1617-257/homework 13 assignment solutions - Revision history

Stefan.divic: /* Student Solutions */

2017-03-31T04:34:30Z

Student Solutions

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	[[Media:333mat257_13.pdf\| Student 1, LaTeX PDF]]		[[Media:333mat257_13.pdf\| Student 1, LaTeX PDF]]

			[[Media:1617-257-pset13.pdf\|Student 2]]

Beach at 20:06, 11 March 2017

2017-03-11T20:06:05Z

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		⚫	{{1617-257/Navigation}}
	==Doing==		==Doing==
	'''Solve''' ''all'' the problems in sections 25-26, but submit only your solutions of problems 4 and 8 in section 25 and problems 5 and 6 in section 26. In addition, solve the following problem, though submit only your solutions of parts d and e:		'''Solve''' ''all'' the problems in sections 25-26, but submit only your solutions of problems 4 and 8 in section 25 and problems 5 and 6 in section 26. In addition, solve the following problem, though submit only your solutions of parts d and e:
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	<u>e</u>. Find <math>\int_MzdV</math> (where <math>z</math> denotes the third coordinate of <math>{\mathbb R}^3</math>).		<u>e</u>. Find <math>\int_MzdV</math> (where <math>z</math> denotes the third coordinate of <math>{\mathbb R}^3</math>).

⚫	{{1617-257/Navigation}}

	==Doing==
	==Student Solutions==		==Student Solutions==

Beach: /* Student Solutions */

2017-03-11T20:05:14Z

Student Solutions

← Older revision		Revision as of 16:05, 11 March 2017
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	<u>e</u>. Find <math>\int_MzdV</math> (where <math>z</math> denotes the third coordinate of <math>{\mathbb R}^3</math>).		<u>e</u>. Find <math>\int_MzdV</math> (where <math>z</math> denotes the third coordinate of <math>{\mathbb R}^3</math>).

			{{1617-257/Navigation}}

			==Doing==
	==Student Solutions==		==Student Solutions==

Beach: /* Student Solutions */

2017-03-11T20:04:49Z

Student Solutions

← Older revision		Revision as of 16:04, 11 March 2017
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	==Student Solutions==		==Student Solutions==

	[[Media:333mat257_13.pdf]] [LaTeX PDF]		[[Media:333mat257_13.pdf\| Student 1, LaTeX PDF]]

Beach: /* Student Solutions */

2017-03-11T19:55:36Z

Student Solutions

← Older revision		Revision as of 15:55, 11 March 2017
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	==Student Solutions==		==Student Solutions==

			[[Media:333mat257_13.pdf]] [LaTeX PDF]

Wangy306: Created page with "==Doing== '''Solve''' ''all'' the problems in sections 25-26, but submit only your solutions of problems 4 and 8 in section 25 and problems 5 and 6 in section 26. In addition,..."

2017-03-09T06:02:44Z

Created page with "==Doing== '''Solve''' ''all'' the problems in sections 25-26, but submit only your solutions of problems 4 and 8 in section 25 and problems 5 and 6 in section 26. In addition,..."

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==Doing==
'''Solve''' ''all'' the problems in sections 25-26, but submit only your solutions of problems 4 and 8 in section 25 and problems 5 and 6 in section 26. In addition, solve the following problem, though submit only your solutions of parts d and e:

'''Problem A.''' Let <math>\alpha\colon\{(u,v)\in{\mathbb R}^2\colon u^2+v^2\leq 1\}\to{\mathbb R}^3</math> be given by <math>\alpha(u,v)=\left(u-v,\,u+v,\,2(u^2+v^2)\right)</math>. Let <math>M</math> be the image of <math>\alpha</math>.

a. Describe <math>M</math>.

b. Show that <math>M</math> is a manifold.

c. Find the boundary <math>\partial M</math> of <math>M</math>.

<u>d</u>. Find the volume <math>V(M)</math> of <math>M</math>.

<u>e</u>. Find <math>\int_MzdV</math> (where <math>z</math> denotes the third coordinate of <math>{\mathbb R}^3</math>).

==Student Solutions==