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    Wesleyan Complex Analysis Preliminary Examination, June 2013

    SRC-WESLEYAN-CA-JUNE-2013

    Area
    Complex Analysis
    Status
    draft
    Source

    12 problems.

    1. Define analyticity on an open set — Theorems and Definitions, item 1
    2. State Cauchy’s Integral Formula — Theorems and Definitions, item 2
    3. State the Residue Theorem — Theorems and Definitions, item 3
    4. Define an essential singularity — Theorems and Definitions, item 4
    5. Define local uniform convergence — Theorems and Definitions, item 5
    6. Classify three singularities and find their residues — Problems, problem 1
    7. Three contour and winding-number calculations — Problems, problem 2
    8. An entire square root forces constancy — as extracted — Problems, problem 3
    9. Products of uniformly convergent uniformly bounded sequences — Problems, problem 4
    10. Analytic l’Hôpital rule from a derivative-ratio limit — Problems, problem 5
    11. Nonconstant entire functions have dense image — Problems, problem 6
    12. Order of the singularity of a sum of two functions with poles — Problems, problem 7