Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 58, Problem 6A
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Theorem: show that XCH) = M(E) M" (6) E +
t
Mcfic
S
a
Solution of ODE
-9CA)-
x = ACE) x + g (t) + X (E) - E
5. (a) State the Residue Theorem. Your answer should include all the conditions required
for the theorem to hold.
(4 marks)
(b) Let y be the square contour with vertices at -3, -3i, 3 and 3i, described in the
anti-clockwise direction. Evaluate
に
dz.
You must check all of the conditions of any results that you use.
(5 marks)
(c) Evaluate
L
You must check all of the conditions of any results that you use.
ཙ
x sin(Tx)
x²+2x+5
da.
(11 marks)
3. (a) Lety: [a, b] C be a contour. Let L(y) denote the length of y. Give a formula
for L(y).
(1 mark)
(b) Let UCC be open. Let f: U→C be continuous. Let y: [a,b] → U be a
contour. Suppose there exists a finite real number M such that |f(z)| < M for
all z in the image of y. Prove that
<
||, f(z)dz| ≤ ML(y).
(3 marks)
(c) State and prove Liouville's theorem. You may use Cauchy's integral formula without
proof.
(d) Let R0. Let w € C. Let
(10 marks)
U = { z Є C : | z − w| < R} .
Let f UC be a holomorphic function such that
0 < |ƒ(w)| < |f(z)|
for all z Є U. Show, using the local maximum modulus principle, that f is constant.
(6 marks)
Chapter 58 Solutions
Mathematics for Machine Technology
Ch. 58 - Find the area of this figure. Round your answer to...Ch. 58 - Prob. 2ACh. 58 - The four holes in the figure are 0.8 cm in...Ch. 58 - Prob. 4ACh. 58 - Prob. 5ACh. 58 - Prob. 6ACh. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Find the unknown area, base, or height for each of...
Ch. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Find the unknown area, base, or height for each of...Ch. 58 - Given three side, find the area of each of the...Ch. 58 - Given three side, find the area of each of the...Ch. 58 - Given three side, find the area of each of the...Ch. 58 - Given three side, find the area of each of the...Ch. 58 - Given three side, find the area of each of the...Ch. 58 - Given three side, find the area of each of the...Ch. 58 - Given three side, find the area of each of the...Ch. 58 - Given three side, find the area of each of the...Ch. 58 - Solve these exercises. Find the cross-sectional...Ch. 58 - Solve these exercises. Two triangular pieces are...Ch. 58 - Solve these exercises. Determine the area of the...Ch. 58 - Solve these exercises. Find the area of the...Ch. 58 - Solve these exercises. The area of the irregularly...
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