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Let u be the solution to the initial boundary value problem for the Heat Equation an(t,r)-301a(t, z), te(0,00), z E (0,3); with initial condition 3 0 and with boundary conditions 6xu(t,0)-0, u(t, 3)...
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z) 28?u(t,z), te (0,00), z (0,3); with initial condition u(0, z)fx), where f(0) 0 and f (3) 0 and with boundary...
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z) 28?u(t,z), te (0,00), z (0,3); with initial condition u(0, z)fx), where f(0) 0 and f (3) 0 and with boundary conditions u(t,0)-0, r 30 Using separation of variables, the solution of this problem is 4X with the normalization conditions un(m3ī)-. n@) : ї, a. (5/10) Find the functions wn with index n1. Wnlz) b. (5/10) Find the functions vn with index n 1. n(t)...
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z 382u(t,z), tE (0,oo), E (0,3); with initial condition u(0,x)-f(x)- and with boundary conditions Find the solu...
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z 382u(t,z), tE (0,oo), E (0,3); with initial condition u(0,x)-f(x)- and with boundary conditions Find the solution u using the expansion u(t,x) n (t) wn(x), with the normalization conditions vn (0)1, Wn (2n -1) a. (3/10) Find the functionswn with index n 1. b. (3/10) Find the functions vn, with index n 1 C. (4/10) Find the coefficients cn , with index n 1.
Let...
Let u be the solution to the initial boundary value problem for the Heat Equation, tE...
Let u be the solution to the initial boundary value problem for the Heat Equation, tE (0, o0), т€ (0, 3)%; дди(t, г) — 4 0?и(t, a), with initial condition E0, , u(0, x) f(x) 3 and with boundary conditions д,u(t, 3) — 0. и(t,0) — 0, Find the solution u using the expansion и(t, 2) 3D У с, чп (t) w,(m), n-1 with the normalization conditions Vn (0) 1, 1. Wn _ (2n 1) a. (3/10) Find the functions...
Let u be the solution to the initial boundary value problem for the Heat Equation u(t,...
Let u be the solution to the initial boundary value problem for the Heat Equation u(t, x) 4ut, x) te (0, o0), т€ (0, 3)%; with initial condition 2. f(x) u(0, x) 3 0. and with boundary conditions ди(t, 0) — 0, и(t, 3) — 0. Find the solution u using the expansion u(t, a) "(2)"п (?)"а " п-1 with the normalization conditions Vn (0) 1, wn(0) = 1 a. (3/10) Find the functions wn. with index n > 1....
Let u be the solution to the initial boundary value problem for the Heat Equation дли(t,...
Let u be the solution to the initial boundary value problem for the Heat Equation дли(t, 2) — 4 әғи(t, 2), te (0, o0), те (0,1); with initial condition , u(0, a)f() and with boundary conditions 0. u(t, 0)0 u(t, 1) Find the solution u using the expansion и(t, г) "(2)"т (?)"а " n 1 with the normalization conditions 1 Vn (0) 1, wn 2n a. (3/10) Find the functions wn, with index n> 1. Wn b. (3/10) Find the...
Let u be the solution to the initial boundary value problem for the Heat Equation, u(t,...
Let u be the solution to the initial boundary value problem for the Heat Equation, u(t, x)20u(t, x) te (0, oo) те (0, 1); with initial condition , u(0, a) f(x) and with boundary conditions и(t, 0) — 0, и(t, 1) — 0. Find the solution u using the expansion "(т)Чт (?)"а " (1')п 1 with the normalization conditions Vn (0) 1, 1. Wn 2n a (3/10) Find the functions w, with index n 1. b. (3/10) Find the functions...
Let u be the solution to the initial boundary value problem for the Heat Equation 202u(t,...
Let u be the solution to the initial boundary value problem for the Heat Equation 202u(t, ) te (0, o0) (0,3); дли(t, 2) хе _ with boundary conditions ut, 0) 0 u(t, 3) 0 and with initial condition 3 9 u(0, ar) f(x){ 5, | 4' 4 0, Те The solution u of the problem above, with the conventions given in class, has the form ()n "(2)"п (г)"а "," n-1 with the normalization conditions 3 Wn 2n vn (0) 1,...
Let u be the solution to the initial boundary value problem for the Heat Equation,
Let u be the solution to the initial boundary value problem for
the Heat Equation,
Hw29 7.3 HE: Problem 7 Problem Value: 10 point(s). Problem Score: 0%. Attempts Remaining: 17 attempts (10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, Stu(t, x)-46?u(t, x), t E (0, 00), x e (0,5); with initial condition 0 and with boundary conditions Find the solution u using the expansion with the normalization conditions 1 a. (3/10)...
Let u be the solution to the initial boundary value problem for the Heat Equation, фа(t,...
Let u be the solution to the initial boundary value problem for the Heat Equation, фа(t, x)-5 &n(t, x), t E (0,00), x E (0, 1); with initial condition 2 r-, 1 and with boundary condition:s n(t, 0)=0, rn(t, 1-0. Find the solution u using the expansion with the normalization conditions vn (0)-1, wn a. (3/10) Find the functions wz, with indexn> 1 b. (3/10) Find the functions v, with index n> 1. c. (4/10) Find the coefficients cn, with...
Let u be the solution to the initial boundary value problem for the Heat Equation, Otu(t, x) = 2 &n(t, x), ț e (0,00), x e (0,5); with initial condition u(0,xf(x)- and with boundary condition:s F...
Let u be the solution to the initial boundary value problem for the Heat Equation, Otu(t, x) = 2 &n(t, x), ț e (0,00), x e (0,5); with initial condition u(0,xf(x)- and with boundary condition:s Find the solution u using the expansion with the normalization conditions (2n - 1) a. (3/10) Find the functions w, with indexn>1. Wnsin(2n-1)pix/10) b. (3/10) Find the functions v, with indexn > 1. Vnexp(-2(2n-1)pi/10)(2)t) 1. C. (4/10) Find the coefficients cn , with index n...
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z) 28?u(t,z), te (0,00), z (0,3); with initial condition u(0, z)fx), where f(0) 0 and f (3) 0 and with boundary conditions u(t,0)-0, r 30 Using separation of variables, the solution of this problem is 4X with the normalization conditions un(m3ī)-. n@) : ї, a. (5/10) Find the functions wn with index n1. Wnlz) b. (5/10) Find the functions vn with index n 1. n(t)...
Let u be the solution to the initial boundary value problem for the Heat Equation, au(t,z 382u(t,z), tE (0,oo), E (0,3); with initial condition u(0,x)-f(x)- and with boundary conditions Find the solution u using the expansion u(t,x) n (t) wn(x), with the normalization conditions vn (0)1, Wn (2n -1) a. (3/10) Find the functionswn with index n 1. b. (3/10) Find the functions vn, with index n 1 C. (4/10) Find the coefficients cn , with index n 1.
Let...
Let u be the solution to the initial boundary value problem for the Heat Equation, tE (0, o0), т€ (0, 3)%; дди(t, г) — 4 0?и(t, a), with initial condition E0, , u(0, x) f(x) 3 and with boundary conditions д,u(t, 3) — 0. и(t,0) — 0, Find the solution u using the expansion и(t, 2) 3D У с, чп (t) w,(m), n-1 with the normalization conditions Vn (0) 1, 1. Wn _ (2n 1) a. (3/10) Find the functions...
Let u be the solution to the initial boundary value problem for the Heat Equation u(t, x) 4ut, x) te (0, o0), т€ (0, 3)%; with initial condition 2. f(x) u(0, x) 3 0. and with boundary conditions ди(t, 0) — 0, и(t, 3) — 0. Find the solution u using the expansion u(t, a) "(2)"п (?)"а " п-1 with the normalization conditions Vn (0) 1, wn(0) = 1 a. (3/10) Find the functions wn. with index n > 1....
Let u be the solution to the initial boundary value problem for the Heat Equation дли(t, 2) — 4 әғи(t, 2), te (0, o0), те (0,1); with initial condition , u(0, a)f() and with boundary conditions 0. u(t, 0)0 u(t, 1) Find the solution u using the expansion и(t, г) "(2)"т (?)"а " n 1 with the normalization conditions 1 Vn (0) 1, wn 2n a. (3/10) Find the functions wn, with index n> 1. Wn b. (3/10) Find the...
Let u be the solution to the initial boundary value problem for the Heat Equation, u(t, x)20u(t, x) te (0, oo) те (0, 1); with initial condition , u(0, a) f(x) and with boundary conditions и(t, 0) — 0, и(t, 1) — 0. Find the solution u using the expansion "(т)Чт (?)"а " (1')п 1 with the normalization conditions Vn (0) 1, 1. Wn 2n a (3/10) Find the functions w, with index n 1. b. (3/10) Find the functions...
Let u be the solution to the initial boundary value problem for the Heat Equation 202u(t, ) te (0, o0) (0,3); дли(t, 2) хе _ with boundary conditions ut, 0) 0 u(t, 3) 0 and with initial condition 3 9 u(0, ar) f(x){ 5, | 4' 4 0, Те The solution u of the problem above, with the conventions given in class, has the form ()n "(2)"п (г)"а "," n-1 with the normalization conditions 3 Wn 2n vn (0) 1,...
Let u be the solution to the initial boundary value problem for
the Heat Equation,
Hw29 7.3 HE: Problem 7 Problem Value: 10 point(s). Problem Score: 0%. Attempts Remaining: 17 attempts (10 points) Let u be the solution to the initial boundary value problem for the Heat Equation, Stu(t, x)-46?u(t, x), t E (0, 00), x e (0,5); with initial condition 0 and with boundary conditions Find the solution u using the expansion with the normalization conditions 1 a. (3/10)...
Let u be the solution to the initial boundary value problem for the Heat Equation, фа(t, x)-5 &n(t, x), t E (0,00), x E (0, 1); with initial condition 2 r-, 1 and with boundary condition:s n(t, 0)=0, rn(t, 1-0. Find the solution u using the expansion with the normalization conditions vn (0)-1, wn a. (3/10) Find the functions wz, with indexn> 1 b. (3/10) Find the functions v, with index n> 1. c. (4/10) Find the coefficients cn, with...
Let u be the solution to the initial boundary value problem for the Heat Equation, Otu(t, x) = 2 &n(t, x), ț e (0,00), x e (0,5); with initial condition u(0,xf(x)- and with boundary condition:s Find the solution u using the expansion with the normalization conditions (2n - 1) a. (3/10) Find the functions w, with indexn>1. Wnsin(2n-1)pix/10) b. (3/10) Find the functions v, with indexn > 1. Vnexp(-2(2n-1)pi/10)(2)t) 1. C. (4/10) Find the coefficients cn , with index n...
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