The steady state temperature u ( r , t ) in an annular plate with the condition as ∂ 2 u ∂ r 2 + 1 r ∂ u ∂ r = ∂ u ∂ t , u ( a , t ) = 0 , u ( b , t ) = 0 , u ( r , 0 ) = f ( r ) a < r < b .

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Answer 1

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Chapter 13, Problem 14RE

To determine

The steady state temperature u(r,t) in an annular plate with the condition as ∂2u∂r2+1r∂u∂r=∂u∂t,u(a,t)=0,u(b,t)=0,u(r,0)=f(r) a<r<b.

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Students have asked these similar questions

1. Consider the surface defined by z = x2 + e9y ln(x-y). Let f(x,y) = x2 + e9y ln(x-y). ○ Compute ∇f at the point (1,0). ○ Compute the derivative of f(x,y) at the point (1,0) in the direction (3,-4). ○ Explain the geometric relationship between the answer found in part (a) and the surface defined above.

II2. Suppose f (x, y, z) and g(x, y, z) are continuously differentiable functions with f(1,2,3) = 5 and g(1,2, 3) = 7. Assume that the surface f(x, y, z) = 5 and the surface g(x,Y, z) = 7 have the same tangent plane at (1,2, 3). Evaluate Vf(1,2, 3) × Vg(1, 2, 3) (remember to give reasons).

V. On the surface z = in what direction is z increasing most rapidly when x =1 and y = 2.

Answer 2

Question

Chapter 13, Problem 14RE

To determine

The steady state temperature u(r,t) in an annular plate with the condition as ∂2u∂r2+1r∂u∂r=∂u∂t,u(a,t)=0,u(b,t)=0,u(r,0)=f(r) a<r<b.

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Answer 3

Question

Chapter 13, Problem 14RE

To determine

The steady state temperature u(r,t) in an annular plate with the condition as ∂2u∂r2+1r∂u∂r=∂u∂t,u(a,t)=0,u(b,t)=0,u(r,0)=f(r) a<r<b.

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Answer 4

Question

Chapter 13, Problem 14RE

To determine

The steady state temperature u(r,t) in an annular plate with the condition as ∂2u∂r2+1r∂u∂r=∂u∂t,u(a,t)=0,u(b,t)=0,u(r,0)=f(r) a<r<b.

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Answer 5

Chapter 13, Problem 14RE

To determine

The steady state temperature u(r,t) in an annular plate with the condition as ∂2u∂r2+1r∂u∂r=∂u∂t,u(a,t)=0,u(b,t)=0,u(r,0)=f(r) a<r<b.

Answer 6

Chapter 13, Problem 14RE

To determine

The steady state temperature u(r,t) in an annular plate with the condition as ∂2u∂r2+1r∂u∂r=∂u∂t,u(a,t)=0,u(b,t)=0,u(r,0)=f(r) a<r<b.

Answer 7

Chapter 13, Problem 14RE

To determine

The steady state temperature u(r,t) in an annular plate with the condition as ∂2u∂r2+1r∂u∂r=∂u∂t,u(a,t)=0,u(b,t)=0,u(r,0)=f(r) a<r<b.

Answer 8

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Answer 9

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Answer 10

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Answer 11

The steady state temperature u ( r , t ) in an annular plate with the condition as ∂ 2 u ∂ r 2 + 1 r ∂ u ∂ r = ∂ u ∂ t , u ( a , t ) = 0 , u ( b , t ) = 0 , u ( r , 0 ) = f ( r ) a < r < b .

Solution Summary: The author describes the steady state temperature u(r,t) in an annular plate.

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The steady state temperature u(r,t) in an annular plate with the condition as ∂2u∂r2+1r∂u∂r=∂u∂t,u(a,t)=0,u(b,t)=0,u(r,0)=f(r) a<r<b.

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Chapter 13 Solutions

The steady state temperature u ( r , t ) in an annular plate with the condition as ∂ 2 u ∂ r 2 + 1 r ∂ u ∂ r = ∂ u ∂ t , u ( a , t ) = 0 , u ( b , t ) = 0 , u ( r , 0 ) = f ( r ) a &lt; r &lt; b .

Solution Summary: The author describes the steady state temperature u(r,t) in an annular plate.

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The steady state temperature u(r,t) in an annular plate with the condition as ∂2u∂r2+1r∂u∂r=∂u∂t,u(a,t)=0,u(b,t)=0,u(r,0)=f(r) a<r<b.

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Chapter 13 Solutions

The steady state temperature u ( r , t ) in an annular plate with the condition as ∂ 2 u ∂ r 2 + 1 r ∂ u ∂ r = ∂ u ∂ t , u ( a , t ) = 0 , u ( b , t ) = 0 , u ( r , 0 ) = f ( r ) a < r < b .