 0 < x < 1 , t > 0 , where u ( 0 , t ) = 0 , ∂ u ∂ t | x = 1 = − h u ( 1 , t ) , h > 0 , t > 0 and u ( x , 0 ) = 1 , 0 < x < 1 .