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subject is differential equations please hurry up (5) (12 poins)(a) Compute the sine series for the function f such that f(z) r(4-z) on the interval l0,4 (b) Compute the solution u(z,t) for the pa...
subject is differential equations please hurry up (5) (12 poins)(a) Compute the sine series for the...
subject is differential equations
please hurry up
(5) (12 poins)(a) Compute the sine series for the function f such that f(z) r(4-z) on the interval l0,4 (b) Compute the solution u(z,t) for the partial differential equation with z in the interval (0,4) and t > 0: 3tit tigr with u(0,t) = u(4,t)-0 for t > 0 u(z, 0)(4-a) for 0 <4 (boundary conditions) (initial conditions)
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, ) luWith u(t, 0) u(t,1)-0...
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, ) luWith u(t, 0) u(t,1)-0 for t>0 (boundary conditions) u(o,z)-3 sin(2x)-5 sin(5z) + sin(6z), for O < < 1 (initial conditions) (20 points)
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, )...
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on the (b) Compute the solution u(t, z) for the partial differential equation on the interval [0, T): 16ut = uzz with...
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on the (b) Compute the solution u(t, z) for the partial differential equation on the interval [0, T): 16ut = uzz with u(t, 0)-u(t, 1) 0 for t>0 (boundary conditions) (0,) 3 sin(2a) 5 sin(5x) +sin(6x). for 0 K <1 (initial conditions) (20 points) Remember to show your work. Good luck.
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on...
8. (a) Determine the Fourier sine series for the function { f(x) L 2 0 (b)...
8. (a) Determine the Fourier sine series for the function { f(x) L 2 0 (b) Using your answer to part (a), solve the diffusion equation at for (a,t):0 < L, t>0} subject to the boundary conditions (0, t) (L, t) (x,0) f(x)
8. (a) Determine the Fourier sine series for the function { f(x) L 2 0 (b) Using your answer to part (a), solve the diffusion equation at for (a,t):0 0} subject to the boundary conditions (0, t)...
Consider the partial differential equation together with the boundary conditions u(0, t) 0 and u(1,t)0 for t20 and the initial condition u(z,0) = z(1-2) for 0 < x < 1. (a) If n is a positive in...
Consider the partial differential equation together with the boundary conditions u(0, t) 0 and u(1,t)0 for t20 and the initial condition u(z,0) = z(1-2) for 0 < x < 1. (a) If n is a positive integer, show that the function , sin(x), satisfies the given partial differential equation and boundary conditions. (b) The general solution of the partial differential equation that satisfies the boundary conditions is Write down (but do not evaluate) an integral that can be used to...
The function u(x, t) satisfies the partial differential equation with the boundary conditions u(0,t) = 0...
The function u(x, t) satisfies the partial differential equation with the boundary conditions u(0,t) = 0 , u(1,t) = 0 and the initial condition u(x,0) = f(x) = 2x if 0<x<} 2(1 – x) if}<x< 1 . The initial velocity is zero. Answer the following questions. (1) Obtain two ODES (Ordinary Differential Equations) by the method of separation of variables and separating variable -k? (2) Find u(x, t) as an infinite series satisfying the boundary condition and the initial condition.
QUESTION 5 (5.1) Compute the Fourer cosine series for the function (5) 0 те (-т, т/2) f(+) 3D {1 z€ |-п/2, т/2] 0 те (т...
QUESTION 5 (5.1) Compute the Fourer cosine series for the function (5) 0 те (-т, т/2) f(+) 3D {1 z€ |-п/2, т/2] 0 те (т/2, т) on the mterval (-T,7T) (5.2) Use separation of varables to find a solution of the partial differential equation (7) ди ди =0, on z, y € (0, со), with boundarу value u(z, 1) - e(1-2)/z [12
QUESTION 5 (5.1) Compute the Fourer cosine series for the function (5) 0 те (-т, т/2) f(+) 3D...
Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary conditions u(0,t1, t)- 0, and the initial condition 1--+ sin(z) u(z,0) = e solution u(z, t)...
Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary conditions u(0,t1, t)- 0, and the initial condition 1--+ sin(z) u(z,0) = e solution u(z, t) by completing each of the following steps Find the equilibrium temperature distribution we r) Find th (b) Denote v, t)t) - ()Derive the IBVP for the function vz,t). (c) Find v(x, t) (d) Find u(x, t)
Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary...
Question 4. Calculate the Fourier sine series and the Fourier cosine series of the function f(x)...
Question 4. Calculate the Fourier sine series and the Fourier cosine series of the function f(x) = sin(x) on the interval [0, 1]. Hint: For the cosine series, it is easiest to use the complex exponential version of Fourier series. Question 5. Solve the following boundary value problem: Ut – 3Uzx = 0, u(0,t) = u(2,t) = 0, u(x,0) = –2? + 22 Question 6. Solve the following boundary value problem: Ut – Uxx = 0, Uz(-7,t) = uz (77,t)...
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)...
subject is differential equations
please hurry up
(5) (12 poins)(a) Compute the sine series for the function f such that f(z) r(4-z) on the interval l0,4 (b) Compute the solution u(z,t) for the partial differential equation with z in the interval (0,4) and t > 0: 3tit tigr with u(0,t) = u(4,t)-0 for t > 0 u(z, 0)(4-a) for 0 <4 (boundary conditions) (initial conditions)
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, ) luWith u(t, 0) u(t,1)-0 for t>0 (boundary conditions) u(o,z)-3 sin(2x)-5 sin(5z) + sin(6z), for O < < 1 (initial conditions) (20 points)
(4) (a) Compute the Fourier series for the function f(s)-- interval [-T, on the (b) Compute the solution u(t,a) for the partial differential equation on the interval [o, )...
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on the (b) Compute the solution u(t, z) for the partial differential equation on the interval [0, T): 16ut = uzz with u(t, 0)-u(t, 1) 0 for t>0 (boundary conditions) (0,) 3 sin(2a) 5 sin(5x) +sin(6x). for 0 K <1 (initial conditions) (20 points) Remember to show your work. Good luck.
(4) (a) Compute the Fourier series for the function f(x) interval [-π, π]. 1-z on...
8. (a) Determine the Fourier sine series for the function { f(x) L 2 0 (b) Using your answer to part (a), solve the diffusion equation at for (a,t):0 < L, t>0} subject to the boundary conditions (0, t) (L, t) (x,0) f(x)
8. (a) Determine the Fourier sine series for the function { f(x) L 2 0 (b) Using your answer to part (a), solve the diffusion equation at for (a,t):0 0} subject to the boundary conditions (0, t)...
Consider the partial differential equation together with the boundary conditions u(0, t) 0 and u(1,t)0 for t20 and the initial condition u(z,0) = z(1-2) for 0 < x < 1. (a) If n is a positive integer, show that the function , sin(x), satisfies the given partial differential equation and boundary conditions. (b) The general solution of the partial differential equation that satisfies the boundary conditions is Write down (but do not evaluate) an integral that can be used to...
The function u(x, t) satisfies the partial differential equation with the boundary conditions u(0,t) = 0 , u(1,t) = 0 and the initial condition u(x,0) = f(x) = 2x if 0<x<} 2(1 – x) if}<x< 1 . The initial velocity is zero. Answer the following questions. (1) Obtain two ODES (Ordinary Differential Equations) by the method of separation of variables and separating variable -k? (2) Find u(x, t) as an infinite series satisfying the boundary condition and the initial condition.
QUESTION 5 (5.1) Compute the Fourer cosine series for the function (5) 0 те (-т, т/2) f(+) 3D {1 z€ |-п/2, т/2] 0 те (т/2, т) on the mterval (-T,7T) (5.2) Use separation of varables to find a solution of the partial differential equation (7) ди ди =0, on z, y € (0, со), with boundarу value u(z, 1) - e(1-2)/z [12
QUESTION 5 (5.1) Compute the Fourer cosine series for the function (5) 0 те (-т, т/2) f(+) 3D...
Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary conditions u(0,t1, t)- 0, and the initial condition 1--+ sin(z) u(z,0) = e solution u(z, t) by completing each of the following steps Find the equilibrium temperature distribution we r) Find th (b) Denote v, t)t) - ()Derive the IBVP for the function vz,t). (c) Find v(x, t) (d) Find u(x, t)
Problem 1. Consider the nonhomogencous heat equation for u(a,t) subject to the nonhomogeneous boundary...
Question 4. Calculate the Fourier sine series and the Fourier cosine series of the function f(x) = sin(x) on the interval [0, 1]. Hint: For the cosine series, it is easiest to use the complex exponential version of Fourier series. Question 5. Solve the following boundary value problem: Ut – 3Uzx = 0, u(0,t) = u(2,t) = 0, u(x,0) = –2? + 22 Question 6. Solve the following boundary value problem: Ut – Uxx = 0, Uz(-7,t) = uz (77,t)...
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)...
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