Homework 0, Not to be turned in, will be discussed in section:
Section 2: 4,11 ; Section 3: 1 ; Section 5: 1,3,4,5,6 ; and:
Find the square roots of 1+i directly by solving (x+iy)^2 = 1+i
Homework 1: due Friday January 20
Section 6: 2,7,14,15
Section 9: 1,4,5cd,6,9,10
Section 11: 1,2,3,6,7
Homework 2: due Friday January 27
Section 12: 1,2,3,6,7 (in 7abd the set that is meant is
{zn : n=1,2,3,...})
Section 14: 1,2,3,6,7 (is the answer given for 1b correct?)
Section 18: 5,9,10,11
Homework 3: due Friday February 3
Section 20: 1,3,4,8b,9
Section 24: 1bc,3bc,4
Homework 4: due Friday February 10
Section 26: 1ad,2ab,4ab,7
Section 30: 2,4,6,7,10
Section 33: 1,2c,3,7,8
Homework 5: due Friday February 17
Section 33: 12
Section 34: 5
Section 36: 2,6,8ac
Section 38: 7,9,15
And the following two exercises:
(1) If f(z) denotes any branch of the analytic log function, we have
seen that df/dz = 1/z at any point where the derivative
exists. Suppose g(z) is another branch of the log function. Then
f(z)-g(z) has derivative zero and ``should'' be a constant. Is
this true? If not, explain why. An example is to take f(z)
= Log (z) to be the principal branch and g(z) to be the branch
where the argument of z is chosen in the interval [0,2π[.
(2) Let f(z) = zz where we use the branch of the power
function corresponding to the principal argument. Where is f(z)
analytic and what is its derivative?
Homework 6: due Friday February 24
Section 40: 1abc,4
Section 42: 2,3,4 (note that problem 4 gives an easier method of
evaluating real integrals that would otherwise require
integration by parts)
Section 46: 3,6,10
Section 47: 2,4,5
Section 49: 5
Homework 7: due Friday March 10
Section 53: 4,6
Section 57: 1acd,2,3,7
Section 59: 1,2,4
Homework 8: due Friday March 17
Section 65: 3,6
Section 68: 4,10
Section 72: 3,6
Section 73: 1,6