Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Textbook Question
Chapter 50, Problem 7A
Refer to Figure 50-22 and identify each of the following as parallel, perpendicular, or oblique lines.
a. Line AB and line CD
b. Line AB and EF
c. Line CD and GH
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Question 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).
1c please
Question 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) = −1
Chapter 50 Solutions
Mathematics For Machine Technology
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