# Math 519, Complex Variables

## Homework

Homework Set 1:
sec. 1.1, p. 7: 1e, 2abe, 3c ;
sec. 1.2, p. 18: 1cd, 4a, 5a, 6, 9a

Homework Set 2:
sec. 1.3, p. 29: 1ace, 4cde, 5 ;
sec. 2.1, p. 44: 1, 2ab, 3cde, 4, 5, 7

Homework Set 3:
sec. 2.2, p. 59: 1bc, 2cd, 3b, 4, 5a;
sec. 2.4, p. 80: 1b, 2de, 3cd, 4, 5, 7

Homework Set 4:
sec. 2.5, p. 90: 1bef, 2a, 4;
sec. 2.6, p. 101: 1ad, 2cd, 3, 5, 7, 9a

Homework Set 5:
sec. 2.6, p. 103: 10a; sec. 3.1, p. 113: 1c, 3, 5b, 6

Homework Set 6:
sec. 3.2, p. 125: 1cd, 2abe, 5a, 6a, 7 8;
sec. 3.3, p. 136: 3, 4a

Homework Set 7: sec. 3.3, p. 136: 4b;
sec. 3.5, p. 156: 1 a-g, 2abc, 3abc, 4
Homework Set 8: sec. 4.1, p. 215: 1(a-e), 2a;
sec. 4.2, p. 235: 1(c,d), 2(a,f);

Problem A: Suppose f and g are analytic in a domain D.
Suppose f(z) g(z) = 0 for all z in D.
Show that either f or g must be identically zero in D.

Homework Set 9: sec. 4.4: 3, 4, 5, 6, 7

Homework Set 10: sec. 6.1: 3;
sec. 6.2: 2;
sec. 7.2: 1;
sec. 3.6: 1(c,d), 3 (OK to use Weierstrass theorem), 5, 6(a-e)

Homework Set 11: sec. 5.2: 1, 2, 3, 4;
sec. 5.7: 1, 2, 3, 4

Practice Problems 1

Practice problems on automorphisms of disk: Conway p. 132: 2, 6, 8

Practice problems on Riemann mapping theorem: Conway p. 163: 1, 2b, 4, 7

Practice problems on Runge's theorem: Conway p. 201: 2 (Here H(G) = the set of functions that are holomorphic (= analytic) on G).

Course Information

**Professor:** M. Cheney** **

**Office:** Weber Bldg. 203

**E-mail:** cheney(at)math(dot)colostate(dot)edu

**Phone:** 491-6478