Question

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

0 0
Add a comment Improve this question Transcribed image text
Know the answer?
Add Answer to:
Problem 4. Solve for the functions u, v, and w, where (1) (∂/∂t + ∂/∂x) u...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • 1. For differentiable vector functions u and v, prove: u'(t) X v(t)+ u(t) X v'(t) lu(t) X v(t)] 2. For the diff...

    1. For differentiable vector functions u and v, prove: u'(t) X v(t)+ u(t) X v'(t) lu(t) X v(t)] 2. For the differentiable vector function u and real-valued function f, prove: lu(f(t)))= f(t)u' (f (t)) 1. For differentiable vector functions u and v, prove: u'(t) X v(t)+ u(t) X v'(t) lu(t) X v(t)] 2. For the differentiable vector function u and real-valued function f, prove: lu(f(t)))= f(t)u' (f (t))

  • (1 point) Let W(s, t) = F(u(s, t), v(s, t)) where u(1,0) = 1, u,(1,0) =...

    (1 point) Let W(s, t) = F(u(s, t), v(s, t)) where u(1,0) = 1, u,(1,0) = 2, 4(1,0) = 4 v(1,0) = -8,0,(1,0) = 3,0,(1,0) = -9 F.(1,-8) = -9, F,(1,-8) = -1 W (1,0) = W (1,0) =

  • Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot...

    Problem 1: Let y()- r(t+2)-r(t+1)+r(t)-r(t-1)-u(t-1)-r(t-2)+r(t-3), where r(t) is the ramp function. a) plot y(t) b) plot y'() c) Plot y(2t-3) d) calculate the energy of y(t) note: r(t) = t for t 0 and 0 for t < 0 Problem 2: Let x(t)s u(t)-u(t-2) and y(t) = t[u(t)-u(t-1)] a) b) plot x(t) and y(t) evaluate graphically and plot z(t) = x(t) * y(t) Problem 3: An LTI system has the impulse response h(t) = 5e-tu(t)-16e-2tu(t) + 13e-3t u(t) The input...

  • Let W(s, t) - F(u(s, t), vis, t)), where F, u, and v are differentiable, and...

    Let W(s, t) - F(u(s, t), vis, t)), where F, u, and v are differentiable, and the following applies. u(6, -6) - 7 v(6, -6) -9 us(6, -6) - 2 vs(6, -6) -7 (6,-6) --4 V:(6, -6) = 3 Fu(7.-9) - - 1 F (7.-9) - -2 Find W (6, -6) and W.(6, -6). Ws(6, -6) W:(6, -6) =

  • (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)...

  • Problem 1. The figure below shows the vectors u, v, and w, along with the images...

    Problem 1. The figure below shows the vectors u, v, and w, along with the images T(u) and T(v) to the right. Copy this figure, and draw onto it the image T(w) as accurately as possible. (Hint: First try writing w as a linear combination of u and v.) TV (u) Problem 2. Let u = | and v Suppose T : R2 + R2 is a linear transformation with 6 1 3) Tu = T(u) = -3 and T(v)...

  • Hollie work #2 (Due April 1 δ) Problem Obtain the Laplace transform of each of the...

    Hollie work #2 (Due April 1 δ) Problem Obtain the Laplace transform of each of the following functions: 2t (a) et cos 3tu(t) (c) e3 cosh 2tu(t) (e) te sin 2tu(t) (b) e2t sin 4tu(t) (d) e4 sinh tu(t) Problem 2. Find the Laplace transform of each of the following functions (b) 3f* e^ut) (c) 2n1(t)-4". δ(t) (e) 5u(t/2) (d) 2e) u(t) 2p-(t-1) (f) 6el3 u(t) d" dt" Problem 3. Find the Laplace transform of the following signals (a) f(t)-(2t...

  • 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...

  • əz2(7,t), 0< < 4, t > 0 3 2,0<<< v(z,t) = { (1 point) Solve the...

    əz2(7,t), 0< < 4, t > 0 3 2,0<<< v(z,t) = { (1 point) Solve the heat problem with non-homogeneous boundary conditions ди au (2,t) at u(0,t) = 0, u(4, t) = 3, t > 0, u(2,0) 2,0<2<4. Recall that we find h(2), set v2,t) = u(2,t) – h(2), solve a heat problem for v2,t) and write uz,t) = v(x, t) +(2). Find h(1) h(x) = The solution u(x, t) can be written as u(x, t)=h(2) +v(2,t), where v(x, t)...

  • 16.2 Find the Fourier series expressions for the periodic voltage functions shown in Fig. P16.2. ...

    16.2 Find the Fourier series expressions for the periodic voltage functions shown in Fig. P16.2. Note that Fig. P16.2(a) illustrates the square wave; Fig. P16.2(b) illustrates the full-wave rectified sine wave, where u(t)-Yn sin(π/T), 0 t s T; and Fig. P16.2(c) illustrates the half-wave rectified sine wave, where Figure P16.2 v(t) 2T 3T rt v(0) 2T 3T v(t) nt T/2 T 3T/2 16.2 Find the Fourier series expressions for the periodic voltage functions shown in Fig. P16.2. Note that Fig....

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT