Need help with problem 4 au(x, t) cau(x,t) + 1Donu(x, t) Ot 3.5.4. Show that the...
Solve the heat flow problem: ot (x, t) au au (x, t) = 2 (x, t), 0 < x <1, t > 0, a x2 uz(0,t) = uz(1, t) = 0, t> 0, u(a,0) = 1 + 3 cos(TTX) – 2 cos(31x), 0<x< 1.
Problem 1: We are interested in solving a modified form of diffusion equation given below using Fourier transforms au(x,t) The domain of the problem is-oo < x < oo and is 0 < t < oo . At time t = 0, the initial condition is given by u (x,0)-0 a) Take the Fourier transform on x and show that the above PDE can be transformed into the following ODE where G() is the Fourier transform of g(x) and U(w,...
please provide me with full working solution. Any help is appreciated. thank you in advance Consider the diffusion equation, au(x,t u(x,t) Here u(x,t) > 0 is the concentration of some diffusing substance, the spatial variable is x, time is t and D is a constant called the diffusivity with dimensions [LT-11. We will consider the diffusion equation on a finite spatial domain (0<x< 1) and an infinite time horizon (t > 0). To solve the diffusion equation we must include...
I need help showing how this argument is valid. 3.5.4 Show Work Determine whether the argument is valid or invalid. All scorpions have stingers. That animal is a scorpion. That animal has stingers. Is the argument valid or invalid? Invalid Valid
4. Show that the equation ut au bu du f(x, t) can be transformed into an equation of the form by first making the transformation ξ-x-ct. T-x + ct and then letting u weaf+dr for some choice of a, β.
I really need help with Part B of this question Problem 2: a) If F(a) is the Fourier transform (FT) of a function qx), show that the inverse FT of ewb F(a) is q -b), with b a constant. This is the shift theorem for Fourier transforms. Hint: Y ou will need the orthogonality relation: where y-y) is the Dirac delta function] [ Joeo(y-y')dus2πδ(y-y'), b) Solve the diffusion equation with convection: vetneuzkat.aax au(x,t) аги, ди with-c < 鱸8: and ux,0)-far)....
Solve the heat flow problem: au t> 0, ди (x, t) = 2 (x, t), 0<x< 1, ot дх2 uz(0, t) = uz(1,t) = 0, t>0, u(x,0) = 1- x, 0 < x < 1.
4 : (Practice Problem, No need to turn it in) Calculate o(t) and ot) for the follow- ing circuit. it). 0.01F | -- " ... ... ... 25 cos20 v (+ + H 0.02 F? 5 . (1)
4) The one-dimensional heat equation is du 02u at = k→ ot ar 2 Where u(x,t)is a measure of the temperature at a location x on a bar at time t and k is a constant. Show by direct substitution thatu(x, t) = 10e-t sin x, satisfies the heat equation.
problem 3: I need help with #4 using Matlab. 4. Given that the input x(t) in problem 3 above is a step function of magnitude 2 [x = 2 u(t), find the output y() by fnding the inverse Laplace transform of Y (s) by the method of partial fraction expansion by MATLAB as explained on page 8 of Handout 2 (ilaplace command).