Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 20, Problem 30A
To determine
The unknown value and verify the result.
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No chatgpt pls will upvote Already got wrong chatgpt answer
(c) Find the harmonic function on the annular region Q = {1 < r < 2} satisfying the
boundary conditions given by
U (1, 0) = 1,
U(2, 0) 1+15 sin (20).
=
Question 3
(a) Find the principal part of the PDE AU + UÃ + U₁ + x + y = 0 and determine
whether it's hyperbolic, elliptic or parabolic.
(b) Prove that if U(r, 0) solves the Laplace equation in R², then so is
V(r, 0) = U (², −0).
(c) Find the harmonic function on the annular region = {1 < r < 2} satisfying the
boundary conditions given by
U(1, 0) = 1,
U(2, 0) = 1 + 15 sin(20).
[5]
[7]
[8]
Chapter 20 Solutions
Mathematics For Machine Technology
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- No chatgpt pls will upvote Already got wrong chatgpt answer Plz .arrow_forward- (c) Suppose V is a solution to the PDE V₁ – V× = 0 and W is a solution to the PDE W₁+2Wx = 0. (i) Prove that both V and W are solutions to the following 2nd order PDE Utt Utx2Uxx = 0. (ii) Find the general solutions to the 2nd order PDE (1) from part c(i). (1)arrow_forwardSolve the following inhomogeneous wave equation with initial data. Utt-Uxx = 2, x = R U(x, 0) = 0 Ut(x, 0): = COS Xarrow_forward
- Could you please solve this question on a note book. please dont use AI because this is the third time i upload it and they send an AI answer. If you cant solve handwritten dont use the question send it back. Thank you.arrow_forward(a) Write down the general solutions for the wave equation Utt - Uxx = 0. (b) Solve the following Goursat problem Utt-Uxx = 0, x = R Ux-t=0 = 4x2 Ux+t=0 = 0 (c) Describe the domain of influence and domain of dependence for wave equations. (d) Solve the following inhomogeneous wave equation with initial data. Utt - Uxx = 2, x ЄR U(x, 0) = 0 Ut(x, 0) = COS Xarrow_forwardQuestion 3 (a) Find the principal part of the PDE AU + Ux +U₁ + x + y = 0 and determine whether it's hyperbolic, elliptic or parabolic. (b) Prove that if U (r, 0) solves the Laplace equation in R2, then so is V (r, 0) = U (², −0). (c) Find the harmonic function on the annular region 2 = {1 < r < 2} satisfying the boundary conditions given by U(1, 0) = 1, U(2, 0) = 1 + 15 sin(20).arrow_forward
- 1c pleasearrow_forwardQuestion 4 (a) Find all possible values of a, b such that [sin(ax)]ebt solves the heat equation U₁ = Uxx, x > 0. (b) Consider the solution U(x,t) = (sin x)e¯t of the heat equation U₁ = Uxx. Find the location of its maxima and minima in the rectangle Π {0≤ x ≤ 1, 0 ≤t≤T} 00} (explain your reasonings for every steps). U₁ = Uxxx>0 Ux(0,t) = 0 U(x, 0) = −1arrow_forwardCould you please solve this question on a note book. please dont use AI because this is the third time i upload it and they send an AI answer. If you cant solve handwritten dont use the question send it back. Thank you.arrow_forward
- Could you please solve this question on a note book. please dont use AI because this is the third time i upload it and they send an AI answer. If you cant solve handwritten dont use the question send it back. Thank you.arrow_forward(b) Consider the equation Ux - 2Ut = -3. (i) Find the characteristics of this equation. (ii) Find the general solutions of this equation. (iii) Solve the following initial value problem for this equation Ux - 2U₁ = −3 U(x, 0) = 0.arrow_forwardQuestion 4 (a) Find all possible values of a, b such that [sin(ax)]ebt solves the heat equation U₁ = Uxx, x > 0. (b) Consider the solution U(x,t) = (sin x)et of the heat equation U₁ = Uxx. Find the location of its maxima and minima in the rectangle πT {0≤ x ≤½,0≤ t≤T} 2' (c) Solve the following heat equation with boundary and initial condition on the half line {x>0} (explain your reasonings for every steps). Ut = Uxx, x > 0 Ux(0,t) = 0 U(x, 0) = = =1 [4] [6] [10]arrow_forward
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