Spring 2004–05

Ma 108c - Classical Analysis
MWF 11:00  // 151 Sloan
Michael Goldberg


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Course Description:

This course serves as an introduction to standard complex analysis. Topics to be covered include:

Complex numbers Analytic functions, Cauchy-Riemann equations Cauchy's theorem, Cauchy's integral formula, Liouville's theorem Residue theorem and argument principle Conformal mappings
Prerequisite: Ma108b or equivalent.

  • Text: There are a lot of introductory textbooks on Complex Analysis. We will use the book by Stein and Shakarmi as our primary source of material. The authors assume more than an average amount of familiarity with Real Analysis techniques, and use this to dig deeper into the subject than most other texts. The recommended text by Krantz and Greene has a more traditional exposition and also contains numerous exercises at the end of each section.

     

  • Required: Complex Analysis, by Elias M. Stein and Rami Shakarchi, Princeton University Press, 2003. ISBN: 0-691-11385-8
     

  • Recommended: Function Theory of One Complex Variable, second edition, by Krantz and Robert Greene, AMS Graduate Studies in Mathematics, 2002.
    ISBN 0-8218-2905-X

     

  • Grading: The final grade will be determined roughly on 50% of the problem sets, 20% of the midterm exam, and 30% of the final exam.
     

  • Homework Policy: You are encouraged to speak with each other and work together on the problem sets. However, everybody has to hand in their own write-up of the assignment. Late homework will be accepted only if there is a prior agreement with the instructor.
     

  • Exams: All exams will be take-home and must be entirely your own work. The only excuses for late submission of exams that will be accepted are medical (with a note from the Health Center) or personal difficulties (with a note from the Dean's Office).