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    Wesleyan Complex Analysis Preliminary Examination, July 8, 2008

    SRC-WESLEYAN-CA-SUMMER-2008

    Area
    Complex Analysis
    Status
    draft
    Source

    9 problems.

    1. Define the multiplicity of an analytic function at a point — Theorems and Definitions, item 1
    2. Define local uniform convergence — Theorems and Definitions, item 2
    3. State Liouville’s Theorem — Theorems and Definitions, item 3
    4. State Cauchy’s Integral Formula — Theorems and Definitions, item 4
    5. Laurent series of \(1/(z^2+1)^2\) about \(i\) — Problems, problem 1
    6. Two contour integrals on large circles — Problems, problem 2
    7. An analytic function attaining a positive minimum modulus is constant — Problems, problem 3
    8. Analytic l’Hôpital rule from a derivative-ratio limit — Problems, problem 4
    9. Residues of sums and products — Problems, problem 5