Drorbn - User contributions [en]

1617-257/Homework Assignment 17 Solutions

2017-04-12T21:26:28Z

Beach:

{{1617-257/Navigation}}
==Doing==
==Student Solutions==

[[media:55mat257 17.pdf|Student 1 LATEX PDF]]

1617-257/Homework Assignment 17 Solutions

2017-04-12T21:26:01Z

Beach: /* Student Solutions */

==Doing==
==Student Solutions==

[[media:55mat257 17.pdf|Student 1 LATEX PDF]]

File:1617-257 55mat257 17.pdf

2017-04-12T21:25:25Z

Beach:

1617-257/Homework Assignment 17 Solutions

2017-04-12T21:25:07Z

Beach: Created page with "==Doing== ==Student Solutions== Student 1 LATEX PDF"

==Doing==
==Student Solutions==

[[media:|Student 1 LATEX PDF]]

1617-257/Navigation

2017-04-12T21:24:25Z

Beach:

<noinclude>Back to [[1617-257]]. </noinclude>
{| border="1px" cellpadding="1" cellspacing="0" width="100%" style="font-size: small; align: left"
|- align=center style="color: red;"
|colspan=3|'''Welcome to Math 257'''
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 12
|[[1617-257/About This Class|About This Class]]; Day 1 Handout ({{pensieve link|Classes/1617-257-AnalysisII/160912/Day1.pdf|pdf}}, {{pensieve link|Classes/1617-257-AnalysisII/160912/Day1.html|html}}); [[1617-257/Classnotes for Monday September 12|Monday]], [[1617-257/Classnotes for Wednesday September 14|Wednesday]], [[1617-257/Classnotes for Friday September 16|Friday]], Day 2 Handout ({{pensieve link|Classes/1617-257-AnalysisII/160914/Day2.pdf|pdf}}, {{pensieve link|Classes/1617-257-AnalysisII/160914/Day2.html|html}}); [[Media:1617-257_Notes_First week.pdf|First Week Notes]].
|- align=left
|align=center|2
|Sep 19
|[[1617-257/Classnotes for Monday September 19|Monday]], [[1617-257/Classnotes for Wednesday September 21|Wednesday]], [[Media:1617-257-Tutorial2Handout.pdf|Tutorial 2 Handout]], [[1617-257/Classnotes for Friday September 23|Friday]], [[Media:1617-257_Notes_second_week.pdf|Second week notes]], [[1617-257/Homework Assignment 1|HW1]], [[1617-257/Homework_Assignment_1_Solutions|HW1 Solutions]].
|- align=left
|align=center|3
|Sep 26
|[[1617-257/Classnotes for Monday September 26|Monday]], [[1617-257/Classnotes for Wednesday September 28|Wednesday]], [[Media:1617-257-Tutorial3Handout.pdf|Tutorial 3 Handout]], [[1617-257/Classnotes for Friday September 30|Friday]], [[Media:1617-257_Notes_Third_week.pdf|Third week notes]], [[1617-257/Class_Photo|Class Photo]], [[1617-257/Homework Assignment 2|HW2]], [[1617-257/Homework_Assignment_2_Solutions|HW2 Solutions]].
|- align=left
|align=center|4
|Oct 3
|[[1617-257/Classnotes for Monday October 3|Monday]], [[1617-257/Classnotes for Wednesday October 5|Wednesday]], [[1617-257/Classnotes for Friday October 7|Friday]], [[Media:1617-257_3rd week_notes.pdf|4th week notes]], [[1617-257/Homework Assignment 3|HW3]], [[1617-257/Homework_Assignment_3_Solutions|HW3 Solutions]].
|- align=left
|align=center|5
|Oct 10
|Monday is Thanksgiving, no class; [[1617-257/Classnotes for Wednesday October 12|Wednesday]], [[1617-257/Classnotes for Friday October 14|Friday]], [[Media:1617-257_Notes_5th_week.pdf|5th week notes]], [[1617-257/Homework Assignment 4|HW4]], [[1617-257/Homework_Assignment_4_Solutions|HW4 Solutions]].
|- align=left
|align=center|6
|Oct 17
|[[1617-257/Classnotes for Monday October 17|Monday]], [[1617-257/Classnotes for Wednesday October 19|Wednesday]], [[1617-257/Classnotes for Friday October 21|Friday]], [[Media:1617-257_Notes_6th_week.pdf|6th week notes]], [[1617-257/Homework Assignment 5|HW5]], [[1617-257/Homework_Assignment_5_Solutions|HW5 Solutions]].
|- align=left
|align=center|7
|Oct 24
|[[1617-257/Classnotes for Monday October 24|Monday]], [[1617-257/Classnotes for Wednesday October 26|Wednesday]], [[1617-257/Classnotes for Friday October 28|Friday]], [[Media:1617-257_Notes_7th_week.pdf|7th week notes]]
|- align=left
|align=center|8
|Oct 31
|Monday is last day to switch to MAT 235; |[[1617-257/Classnotes for Monday October 31|Monday]]; [[1617-257/Term Test 1|Term test 1]]; [[1617-257/Classnotes for Wednesday November 2|Wednesday]], [[1617-257/Homework Assignment 6|HW6]], [[Media:1617-257_HW6_assignment.pdf|HW6 pdf]], [[1617-257/Homework_Assignment_6_Solutions|HW6 Solutions]], [[1617-257/Classnotes for Friday November 4|Friday]], [[Media:1617-257_Notes_8th_week.pdf|8th week notes]].
|- align=left
|align=center|9
|Nov 7
|Monday is last day to switch to MAT 237; Monday-Tuesday is UofT Fall Break; [[1617-257/Classnotes for Wednesday November 9|Wednesday]], [[1617-257/Homework Assignment 7|HW7]], [[1617-257/Homework_Assignment_7_Solutions|HW7 Solutions]], [[1617-257/Classnotes for Friday November 11|Friday]], [[Media:1617-257_Notes_9th_week.pdf|9th week notes]].
|- align=left
|align=center|10
|Nov 14
||[[1617-257/Classnotes for Monday November 14|Monday]], [[1617-257/Classnotes for Wednesday November 16|Wednesday]], [[1617-257/Homework Assignment 8|HW8]], [[Media:1617-257_HW8_assignment.pdf|HW8 pdf]], [[1617-257/Homework_Assignment_8_Solutions|HW8 Solutions]], [[1617-257/Classnotes for Friday November 18|Friday]], [https://1drv.ms/f/s!AoMe0QL0ZvZBhfcU4r7HYPTGFJObSg Lecture recordings], [[Media:1617-257_Notes_10th_week.pdf|10th week notes]].
|- align=left
|align=center|11
|Nov 21
||[[1617-257/Classnotes for Monday November 21|Monday]], [[1617-257/Classnotes for Wednesday November 23|Wednesday]], [[1617-257/Homework Assignment 9|HW9]], [[Media:1617-257_HW9_assignment.pdf|HW9 pdf]], [[1617-257/Homework_Assignment_9_Solutions|HW9 Solutions]], [[1617-257/Classnotes for Friday November 25|Friday]], [https://1drv.ms/f/s!AoMe0QL0ZvZBhfcsEu9fys-1mtsIGw Lecture recordings], [[Media:1617-257_notes_11th_week.pdf|11th week notes]].
|- align=left
|align=center|12
|Nov 28
||[[1617-257/Classnotes for Monday November 28|Monday]], [[1617-257/Classnotes for Wednesday November 30|Wednesday]], [[1617-257/Homework Assignment 10|HW10]], [[1617-257/Homework_Assignment_10_Solutions|HW10 Solutions]], makeup class on [[1617-257/Classnotes for Thursday December 1|Thursday]] at GB 120 at 5PM, no class and no DBN office hours Friday! [[Media:1617-257_notes_12th_week.pdf|12th week notes]].
|- align=left
|align=center|13
|Dec 5
||[[1617-257/Classnotes for Monday December 5|Monday]], [[1617-257/Classnotes for Wednesday December 7|Wednesday]], [[Media:1617-257_notes_13th_week.pdf|13th week notes]] Semester ends on Wednesday - no class Friday.
|- align=left
|align=center|B
|Dec 12,19,26
|No classes: other classes' finals, winter break.
|- align=left
|align=center|14
|Jan 2
|Class resumes Friday at RS211, no tutorials or office hours this week, [[1617-257/Classnotes for Friday January 6|Friday]], [[Media: 1617-257_notes_Jan_06_handwriting.pdf|Friday notes]].
|- align=left
|align=center|15
|Jan 9
||[[1617-257/Classnotes for Monday January 9|Monday]], [[1617-257/Classnotes for Wednesday January 11|Wednesday]], [[1617-257/Classnotes for Friday January 13|Friday]], [[Media:1617-257_notes_jan9-jan13.pdf|Weekly notes]]
|- align=left
|align=center|16
|Jan 16
||[[1617-257/Classnotes for Monday January 16|Monday]], [[1617-257/Term Test 2|Term test 2]]; [[1617-257/Classnotes for Wednesday January 18|Wednesday]], [[1617-257/Homework Assignment 11|HW11]], [[Media:1617-257_HW11_assignment.pdf|HW11 inline pdf]],[[1617-257/homework 11 assignment solutions|HW11 solutions]], [[1617-257/Classnotes for Friday January 20|Friday]], [[Media:1617-257_notes_jan16-jan20.pdf|Weekly notes]]
|- align=left
|align=center|17
|Jan 23
||[[1617-257/Classnotes for Monday January 23|Monday]]; Hour 44 Handout ({{pensieve link|Classes/1617-257b-AnalysisII/Hour44Handout.pdf|pdf}}, {{pensieve link|Classes/1617-257b-AnalysisII/Hour44Handout.html|html}}); [[1617-257/Classnotes for Wednesday January 25|Wednesday]], [[1617-257/Homework Assignment 12|HW12]], [[Media:1617-257_HW12_assignment.pdf|HW12 inline pdf]], [[1617-257/homework 12 assignment solutions|HW12 Solutions]], [[1617-257/Classnotes for Friday January 27|Friday]], [[Media:1617-257_classnotes Jan23-27.pdf|Weekly notes]]
|- align=left
|align=center|18
|Jan 30
||[[1617-257/Classnotes for Monday January 30|Monday]], [[1617-257/Classnotes for Wednesday February 1|Wednesday]], [[1617-257/Homework Assignment 13|HW13]], [[Media:1617-257_HW13_assignment.pdf|HW13 inline pdf]], [[1617-257/homework 13 assignment solutions|HW13 Solutions]],[[1617-257/Classnotes for Friday February 3|Friday]], [[Media:1617-257_Notes_Week18.pdf|Weekly Notes]]
|- align=left
|align=center|19
|Feb 6
||[[1617-257/Classnotes for Monday February 6|Monday]], [[1617-257/Classnotes for Wednesday February 8|Wednesday]], [[1617-257/Homework Assignment 14|HW14]], [[Media:1617-257_HW14_assignment.pdf|HW14 inline pdf]], [[1617-257/Classnotes for Friday February 10|Friday]], [[Media:1617-257_Notes_Week19.pdf|Weekly Notes]]
|- align=left
|align=center|20
|Feb 13
||[[1617-257/Classnotes for Monday February 13|Monday]], [[1617-257/Classnotes for Wednesday February 15|Wednesday]], [[1617-257/Homework Assignment 15|HW15]], [[Media:1617-257_HW15_assignment.pdf|HW15 inline pdf]], [[1617-257/homework 15 assignment solutions|HW15 solutions]], [[1617-257/Classnotes for Friday February 17|Friday]],[[Media:1617-257_Notes_Week20.pdf|Weekly Notes]], UofT examination table posted on Friday.
|- align=left
|align=center|R
|Feb 20
|Reading week - no classes; Tuesday is the last day to drop this class.
|- align=left
|align=center|21
|Feb 27
||[[1617-257/Classnotes for Monday February 27|Monday]], [[1617-257/Classnotes for Wednesday March 1|Wednesday]], [[1617-257/Homework Assignment 16|HW16]], [[Media:1617-257_HW16_assignment.pdf|HW16 inline pdf]], [[1617-257/Classnotes for Friday March 3|Friday]], [[Media:1617-257_Notes_Week21.pdf|Weekly Notes]]
|- align=left
|align=center|22
|Mar 6
||[[1617-257/Classnotes for Monday March 6|Monday]], [[1617-257/Classnotes for Wednesday March 8|Wednesday]], [[1617-257/Classnotes for Friday March 10|Friday]], [[Media:1617-257_Notes_Week22.pdf|Weekly Notes]]
|- align=left
|align=center|23
|Mar 13
||[[1617-257/Classnotes for Monday March 13|Monday]], [[1617-257/Term Test 3|Term test 3]] on Tuesday at 5-7PM; [[1617-257/Classnotes for Wednesday March 15|Wednesday]], [[1617-257/Homework Assignment 17|HW17]], [[Media:1617-257_HW17_assignment.pdf|HW17 inline pdf]], [[1617-257/Homework_Assignment_17_Solutions|HW17 Solutions]], [[1617-257/Classnotes for Friday March 17|Friday]], [[Media:1617-257_Notes_Week23.pdf|Weekly Notes]],[[1617-257/orientation notes|Orientation_notes]]
|- align=left
|align=center|24
|Mar 20
||[[1617-257/Classnotes for Monday March 20|Monday]], [[1617-257/Classnotes for Wednesday March 22|Wednesday]], [[1617-257/Homework Assignment 18|HW18]], [[Media:1617-257_HW18_assignment.pdf|HW18 inline pdf]], [[1617-257/Classnotes for Friday March 24|Friday]]
|- align=left
|align=center|25
|Mar 27
|No Monday class, [[1617-257/Classnotes for Wednesday March 29|Wednesday]], [[1617-257/Classnotes for Thursday March 30|Thursday]] (makeup for Monday), [[1617-257/Homework Assignment 19|HW19]], [[Media:1617-257_HW19_assignment.pdf|HW19 inline pdf]], [[1617-257/Classnotes for Friday March 31|Friday]]
|- align=left
|align=center|26
|Apr 3
||[[1617-257/Classnotes for Monday Apr 3|Monday]], [[1617-257/Classnotes for Wednesday Arl 5|Wednesday]]; Semester ends on Wednesday - no tutorials Wednesday and Thursday, no class Friday.
|- align=left
|align=center|F
|Apr 10-28
|[[1617-257/The Final Exam|The Final Exam]] on Thursday April 20 (and some office hours sessions before).
|- align=left
|colspan=3 align=center|[[1617-257/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[1617-257/Riddle Repository|Riddle Repository]]
|- align=left
|colspan=3 align=center|[[Image:1617-257-ClassPhoto.jpg|310px|Class Photo]] [[1617-257/Class Photo|Add your name / see who's in!]]
|- align=left
|colspan=3 align=center|<math>\int_M d\omega=\int_{\partial M}\omega</math>
|}

1617-257/homework 13 assignment solutions

2017-03-11T20:06:05Z

Beach:

{{1617-257/Navigation}}
==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>.

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

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

==Student Solutions==

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

1617-257/homework 13 assignment solutions

2017-03-11T20:05:14Z

Beach: /* Student Solutions */

==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>.

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

e. 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==

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

1617-257/homework 13 assignment solutions

2017-03-11T20:04:49Z

Beach: /* Student Solutions */

==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>.

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

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

==Student Solutions==

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

1617-257/homework 15 assignment solutions

2017-03-11T20:04:25Z

Beach: Created page with "{{1617-257/Navigation}} ==Doing== ==Student Solutions== Student 1, LaTeX PDF"

{{1617-257/Navigation}}

==Doing==

==Student Solutions==
[[Media:222mat257_15.pdf|Student 1, LaTeX PDF]]

1617-257/Navigation

2017-03-11T20:03:28Z

Beach:

<noinclude>Back to [[1617-257]]. </noinclude>
{| border="1px" cellpadding="1" cellspacing="0" width="100%" style="font-size: small; align: left"
|- align=center style="color: red;"
|colspan=3|'''Welcome to Math 257'''
|- align=left
!#
!Week of...
!Notes and Links
|- align=left
|align=center|1
|Sep 12
|[[1617-257/About This Class|About This Class]]; Day 1 Handout ({{pensieve link|Classes/1617-257-AnalysisII/160912/Day1.pdf|pdf}}, {{pensieve link|Classes/1617-257-AnalysisII/160912/Day1.html|html}}); [[1617-257/Classnotes for Monday September 12|Monday]], [[1617-257/Classnotes for Wednesday September 14|Wednesday]], [[1617-257/Classnotes for Friday September 16|Friday]], Day 2 Handout ({{pensieve link|Classes/1617-257-AnalysisII/160914/Day2.pdf|pdf}}, {{pensieve link|Classes/1617-257-AnalysisII/160914/Day2.html|html}}); [[Media:1617-257_Notes_First week.pdf|First Week Notes]].
|- align=left
|align=center|2
|Sep 19
|[[1617-257/Classnotes for Monday September 19|Monday]], [[1617-257/Classnotes for Wednesday September 21|Wednesday]], [[Media:1617-257-Tutorial2Handout.pdf|Tutorial 2 Handout]], [[1617-257/Classnotes for Friday September 23|Friday]], [[Media:1617-257_Notes_second_week.pdf|Second week notes]], [[1617-257/Homework Assignment 1|HW1]], [[1617-257/Homework_Assignment_1_Solutions|HW1 Solutions]].
|- align=left
|align=center|3
|Sep 26
|[[1617-257/Classnotes for Monday September 26|Monday]], [[1617-257/Classnotes for Wednesday September 28|Wednesday]], [[Media:1617-257-Tutorial3Handout.pdf|Tutorial 3 Handout]], [[1617-257/Classnotes for Friday September 30|Friday]], [[Media:1617-257_Notes_Third_week.pdf|Third week notes]], [[1617-257/Class_Photo|Class Photo]], [[1617-257/Homework Assignment 2|HW2]], [[1617-257/Homework_Assignment_2_Solutions|HW2 Solutions]].
|- align=left
|align=center|4
|Oct 3
|[[1617-257/Classnotes for Monday October 3|Monday]], [[1617-257/Classnotes for Wednesday October 5|Wednesday]], [[1617-257/Classnotes for Friday October 7|Friday]], [[Media:1617-257_3rd week_notes.pdf|4th week notes]], [[1617-257/Homework Assignment 3|HW3]], [[1617-257/Homework_Assignment_3_Solutions|HW3 Solutions]].
|- align=left
|align=center|5
|Oct 10
|Monday is Thanksgiving, no class; [[1617-257/Classnotes for Wednesday October 12|Wednesday]], [[1617-257/Classnotes for Friday October 14|Friday]], [[Media:1617-257_Notes_5th_week.pdf|5th week notes]], [[1617-257/Homework Assignment 4|HW4]], [[1617-257/Homework_Assignment_4_Solutions|HW4 Solutions]].
|- align=left
|align=center|6
|Oct 17
|[[1617-257/Classnotes for Monday October 17|Monday]], [[1617-257/Classnotes for Wednesday October 19|Wednesday]], [[1617-257/Classnotes for Friday October 21|Friday]], [[Media:1617-257_Notes_6th_week.pdf|6th week notes]], [[1617-257/Homework Assignment 5|HW5]], [[1617-257/Homework_Assignment_5_Solutions|HW5 Solutions]].
|- align=left
|align=center|7
|Oct 24
|[[1617-257/Classnotes for Monday October 24|Monday]], [[1617-257/Classnotes for Wednesday October 26|Wednesday]], [[1617-257/Classnotes for Friday October 28|Friday]], [[Media:1617-257_Notes_7th_week.pdf|7th week notes]]
|- align=left
|align=center|8
|Oct 31
|Monday is last day to switch to MAT 235; |[[1617-257/Classnotes for Monday October 31|Monday]]; [[1617-257/Term Test 1|Term test 1]]; [[1617-257/Classnotes for Wednesday November 2|Wednesday]], [[1617-257/Homework Assignment 6|HW6]], [[Media:1617-257_HW6_assignment.pdf|HW6 pdf]], [[1617-257/Homework_Assignment_6_Solutions|HW6 Solutions]], [[1617-257/Classnotes for Friday November 4|Friday]], [[Media:1617-257_Notes_8th_week.pdf|8th week notes]].
|- align=left
|align=center|9
|Nov 7
|Monday is last day to switch to MAT 237; Monday-Tuesday is UofT Fall Break; [[1617-257/Classnotes for Wednesday November 9|Wednesday]], [[1617-257/Homework Assignment 7|HW7]], [[1617-257/Homework_Assignment_7_Solutions|HW7 Solutions]], [[1617-257/Classnotes for Friday November 11|Friday]], [[Media:1617-257_Notes_9th_week.pdf|9th week notes]].
|- align=left
|align=center|10
|Nov 14
||[[1617-257/Classnotes for Monday November 14|Monday]], [[1617-257/Classnotes for Wednesday November 16|Wednesday]], [[1617-257/Homework Assignment 8|HW8]], [[Media:1617-257_HW8_assignment.pdf|HW8 pdf]], [[1617-257/Homework_Assignment_8_Solutions|HW8 Solutions]], [[1617-257/Classnotes for Friday November 18|Friday]], [https://1drv.ms/f/s!AoMe0QL0ZvZBhfcU4r7HYPTGFJObSg Lecture recordings], [[Media:1617-257_Notes_10th_week.pdf|10th week notes]].
|- align=left
|align=center|11
|Nov 21
||[[1617-257/Classnotes for Monday November 21|Monday]], [[1617-257/Classnotes for Wednesday November 23|Wednesday]], [[1617-257/Homework Assignment 9|HW9]], [[Media:1617-257_HW9_assignment.pdf|HW9 pdf]], [[1617-257/Homework_Assignment_9_Solutions|HW9 Solutions]], [[1617-257/Classnotes for Friday November 25|Friday]], [https://1drv.ms/f/s!AoMe0QL0ZvZBhfcsEu9fys-1mtsIGw Lecture recordings], [[Media:1617-257_notes_11th_week.pdf|11th week notes]].
|- align=left
|align=center|12
|Nov 28
||[[1617-257/Classnotes for Monday November 28|Monday]], [[1617-257/Classnotes for Wednesday November 30|Wednesday]], [[1617-257/Homework Assignment 10|HW10]], [[1617-257/Homework_Assignment_10_Solutions|HW10 Solutions]],makeup class on [[1617-257/Classnotes for Thursday December 1|Thursday]] at GB 120 at 5PM, no class and no DBN office hours Friday! [[Media:1617-257_notes_12th_week.pdf|12th week notes]].
|- align=left
|align=center|13
|Dec 5
||[[1617-257/Classnotes for Monday December 5|Monday]], [[1617-257/Classnotes for Wednesday December 7|Wednesday]], [[Media:1617-257_notes_13th_week.pdf|13th week notes]] Semester ends on Wednesday - no class Friday.
|- align=left
|align=center|B
|Dec 12,19,26
|No classes: other classes' finals, winter break.
|- align=left
|align=center|14
|Jan 2
|Class resumes Friday at RS211, no tutorials or office hours this week, [[1617-257/Classnotes for Friday January 6|Friday]], [[Media: 1617-257_notes_Jan_06_handwriting.pdf|Friday notes]].
|- align=left
|align=center|15
|Jan 9
||[[1617-257/Classnotes for Monday January 9|Monday]], [[1617-257/Classnotes for Wednesday January 11|Wednesday]], [[1617-257/Classnotes for Friday January 13|Friday]], [[Media:1617-257_notes_jan9-jan13.pdf|Weekly notes]]
|- align=left
|align=center|16
|Jan 16
||[[1617-257/Classnotes for Monday January 16|Monday]], [[1617-257/Term Test 2|Term test 2]]; [[1617-257/Classnotes for Wednesday January 18|Wednesday]], [[1617-257/Homework Assignment 11|HW11]], [[Media:1617-257_HW11_assignment.pdf|HW11 inline pdf]],[[1617-257/homework 11 assignment solutions|HW11 solutions]], [[1617-257/Classnotes for Friday January 20|Friday]], [[Media:1617-257_notes_jan16-jan20.pdf|Weekly notes]]
|- align=left
|align=center|17
|Jan 23
||[[1617-257/Classnotes for Monday January 23|Monday]]; Hour 44 Handout ({{pensieve link|Classes/1617-257b-AnalysisII/Hour44Handout.pdf|pdf}}, {{pensieve link|Classes/1617-257b-AnalysisII/Hour44Handout.html|html}}); [[1617-257/Classnotes for Wednesday January 25|Wednesday]], [[1617-257/Homework Assignment 12|HW12]], [[Media:1617-257_HW12_assignment.pdf|HW12 inline pdf]], [[1617-257/homework 12 assignment solutions|HW12 Solutions]], [[1617-257/Classnotes for Friday January 27|Friday]], [[Media:1617-257_classnotes Jan23-27.pdf|Weekly notes]]
|- align=left
|align=center|18
|Jan 30
||[[1617-257/Classnotes for Monday January 30|Monday]], [[1617-257/Classnotes for Wednesday February 1|Wednesday]], [[1617-257/Homework Assignment 13|HW13]], [[Media:1617-257_HW13_assignment.pdf|HW13 inline pdf]], [[1617-257/homework 13 assignment solutions|HW13 Solutions]],[[1617-257/Classnotes for Friday February 3|Friday]], [[Media:1617-257_Notes_Week18.pdf|Weekly Notes]]
|- align=left
|align=center|19
|Feb 6
||[[1617-257/Classnotes for Monday February 6|Monday]], [[1617-257/Classnotes for Wednesday February 8|Wednesday]], [[1617-257/Homework Assignment 14|HW14]], [[Media:1617-257_HW14_assignment.pdf|HW14 inline pdf]], [[1617-257/Classnotes for Friday February 10|Friday]], [[Media:1617-257_Notes_Week19.pdf|Weekly Notes]]
|- align=left
|align=center|20
|Feb 13
||[[1617-257/Classnotes for Monday February 13|Monday]], [[1617-257/Classnotes for Wednesday February 15|Wednesday]], [[1617-257/Homework Assignment 15|HW15]], [[Media:1617-257_HW15_assignment.pdf|HW15 inline pdf]], [[1617-257/homework 15 assignment solutions|HW15 solutions]], [[1617-257/Classnotes for Friday February 17|Friday]],[[Media:1617-257_Notes_Week20.pdf|Weekly Notes]], UofT examination table posted on Friday.
|- align=left
|align=center|R
|Feb 20
|Reading week - no classes; Tuesday is the last day to drop this class.
|- align=left
|align=center|21
|Feb 27
||[[1617-257/Classnotes for Monday February 27|Monday]], [[1617-257/Classnotes for Wednesday March 1|Wednesday]], [[1617-257/Homework Assignment 16|HW16]], [[Media:1617-257_HW16_assignment.pdf|HW16 inline pdf]], [[1617-257/Classnotes for Friday March 3|Friday]], [[Media:1617-257_Notes_Week21.pdf|Weekly Notes]]
|- align=left
|align=center|22
|Mar 6
||[[1617-257/Classnotes for Monday March 6|Monday]], [[1617-257/Classnotes for Wednesday March 8|Wednesday]], [[1617-257/Classnotes for Friday March 10|Friday]]
|- align=left
|align=center|23
|Mar 13
||[[1617-257/Classnotes for Monday March 13|Monday]], [[1617-257/Term Test 3|Term test 3]] on Tuesday at 5-7PM; [[1617-257/Classnotes for Wednesday March 15|Wednesday]], [[1617-257/Homework Assignment 17|HW17]], [[1617-257/Classnotes for Friday March 17|Friday]]
|- align=left
|align=center|24
|Mar 20
||[[1617-257/Classnotes for Monday March 20|Monday]], [[1617-257/Classnotes for Wednesday March 22|Wednesday]], [[1617-257/Homework Assignment 18|HW18]], [[1617-257/Classnotes for Friday March 24|Friday]]
|- align=left
|align=center|25
|Mar 27
||[[1617-257/Classnotes for Monday March 27|Monday]], [[1617-257/Classnotes for Wednesday March 29|Wednesday]], [[1617-257/Homework Assignment 19|HW19]], [[1617-257/Classnotes for Friday March 31|Friday]]
|- align=left
|align=center|26
|Apr 3
||[[1617-257/Classnotes for Monday Apr 3|Monday]], [[1617-257/Classnotes for Wednesday Arl 5|Wednesday]]; Semester ends on Wednesday - no tutorials Wednesday and Thursday, no class Friday.
|- align=left
|align=center|F
|Apr10-28
|[[1617-257/The Final Exam|The Final Exam]].
|- align=left
|colspan=3 align=center|[[1617-257/Register of Good Deeds|Register of Good Deeds]]
|- align=left
|colspan=3 align=center|[[1617-257/Riddle Repository|Riddle Repository]]
|- align=left
|colspan=3 align=center|[[Image:1617-257-ClassPhoto.jpg|310px|Class Photo]] [[1617-257/Class Photo|Add your name / see who's in!]]
|- align=left
|colspan=3 align=center|<math>\int_M d\omega=\int_{\partial M}\omega</math>
|}

File:1617-257 222mat257 15.pdf

2017-03-11T20:00:24Z

Beach:

1617-257/homework 13 assignment solutions

2017-03-11T19:55:36Z

Beach: /* Student Solutions */

==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>.

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

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

==Student Solutions==

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

File:1617-257 333mat257 13.pdf

2017-03-11T19:54:50Z

Beach:

1617-257/Class Photo

2016-10-03T23:09:39Z

Beach:

Our class on September 30, 2016:

[[Image:1617-257-ClassPhoto.jpg|thumb|centre|800px|Class Photo: click to enlarge]]
{{1617-257/Navigation}}

Please identify yourself in this photo! There are two ways to do that:

* [[Special:Userlogin|Log in]] to this Wiki and edit this page. Put your name, userid, email address and location in the picture in the alphabetical list below.
* Send [[User:Drorbn|Dror]] an email message with this information.

The first option is more fun but less private.

===Who We Are...===

{| align=center border=1 cellspacing=1

{{Photo Entry|last=Bar-Natan|first=Dror|userid=Drorbn|email=drorbn@ math. toronto. edu|location=facing everybody, as the photographer|comments=Take this entry as a model and leave it first. Otherwise alphabetize by last name. Feel free to leave some fields blank. For better line-breaking, leave a space next to the "@" in email addresses.}}



{{Photo Entry|last=Beach|first=Isabel|userid=Beach|email=isabel. beach@ mail. utoronto. ca|location=first row, third from left, burgundy U of T sweater|comments=Artist, wannabe astronomer, nature enthusiast.}}

{{Photo Entry|last=Hu|first=Janelle|userid=Janelle|email=janelle.hu@ mail. utoronto. ca|location=third row, third from the right|comments=Joined a dance crew this year.
Math related: my roommates are 4th year math specialists}}

{{Photo Entry|last=Im|first=Jeffrey|userid=jeffim|email=jim@ math. toronto. edu|location=bottom-right corner|comments=One of two TAs for this class. Student of George Elliott. Interested in C*-algebras/K-theory.}}

{{Photo Entry|last=Li|first=Xiaoyang|userid=Witchofagnesi|email=xiaoyang. li@ mail. utoronto. ca|location=fifth row, on the middle-left, head sticking out|comments=Loves classical music and poetry.}}

{{Photo Entry|last=Moore|first=Darren|userid=DarrenMoo|email=da.moore@ mail. utoronto. ca|location=fourth row, standing, white UofT shirt|comments=Wannabe game dev, mathematician, musician, etc.}}

{{Photo Entry|last=Moturu|first=Abhishek|userid=Abhi.saim|email=abhi.saim@ gmail.com|location=first row, third from the right, white pants|comments=Two loves: math and chicken.}}

{{Photo Entry|last=Xu|first=Xinyi|userid=Maggie|email=xinyi. xu97@ gmail. com|location=fourth row, first girl from right,with red glasses|comments=Interested in modern Origami.}}


|}