Time and place: MW 11:00 am - 12:30 pm, 2-142
Instructor: Shaoyun Bai
Textbook: Differential Forms by Victor Guillemin and Peter Haine, online version.
Lectures notes (Warning: these notes are simply a partial extraction from the textbook.)
Week 1
Week 3
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Problem sets (from the textbook)
HW1 (Due 2/18): 1.2.vi, xii; 1.3.vi-ix; 1.4.vi, vii, x; 1.5.i, iii, iv, viii, x; 1.6.iii, v, vi; 1.7.iv, v, vi; 1.8.iii, vii, viii.
HW2 (Due 3/3):2.1.iii, iv, viii, ix; 2.2.iv, viii, x, xi; 2.3.ii, iii, v; 2.4.ii, iii, v, vi; 2.5.iv, v, vi, viii; 2.6.iv, v, vi, ix, x, xi.
HW3 (Due 3/17): 3.2.iv, v, viii; 3.4. ii, iii, x; 3.5.iv, v; 3.6.i, iii, iv, vi, vii, x.
HW4 (Due 4/14): 4.1.iv, v, vi; 4.2.ii, vi; 4.3.iii, vii, xii; 4.4.ii, iii, v, vii, viii; 4.5.iv, v; 4.6.i, iii, vii, x; 4.7.ii, v, vi, viii, ix.
HW5 (Due 4/30): 4.8.i, ii; 5.1.i, v-vii, x; 5.2.i-iii, v, vii; 5.3.iii, iv, ix, xii; 5.8.i.
Problems for extra credits (Due 5/7): 4.8.iii-x; Figure out the complete proof of the Gauss-Bonnet Theorem for surfaces (Application 4.8.17); 4.1.vii-xii.