Homework

Administrative note: our grader is Kwong Sze Hong (shkwong@umd.edu).

HW1 (Due 9/8):

1.1.4, 1.2.1, 1.2.2, 1.4.1, 1.1.2, 1.3.1. Extra credit: 1.3.2

HW2 (Due 9/15)

2.1.1.(i), 2.1.1.(iv), 2.1.2, 2.2.1, 2.2.5, 2.2.6

HW3 (Due 9/22)

2.3.1, 2.3.2, 2.3.4, 2.3.6, 3.2.2, 3.3.2

HW4 (Due 9/29)

4.1.1, 4.1.2, 4.1.3, 4.2.2, 4.2.5, 4.4.1

HW5 (Due 10/6)

4.5.1 5.1.1, 5.1.2, 5.2.3, 5.2.4, 6.1.3

Prove that "in co-ordinates", the derivative of a smooth map between surfaces is given by the Jacobian matrix. More precisely, if f: S_1 \to S_2 is a surface map, s_1 is a surface patch containing a point p, s_2 is a surface path containing f(p), and f(s_1(u,v)) = s_2( g(u,v), h(u,v) ), then in the basis induced by s_1 and s_2 (as in class or the book), the derivative of f is the Jacobian of the map (u,v) -> (g(u,v), h(u,v) ). [This is proved in your book, but please try it without using the book! It is important.]

HW6 (Due 10/20)

6.3.1, 6.3.4, 5.6.3, 5.6.4, 6.2.1, 6.2.2

HW7 (Due 10/27)

7.1.1, 7.1.2, 7.1.3, 7.2.1, 7.3.2, 7.3.6

HW8 (Due 11/3)

7.4.1, 7.4.2, 7.4.3, 7.3.1, 7.3.3, 8.1.1. Extra credit: 7.3.5

HW9 (Due 11/10)

8.1.2, 8.1.5, 8.2.1, 8.2.2, 8.2.5. Extra credit: 8.2.7

HW10 (Due 12/1)

8.3.1, 9.1.2, 9.1.6. Extra credit: 9.1.5

HW11 (Due 12/8)

9.2.1, 9.2.3, 9.2.6, 9.3.2, 9.3.4. Extra credit: 9.4.2