Stuff that will NOT be covered in the final:
The final will be held on Tuesday March 21, 8-11 a.m, MS 5138.
One 5 x 7 index card is allowed into the exam (I'll distribute these cards
on Friday). No other notes, books, or calculators are allowed.
There are 10 questions, each of equal value. Each question has one
to three parts. Read each question carefully. If you are not
sure what is intended by the question, ask!
A sample final is provided on the class web page, together with brief solutions.
The actual final will be similar to the sample final.
The final covers almost all subjects in the course, but has an emphasis
on material covered after the second midterm (i.e. Laurent series, singularities,
residue calculus, definite integrals).
Most questions are computational. There may be one or two theoretical
Chapter 2: Properties of harmonic functions. Section 2.6.
Chapter 3: Inverse trig and inverse hyperbolic functions. Section
Chapter 4: Cauchy inequalities, Morera's theorem, Mean-value theorem, simply
connected domains, deformation of contours. Proofs of Cauchy's theorem,
integral formulae, Fundamental theorem of Algebra. Section 4.7.
Chapter 5: Anything involving uniform convergence or Section 5.4, 5.8.
Proof of existence and uniqueness of Taylor/Laurent series.
Chapter 6: Proof of Jordan's lemma, Argument principle, Rouche's theorem.
If there is a question involving material from Chapter 6.6, the contours
and branches will be provided. There will only be one part of one
question devoted to 6.7.
Chapter 7: Cross-ratios, conformal transformations, symmetry principle.