where M=7 322-M2 4) Find the inverse - transform of F(z) = (2-1)(2-2M)' (15 marks) 0...
b) i. Form partial differential equation from z = ax - 4y+b [4 marks] a +1 ii. Solve the partial differential equation 18xy2 + sin(2x - y) = 0 дх2ду c) i. Solve the Lagrange equation [4 Marks] az -zp + xzq = y2 where p az and q = ду [5 Marks] x ax ii. A special form of the second order partial differential equation of the function u of the two independent variables x and t is given...
(b) The signal f(t) is shown in the figure below 3 2 f(t) _ 0 I 1 -4 -3 -2 -1 0 1 2 3 4 5 6 7 t and is given by 21 (1) + 3A (132), where A is the triangle function defined as 10-{ It a It <a It > a 0 Write the Fourier transform F [A(t)] (s) of f(t) exploiting the fact that FA(t)](s) = sinc-(s) where sin(TTS) sinc(s) ITS and the theorem for...
Find the Inverse Fourier transform of: Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t) = sin (20u)e-7ίω F(u) Question 14 (2 marks) Attempt 1 14 Find the Inverse Fourier transform of F(u)-sin(2Oue-Tu Your answer should be expressed as a function of t using the correct syntax. 20 inverse FT. is f(t) = Skipped sin (20u)e-7ίω F(u) Question 14 (2 marks) Attempt 1 14 Find the Inverse Fourier transform of F(u)-sin(2Oue-Tu...
Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2 <Iz 5 markS ii) 2 2 (+2z Solve any three Q4A] 15 marks Is the following function even or odd? Find its Fourier series: i) 2 Find Z-Transform of f(k) = e-2ksinh4k , k 0 Find inverse Z-Transform of -1T-2
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)....
(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...
Find the Inverse Fourier transform of: Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t) = 143w e-11ιω Question 13 (2 marks) Attempt 1 F(u)=# Find the Inverse Fourier transform of: e-11u Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped 143w e-11ιω Question 13 (2 marks) Attempt 1 F(u)=# Find the Inverse Fourier transform of: e-11u Your answer should be...
Question 13 (2 marks) Attempt 1 ,2/144-aw Find the Inverse Fourier transform of: Te-v F(u)--3 Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped a Screen Shot 2019-05-17 at 2.07.40 AM Search Question 14 (2 marks) Attempt 1 Find the inverse Fourier transform of: F(w-5 π w sgn(w) e-Tw Your answer should be expressed as a function of t using the correct syntax. Inverse F.T. is f(t)- Skipped Question 15...
3 B 1. Find the third roots of 21+ Find the inverse of the Laplace transform 2. tan" G) 3. Check the existence of the Laplace transform for the given function and hence she that -02:49 in 133+ 4 S- where LF(t)) is represent the place transform of (1) [Hint: 2 cos Acos B = (A-2).sin(A+B) + sin(A - m = sin cos sin(A + B) - Sin(A) = 0 4. Find the Fourier Sine series of f(x) <rci 5....
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...