Week

Sections

References

Homework (lecture notes)

Week 1: 8/218/25

Geometry of surfaces

[Boothby, VIII.1] [DoCarmo, 22 to 25]

1,2,3,4,5,6
Solution by T.W.Liu
Solution by E.Ng

Week 2: 8/289/1

Gauss curvature, mean curvature

[Boothby, VIII.2] [DoCarmo, 32 to 33]

Week 3: 9/49/8

Gauss's Theorem Egregium

[Boothby, VIII.2] [DoCarmo, 43]

7,8,9,10,11
Solution by C. Meng et al.
Solution by E.Ng

Week 4: 9/119/15

GaussBonnet formula

[DoCarmo, 45]

Week 5: 9/189/22

Differentiable manifolds
Examples

[Boothby, III.12]

12, 13, 14, 15, 16, 17, 18 (due on Oct 6)
HW 3 Solution by C. Meng et al.

Week 6: 9/259/29

Submanifolds
Differentiable mapping, Immersions

[Boothby, III.35]

Week 7: 10/210/6

Lie groups

[Boothby, III.68]

1925 (due on Oct 20)
HW4 Solution by Huang/Meng

Week 8: 10/910/13

Tangent and cotangent spaces

[Boothby, IV.12]

10/910/10: October Break
homework: 2633 (due Nov 3)
HW5 Solution by Huang/Meng

Week 9: 10/1610/20

Vector fields, Lie bracket
One paramter groups

[Boothby, IV.25]


Week 10: 10/2310/27

Frobenius theorem

[Boothby, IV.78]

homework: 3442 (due Nov 17)
HW6 Solution by Huang/Meng

Week 11: 10/3011/3

Differential forms
Orientation and volume elements



Week 12: 11/611/10

Manifolds with boundary
Integration on manifolds


homework: 4357 (due Dec 1)
HW7 Solution by Huang/Meng

Week 13: 11/1311/17

Stokes' Theorem on manifolds



Week 14: 11/2011/24

De Rham cohomology groups


11/2211/25: Thanksgiving Vacation

Week 15: 11/2712/1

Applications of De Rham cohomology groups
Riemannian metrics, Covariant derivative



Week 16: 12/412/8

Curvature, geodesics



Final week

Final exam problem

Final solutions
