Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 13, Problem 34A
In the following table, the lengths of the sides of cubes are given. Determine the volumes of the cubes. Round answers to 2 decimal places where necessary.
34.
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3. (a) Let A be an algebra. Define the notion of an A-module M. When is a module M
a simple module?
(b) State and prove Schur's Lemma for simple modules.
(c) Let AM(K) and M = K" the natural A-module.
(i) Show that M is a simple K-module.
(ii) Prove that if ƒ € Endд(M) then ƒ can be written as f(m) = am, where a
is a matrix in the centre of M, (K).
[Recall that the centre, Z(M,(K)) == {a Mn(K) | ab
M,,(K)}.]
= ba for all bЄ
(iii) Explain briefly why this means End₁(M) K, assuming that Z(M,,(K))~
K as K-algebras.
Is this consistent with Schur's lemma?
(a) State, without proof, Cauchy's theorem, Cauchy's integral formula and Cauchy's
integral formula for derivatives. Your answer should include all the conditions
required for the results to hold.
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(b) Let U{z EC: |z| -1}. Let 12 be the triangular contour with vertices at
0, 2-2 and 2+2i, parametrized in the anticlockwise direction. Calculate
dz.
You must check the conditions of any results you use.
(d) Let U C. Calculate
Liz-1ym dz,
(z - 1) 10
(5 marks)
where 2 is the same as the previous part. You must check the conditions of any
results you use.
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(2 marks)
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dk
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classify it and calculate its residue.
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(3 marks)
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Chapter 13 Solutions
Mathematics for Machine Technology
Ch. 13 - Subtract 7516278 .Ch. 13 - Multiply 7238 . Express the result as a mixed...Ch. 13 - Multiply 1.7022.35 .Ch. 13 - Prob. 4ACh. 13 - Prob. 5ACh. 13 - Prob. 6ACh. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...
Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - Raise the following numbers to the indicated...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the lengths of the sides...Ch. 13 - In the following table, the radii of circles are...Ch. 13 - In the following table, the radii of circles are...Ch. 13 - In the following table, the radii of circles are...Ch. 13 - In the following table, the radii of circles are...Ch. 13 - In the following table, the radii of circles are...Ch. 13 - In the following table, the diameters of spheres...Ch. 13 - In the following table, the diameters of spheres...Ch. 13 - In the following table, the diameters of spheres...Ch. 13 - In the following table, the diameters of spheres...Ch. 13 - In the following table, the diameters of spheres...Ch. 13 - In the following table, the radii and heights of...Ch. 13 - In the following table, the radii and heights of...Ch. 13 - In the following table, the radii and heights of...Ch. 13 - In the following table, the radii and heights of...Ch. 13 - In the following table, the radii and heights of...Ch. 13 - In the following table, the diameters and heights...Ch. 13 - In the following table, the diameters and heights...Ch. 13 - In the following table, the diameters and heights...Ch. 13 - In the following table, the diameters and heights...Ch. 13 - Prob. 55ACh. 13 - Prob. 56ACh. 13 - Prob. 57ACh. 13 - Find the area of this plate. All dimensions are in...Ch. 13 - Find the metal volume of this bushing. All...Ch. 13 - Find the volume of this pin. All dimensions are in...Ch. 13 - Prob. 61A
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