Due Fri, Sept 12
p.4, ex 1-4
p.7, ex 1,2
p.11, ex 1-4
p.13, ex 1,2,8
p.21, ex 1,5,6,10
p.29, ex 1, 3, 6
p.33, ex 1, 2, 3, 7
=====================================
Due Fri, Sept 19
p37, ex 2,3,4
p44, ex 1, 3a, 4, 5 
===================================
Due Fri, Sept 26
p44, ex 6,7
p56, ex 10,11 (Justification on these ex. not required).
p62, ex 1,2 (Justification not required), and 3 (do this by 
                                    difference quotient)
p.71, ex 1, 2a,b,c, 3.
p. 77, ex 1a,c,d, 2, 7
======================================
MIDTERM I on Wed. will cover up to and including
Harmonic functions (p.81)

Due Friday, Oct 3
p. 81, ex 1,2, 7, 8, 9 (to show orthogonality you can instead cite what we
                   did in class)
p. 92, ex 5, 6, 7, 8 
======================================
Due Friday, Oct 10

p.97, ex 1, 2, 3, 5, 7  (use ALL values of log, not just principal branches)
p. 100, ex 6
p. 104, ex 1, 2(find ALL values).
p. 108, ex 2, 3, 8, 14. 
p. 114, 1a,b, 2, 3.

=======================================
Due Friday, Oct 17         NOTE:You do not have to distinguish between
                            Log and ln as in the book. All complex
                            logs should be treated the same:
                            They are only defined up to multiples of
                            2\pi ni, unless specified otherwise.
p. 121, ex 2, 3, 4,       
p. 135, ex 1-7
p. 140, ex 1-7.
=======================================
Due Friday, Oct 24

p149, ex 5
p160, ex 1-4, 6, 7  You can use Cauchy's thm as presented in class:
                    \int_\partial R f(z)dz =0, where f is analytic
                    in R and on its boundry \partial R which
                    is oriented positively with respect to R.

================================================================

ATTENTION!!!  
MIDTERM II WILL BE GIVEN ON FRIDAY, NOVEMBER 7 
         (not Nov 5 or Nov 12)

THERE WILL BE NO CLASS ON WEDNESDAY, NOVEMBER 5 
        (study day and election recovery day)

==================================================================

Due Friday, Oct. 31

p. 170, ex 1-8.
p. 178, ex 1, 2, 5, 9.

+++++++++++++++++++++++++++++++++++++++++

Midterm II will cover from p.82 to p. 180 = the end of Ch 4.
    2/5 of the exam will be on interplay between harmonic and analytic
    functions.

No homework assignment for Friday, Nov 7. 

=================================================================

Due Friday, Nov 14

p. 188, ex 2, 3, 4, 9a.
p. 197, ex 2 - 8, 13.

=================================================================

Due Friday, Nov 21

p. 205, ex 1-6, 8, 10.
p. 219, ex 1-3.
ADD 
p. 220, ex 6,7
p. 225, ex 1


==================================================

No homework due on November 28

==================================================

Wednesday, Nov 26: A Special Thankgiving Program:
  `Outside In' and `Not Knot', two award winning math
   videos made at UMN about 15 years ago.

  'Outside In' is a visual `proof' of the theorem that in 3D a
   sphere can be turned inside out smoothly. Steve Smale won a
   Fields medal for proving this, but it took a while before
   anyone could figure out what the process really looked like.

  `Not Knot' is the first and only video ever made to show what it
   would be like to live in a space where light follows not
   euclidean straight lines but lines in a different, noneuclidean
   metric: a metric with a negative "curvature"---euclidean space
   has 0 curvature, the 2-sphere has positive curvature.
   It was thought for a time that the universe itself
   might be a hyperbolic space.  Some scenes are quite spectacular and
   are often copied in mathematical papers, lectures, and bar rooms
   (because of the exotic otherworldly quality of the pictures.)

=======================================================

Due Friday, December 5 : LAST HOMEWORK ASSIGNMENT

Advice: Dont wait to the last minute before doing the problems.

p. 239, ex 1a,b,c,d, 2, 3, 4
p. 243, ex 1, 2b,c
p. 248, ex 1, 2, 3, 4  (Note that the book doesnt use the factor
    1/2\pi i in defining residue)
p. 267, ex 1, 2, 4, 6
p. 275, ex 1, 5, 6
p. 290, ex 1, 2
p. 318, ex 4, 5 
p. 324, ex 5, 6, 7, 9
p. 330, ex 2(just use the fact circles/lines go to circles/lines, in
        particular, what happens to the real line? Also Mobs like all
        conformal maps, preserve orientation),  7.

=========================================================
FINAL EXAM INFO

Know about:

Using complex derivatives
Elementary conformal mapping
Mobs
Cauchy Integral Theorem and its application to
     derivatives
     deriving Tayor expansions
     residues
Harmonic functions     
Taylor series and manipulations, e.g. derivatives
Application of residues to evaluating integrals