Day
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Topic and Section
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Homework Assigned or Due
|
January
Th 1/16 |
Introduction. Parameterized curves.
1-2
|
Assignment #1
(PDF)
|
| T 1/21 |
Regular curves and arclength. Arclength
parameterization. 1-3
|
|
| Th 1/23 |
Vector (cross) product in R3.
1-4
|
Assignment # 1 Due.
A#1 Solutions (PDF)
Assignment # 2:
1-3 Exercise # 10 (pages 7 - 11);
1-4 # 1b, 3, 5, 7 (pp 14 - 16);
1-5 # 1, 8a, 9 (pp 22 - 26).
|
| T 1/28 |
Tidbits: conic sections, quadric surfaces,
proof style.
|
|
| Th 1/30 |
Curvature of curves in space. 1-5
|
|
February
T 2/4 |
Frenet frame and fundamental theorem of
curves. 1-5
|
Assignment # 2 Due.
A#2 Solutions (PDF)
Assignment # 3:
1-5 # 2, 10, 11, 12acd [12b was done in class]
(pp 22 - 26);
1-7 # 1, 3 [read four vertex theorem], 15a, 15b
(pp 47 -
50).
|
| Th 2/6 |
The isoperimetric inequality and the
calculus of variations. 1-7
|
|
| T 2/11 |
Proof of the isoperimetric inequality.
1-7
|
Assignment # 3 Due.
A#3 Solutions (PDF)
|
Th 2/13
|
An introduction to surfaces. 2-2
|
Assignment # 4:
2-2 # 1, 10, 16
2-3 # 3
|
T 2/18
|
Regular surfaces and parameterization.
2-2
|
|
Th 2/20
|
Regular surfaces, cont.
|
Assignment # 5:
2-2 # 6 [see in-class version of Prop. 2], 11a
2-3 # 14, 15 [see definition of "regular curve" on
page 75; a
"regular curve" is different from a "regular parameterized
curve," yes?]
|
T 2/25
|
Regular surfaces
|
Assignment #4 Due.
A#4 Solutions (PDF)
|
Th 2/27
|
Change of parameters.
2-3
|
|
March
T 3/4
|
MIDTERM EXAM In
class.
|
MIDTERM EXAM:
One hour in class. Be sure to get a copy of my handout
"Regarding
the Midterm", given in class on 2/27.
|
Th 3/6
|
Change of parameters.
2-3
|
|
T 3/11
|
The tangent plane. 2-4
|
Assignment #5 Due.
A#5 Solutions (PDF)
Assignment # 6:
2-4 # 1, 2, 9, 11
2-5 # 1a, 1c, 1d, 5, 14a
|
Th 3/13
|
VIDEO: Not Knot
(Note Fri. 3/14 is last day for "W".)
|
|
Spring Break:
3/17 - 3/21
|
|
|
T 3/25
|
Area and the first fundamental form.
2-5
|
|
Th 3/27
|
Orientation and area. 2-6
|
|
April
T 4/1
|
Orientation, cont. 2-6
|
Assignment #6 Due.
A#6 Solutions (PDF)
Assignment #7:
2-6 # 3
3-2 # 2, 8
3-3 #1
|
Th 4/3
|
Definition of the Gauss map. 3-2
|
|
T 4/8
|
Gauss map cont. 3-2
|
|
Th 4/10
|
Self-adjoint 2x2 matrices; Ouside In
|
|
T 4/15
|
Gauss map in local coordinates 3-3
|
Assignment # 7 Due.
A#7 Solutions (PDF)
Assignment #8 (PDF)
|
Th 4/17
|
3-3 curvature in local
coordinates
|
|
T 4/22
|
3-3 meaning of curvature
3-5 minimal surfaces
|
|
Th 4/24
|
4-2 isometries
|
|
T 4/29
|
4-3 Gauss' great theorem
[& 4-4 geodesic curvature only]
|
Assignment # 8 Due. FIRM DATE!
A#8 Solutions (PDF)
Final Exam!!
(PDF)
|
May
Th 5/1
|
4-5 Gauss-Bonnet theorem, cont
|
|
T 5/6
|
HINTS SESSION
Regular class time and place: 3:40 -- 4:00pm, Chap 107.
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Th 5/8
|
FINAL DUE
5:15pm at my office.
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