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Given v (678) = U (,1;8%)*(x",0)de where U (,t;a") = ( 217 )* <im(8=e")°/2nt and 1...
(1 point) Solve the heat problem with non-homogeneous boundary conditions ∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0 u(0,t)=0, u(3,t)=2, t>0,
(1 point) Solve the heat problem with non-homogeneous boundary
conditions
∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0
u(0,t)=0, u(3,t)=2, t>0,u(0,t)=0, u(3,t)=2, t>0,
u(x,0)=23x, 0<x<3.u(x,0)=23x, 0<x<3.
Recall that we find h(x)h(x), set
v(x,t)=u(x,t)−h(x)v(x,t)=u(x,t)−h(x), solve a heat problem for
v(x,t)v(x,t) and write u(x,t)=v(x,t)+h(x)u(x,t)=v(x,t)+h(x).
Find h(x)h(x)
h(x)=h(x)=
The solution u(x,t)u(x,t) can be written as
u(x,t)=h(x)+v(x,t),u(x,t)=h(x)+v(x,t),
where
v(x,t)=∑n=1∞aneλntϕn(x)v(x,t)=∑n=1∞aneλntϕn(x)
v(x,t)=∑n=1∞v(x,t)=∑n=1∞
Finally, find
limt→∞u(x,t)=limt→∞u(x,t)=
Please show all work.
(1 point) Solve the heat problem with non-homogeneous boundary conditions au ди (x, t) at (2, t), 0<x<3, t> 0 ar2 u(0,t) = 0, u(3, t) = 2, t>0, u(t,0)...
Solve the DE for x(t) given the following DE and volume solution of V(t) then answer...
Solve the DE for x(t) given the following DE and volume
solution of V(t)
then answer the case1 and case 2 questions
V(t)=180-100e-0.01t+20e-0.05t
Case 1 Let i(t) = e-0.01t and r(t) =
e-0.05t
Solve for x(t) and plot a graph for x(t) and the function V(t)
What is the limiting value of x(t) that is what is x(t) as t goes
to infinity.
How does the solution vary as a function given the initial
conditions of X0=0,...
l, t)4u (x, t), 0<x< L, 0 <t Evaluate u(1.1; 0.3) where u(x, t) u(0, 1)=...
l, t)4u (x, t), 0<x< L, 0 <t Evaluate u(1.1; 0.3) where u(x, t) u(0, 1)= u(L, t)- 0v1> 0 u(x, 0)= f(x), u,(x, 0)- g(x), 0<x< L L=T al f(x) 3sin 2x, g(x)=-2sin 3x b/ For f(x)-xn-x & g(x)-0, approximate numerically u(x, t) by the first term. L-S c/f(x)=-3sin g(x)- 5 2sin d/ f(x)-0, g()= .3 x +1 approximate numerically u(x, t) by the first term c/ f(x)-2(5-xx, g(x) x+1 3 approximate numerically u(x, t) by the first couple...
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square...
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
Solve u, = 4 for 0 5xs1, given u(0,t) = 0, u,(1,t) = 0, u(x,0)=1. 2...
Solve u, = 4 for 0 5xs1, given u(0,t) = 0, u,(1,t) = 0, u(x,0)=1. 2 fomu sin 1 Answer: u(x,t) = { e "sin( n +) 7x 0 1 +
Problem 4. Solve for the functions u, v, and w, where (1) (∂/∂t + ∂/∂x) u...
Problem 4. Solve for the functions u, v, and w, where (1) (∂/∂t + ∂/∂x) u = a, (2) (∂/∂t − ∂/∂x) v = b, and (3) (∂/∂t + 3 ∂/∂x) w = c, where a, b, and c are the functions that you calculated in Problem 3... a=f(x+t)= (x+t)^2+(x+t)+1 b=f(x-2t)= (x-2t)^2+(x-2t)+1 c=f(x-3t)= (x-3t)^2+(x-3t)+1
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0 < u 2, 0 £1 3 Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0 < u 2, 0 £1 3
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0
Ut = Kuzz-cr(z-L) where u = u(x, t) for 0 L and t 0 a(0,t) = 1 (a(L, t) = 1 where к.с > 0 are con...
ut = Kuzz-cr(z-L) where u = u(x, t) for 0 L and t 0 a(0,t) = 1 (a(L, t) = 1 where к.с > 0 are constants. For all plots in this lab, we will take c-2, к-3. L-1, but L will otherwise be left unspecified We were unable to transcribe this image
ut = Kuzz-cr(z-L) where u = u(x, t) for 0 L and t 0 a(0,t) = 1 (a(L, t) = 1 where к.с > 0 are constants....
2. Use eigenfunction expansion to solve the following IBVP: u,(x, t) ="-(x,t) + (t-1)sin(m), 0 0 ...
2. Use eigenfunction expansion to solve the following IBVP: u,(x, t) ="-(x,t) + (t-1)sin(m), 0
(1)x() = 0; forn > U, (20 > 1, ( m my (e) = sinw -...
(1)x() = 0; forn > U, (20 > 1, ( m my (e) = sinw - sin 2w V) 2 *- |X (ejw)/2dw = 3. 9. Consider a finite duration sequence x(n) = {0, 1,2,3}. Sketch the sequence s(n) with six-point DFT S(I) = W X (k), k = 0,1,2,..,6. Determine the sequence y(n) with six-point DFT Y(K) = ReX(10). Determine the sequence v(n) with six-point DFT V(k) = Im X(k): (5 marks) OR
(1 point) Solve the heat problem with non-homogeneous boundary
conditions
∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0∂u∂t(x,t)=∂2u∂x2(x,t), 0<x<3, t>0
u(0,t)=0, u(3,t)=2, t>0,u(0,t)=0, u(3,t)=2, t>0,
u(x,0)=23x, 0<x<3.u(x,0)=23x, 0<x<3.
Recall that we find h(x)h(x), set
v(x,t)=u(x,t)−h(x)v(x,t)=u(x,t)−h(x), solve a heat problem for
v(x,t)v(x,t) and write u(x,t)=v(x,t)+h(x)u(x,t)=v(x,t)+h(x).
Find h(x)h(x)
h(x)=h(x)=
The solution u(x,t)u(x,t) can be written as
u(x,t)=h(x)+v(x,t),u(x,t)=h(x)+v(x,t),
where
v(x,t)=∑n=1∞aneλntϕn(x)v(x,t)=∑n=1∞aneλntϕn(x)
v(x,t)=∑n=1∞v(x,t)=∑n=1∞
Finally, find
limt→∞u(x,t)=limt→∞u(x,t)=
Please show all work.
(1 point) Solve the heat problem with non-homogeneous boundary conditions au ди (x, t) at (2, t), 0<x<3, t> 0 ar2 u(0,t) = 0, u(3, t) = 2, t>0, u(t,0)...
Solve the DE for x(t) given the following DE and volume
solution of V(t)
then answer the case1 and case 2 questions
V(t)=180-100e-0.01t+20e-0.05t
Case 1 Let i(t) = e-0.01t and r(t) =
e-0.05t
Solve for x(t) and plot a graph for x(t) and the function V(t)
What is the limiting value of x(t) that is what is x(t) as t goes
to infinity.
How does the solution vary as a function given the initial
conditions of X0=0,...
l, t)4u (x, t), 0<x< L, 0 <t Evaluate u(1.1; 0.3) where u(x, t) u(0, 1)= u(L, t)- 0v1> 0 u(x, 0)= f(x), u,(x, 0)- g(x), 0<x< L L=T al f(x) 3sin 2x, g(x)=-2sin 3x b/ For f(x)-xn-x & g(x)-0, approximate numerically u(x, t) by the first term. L-S c/f(x)=-3sin g(x)- 5 2sin d/ f(x)-0, g()= .3 x +1 approximate numerically u(x, t) by the first term c/ f(x)-2(5-xx, g(x) x+1 3 approximate numerically u(x, t) by the first couple...
Question 19: Linear Transformations Let S = {(u, v): 0 <u<1,0 <v<1} be the unit square and let RCR be the parallelogram with vertices (0,0), (2, 2), (3,-1), (5,1). a. Find a linear transformation T:R2 + R2 such that T(S) = R and T(1,0) = (2, 2). What is T(0, 1)? T(0,1): 2= y= b. Use the change of variables theorem to fill in the appropriate information: 1(4,)dA= S. ° Sºf(T(u, v)|Jac(T)| dudv JA JO A= c. If f(x, y)...
Solve u, = 4 for 0 5xs1, given u(0,t) = 0, u,(1,t) = 0, u(x,0)=1. 2 fomu sin 1 Answer: u(x,t) = { e "sin( n +) 7x 0 1 +
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0 < u 2, 0 £1 3
Jc z, y, z-t-2, s is the surface given by r(u, v) = 〈u, u2y?, 1), 0
ut = Kuzz-cr(z-L) where u = u(x, t) for 0 L and t 0 a(0,t) = 1 (a(L, t) = 1 where к.с > 0 are constants. For all plots in this lab, we will take c-2, к-3. L-1, but L will otherwise be left unspecified We were unable to transcribe this image
ut = Kuzz-cr(z-L) where u = u(x, t) for 0 L and t 0 a(0,t) = 1 (a(L, t) = 1 where к.с > 0 are constants....
2. Use eigenfunction expansion to solve the following IBVP: u,(x, t) ="-(x,t) + (t-1)sin(m), 0
(1)x() = 0; forn > U, (20 > 1, ( m my (e) = sinw - sin 2w V) 2 *- |X (ejw)/2dw = 3. 9. Consider a finite duration sequence x(n) = {0, 1,2,3}. Sketch the sequence s(n) with six-point DFT S(I) = W X (k), k = 0,1,2,..,6. Determine the sequence y(n) with six-point DFT Y(K) = ReX(10). Determine the sequence v(n) with six-point DFT V(k) = Im X(k): (5 marks) OR
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