Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 18, Problem 13A
To determine
Evaluation of the lowest fraction form of the given ratio.
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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
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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 18 Solutions
Mathematics for Machine Technology
Ch. 18 - Use a decimal equivalents table to find the...Ch. 18 - Compute (27.52.5+4.36)21.75 . Express the result...Ch. 18 - A cylinder has a volume, V, of 32.85 mm3. Use the...Ch. 18 - The volume V of a cube is V=s3 , where s is the...Ch. 18 - Multiply 15.328.75 .Ch. 18 - Express the decimal fraction 0.4275 as a common...Ch. 18 - Prob. 7ACh. 18 - Express the following ratios in lowest fractional...Ch. 18 - Prob. 9ACh. 18 - Express the following ratios in lowest fractional...
Ch. 18 - Prob. 11ACh. 18 - Prob. 12ACh. 18 - Prob. 13ACh. 18 - Express the following ratios in lowest fractional...Ch. 18 - Prob. 15ACh. 18 - Express the following ratios in lowest fractional...Ch. 18 - Prob. 17ACh. 18 - Prob. 18ACh. 18 - Prob. 19ACh. 18 - In Figure 18-8, gear A is turning at 120...Ch. 18 - Solve for the unknown value in each of the...Ch. 18 - Solve for the unknown value in each of the...Ch. 18 - Prob. 23ACh. 18 - Prob. 24ACh. 18 - Prob. 25ACh. 18 - Prob. 26ACh. 18 - Prob. 27ACh. 18 - Solve for the unknown value in each of the...Ch. 18 - Solve for the unknown value in each of the...Ch. 18 - Prob. 30ACh. 18 - Prob. 31ACh. 18 - Prob. 32ACh. 18 - Prob. 33ACh. 18 - Prob. 34ACh. 18 - Prob. 35ACh. 18 - Prob. 36ACh. 18 - Prob. 37ACh. 18 - Prob. 38ACh. 18 - Prob. 39ACh. 18 - Prob. 40ACh. 18 - Prob. 41ACh. 18 - Prob. 42ACh. 18 - Prob. 43ACh. 18 - Prob. 44ACh. 18 - Prob. 45ACh. 18 - Prob. 46ACh. 18 - Prob. 47ACh. 18 - A drawing has a scale of 14=3 . Determine the...
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