MW, 2:30-3:50 P.M. over Zoom (via Blackboard)
Kevin Sackel, kevin.sackel(at)stonybrook.edu, Math 3-118
Office Hours: Held via Zoom, Monday, 4-5 PM; Tuesday, 2-3 PM; by appointment
Required: Munkres Analysis on Manifolds
Recommended: Spivak Calculus on Manifolds
Miao Song
Homework 1, due M, February 3 (covering Sections 1-3)
p. 9 #1, 4; p. 24 #1, 4; p.30 #2, 6, 8
Solutions (password protected)
Homework 2, due W, February 12 (covering Sections 4, 5)
p. 39 #3; p. 48 #1, 2, 3, 4
Solutions (password protected)
Homework 3, due W, February 19 (covering Sections 6, 7)
p. 54 #1, 4, 5, 7, 9, 10; p. 63 #2, 3
Solutions (password protected)
Homework 4, due W, February 26 (covering Sections 8, 9)
p. 70 #1, 3, 4, 5; p. 78 #1, 4, 6
Solutions (password protected)
Suggested Exercises in preparation for Midterm 1 (covering Sections 10, 11, 12)
p. 90 # 1, 5, 6; p. 97 #1, 6, 9; p.103 #2, 3
Solutions (password protected)
Homework 5, due W, April 1
p. 111 # 2, 4, 7; p. 120 # 2, 5; p. 143 # 1, 3; p. 151 # 5, 6
Solutions (password protected)
Homework 6, due W, April 8
p. 160 #2 (worth 20 points), 3; p. 167 # 5(a,b); p. 177 # 2, 4
Solutions (password protected)
Homework 7, due M, April 20
p. 187 # 5; p. 193 # 3; p. 202 # 5, 6; p. 208 # 2, 5; p. 218 # 3, 8
Solutions (password protected)
Homework 8, due W, April 29
p. 226 # 1, 4, 6, 8; p. 236 # 1, 2, 5; p. 243 # 1, 2, 5; p. 251 # 2, 3
Solutions (password protected)
Homework 9, due F, May 8
p. 260 # 2, 5 (see p. 259 for the definition of closed / exact); p. 266 # 5; p. 273 # 3; p. 280 # 2, 4; p. 291 # 4, 7
Solutions (password protected)
Not for handing in (since the HW would be too long), but some helpful suggested exercises:
Suggested Exercise on "non-naturality of div/grad/curl": p. 273 # 6
Suggested Exercises on Stokes' Theorem: p. 308 # 3, 4, 6; also both of p. 296 # 3 + p. 308 # 2 (c.f. p 260 #5, 6, one of which is on your homework)
Midterm 1, W, March 4, in class
Take-Home Final Exam, due Sat, May 16 at 11:59 PM (on Blackboard)
LECTURES 1-19 ALL TOGETHER (last updated May 9)
LECTURES 20, 21, 22, 23, 24, 25
Extra note: What is d?
Lecture 1 (M, Jan 27): Overview, Sections 1 and 2
Lecture 2 (W, Jan 29): Section 3
Lecture 3 (M, Feb 3): Start Section 4
Lecture 4 (W, Feb 5): Finish Section 4, Start Section 5
Lecture 5 (M, Feb 10): Finish Section 5, Start Section 6
Lecture 6 (W, Feb 12): Finish Section 6, Start Section 7
Lecture 7 (M, Feb 17): Finish Section 7, Start Section 8
Lecture 8 (W, Feb 19): Finish Section 8, Section 9
Lecture 9 (M, Feb 24): Section 10, Start Section 11
Lecture 10 (W, Feb 26): Finish Section 11, Section 12 (end of material on Midterm 1)
Lecture 11 (M, Mar 2): Parts of Sections 13, 14
****MIDTERM 1**** (W, Mar 4)
Lecture 12 (M, Mar 9): Finish Sections 13, 14, Start Section 16
Lecture 13 (W, Mar 11): Finish Section 16, Section 17
*Spring Recess* EXTENDED TO TWO WEEKS
Lecture 14 (M, Mar 30): Sections 18, 19: Recording; Slides
Lecture 15 (W, Apr 1): Sections 20, 21: Recording; Partial Slides (my internet dropped out for 5 minutes, and we lost the first 2/3 of the slides, but the recording is complete)
Lecture 16 (M, Apr 6): Sections 22, Start Section 23: Recording; Slides
Lecture 17 (W, Apr 8): Finish Section 23, Section 24: Recording; Slides
Lecture 18 (M, Apr 13): Sections 25, Start Section 26: Recording; Slides
Lecture 19 (W, Apr 15): Finish Section 26, Start Section 27: Recording; Slides
Lecture 20 (M, Apr 20): Finish Section 27, Section 28, Start Section 29: Recording; Slides
Lecture 21 (W, Apr 22): Finish Section 29, Section 30: Recording; Slides
Lecture 22 (M, Apr 27): Sections 31, 32: Recording; Slides; Extra note: What is d?
Lecture 23 (W, Apr 29): Sections 33, 34: Recording; Slides
Lecture 24 (M, May 4): Sections 35, 37: Recording; Slides
Lecture 25 (W, May 6): Sections 39, 40: Recording; Slides
****TAKE-HOME FINAL EXAM**** due Sat, May 16