You may check the exam out at any time for a 24 hour period. All exams should be don by Saturday May 13.
Sign the front of the exam acknowledging the conditions for taking the midterm as a take-home exam.
Linear fractional transformations
Hand in starred exercises.
Do exercises on pages 35, 48, and 53.
Do exercises on pages 68, 73, and 78.
There was an oversight on my part; do exercises on page 59 as well, and hand in #8 by Tuesday.
Do exercises on pages 89, 94, 96, 99, 103, 107, 110. Hand in starred ones.
Do exercises on pages 115, 120, 128, 133. Hand in starred ones.
Do exercises on page 142. Hand in starred ones.
Do exercises on page 153, 162 (and 171 depending on how much we cover in class by Tuesday 3/7) . Hand in starred ones.
Do exercises on page 171 181, 189, 198. Hand in starred ones.
Do exercises on page 212, 218, 233. Hand in starred ones.
Exercise: Show that the principal part of the Laurent expansion of a function f(z) at a point "a", is a function analytic on the whole complex plane except at "a".
Do exercises on page 238, 244. Do exercises 2, 4*, 6* on page 257. Hand in starred ones.
Do exercises on page 265, 276, 280, 286. Hand in starred ones.
Read the examples in section 82. Do exercises on page 296, and the supplementary problem at the bottom of the page. Hand in starred ones.
Do exercises on pages 305, 312, 316, 322, 328. Hand in starred ones.
Extra problems:
(1) Show that if an analytic function f:D--->C is 1-1 then its derivative f '(z) is nonzero for any z in D.
(2) Show that for any nonconstant analytic function f:D--->C, the image of an open set is open.
(3) Show that any linear fractional transformation that maps the unit
disk U to U and a given point "a" to 0, must be of the form given in class.
Do exercises on pages 350: 2*, 5*, 6*. Hand in starred ones.
1. Problems on infinite products (Saks&Zygmund)
2. Problems on zeores of polynomials (Saks&Zygmund)
3. Problems on integration (Saks&Zygmund)
4. Complete the proof of the lemma in section 50 by
doing exercises 7(b) in section 24