Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 65, Problem 9A
To determine
(a)
Comparison of the side
To determine
(b)
Comparison of the side
To determine
(c)
Comparison of the side
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Theorem: show that XCH) = M(E) M" (6) E +
t
Mcfic
S
a
Solution of ODE
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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
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に
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(5 marks)
(c) Evaluate
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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
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(d) Let R0. Let w € C. Let
(10 marks)
U = { z Є C : | z − w| < R} .
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0 < |ƒ(w)| < |f(z)|
for all z Є U. Show, using the local maximum modulus principle, that f is constant.
(6 marks)
Chapter 65 Solutions
Mathematics for Machine Technology
Ch. 65 - If tan A=4.13792 , determine the value of angle A...Ch. 65 - Find the number of cubic inches of material...Ch. 65 - Find the number of cubic inches of material...Ch. 65 - The sector of a circle has an area of 231.3 sq in....Ch. 65 - Determine the arc length ABC if r=5.75in. and...Ch. 65 - Identify each of the following angles as acute....Ch. 65 - Prob. 7ACh. 65 - Refer to Figure 65-3 in answering exercises 1...Ch. 65 - Prob. 9ACh. 65 - Refer to Figure 65-3 in answering exercises 1...
Ch. 65 - Prob. 11ACh. 65 - Refer to Figure 65-3 in answering exercises 1...Ch. 65 - Prob. 13ACh. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - For each exercise, functions of two angles are...Ch. 65 - Prob. 25ACh. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - Prob. 41ACh. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - For each function of an angle, write the...Ch. 65 - Prob. 45ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 47ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 49ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 51ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 53ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 55ACh. 65 - For each exercise, functions and cofunctions of...Ch. 65 - Prob. 57A
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