• Complex Analysis
    • Department of Mathematics
    • Credit. 4
    • MA214
    • Enroll
    • WILL BEGIN
    • Fall , 2015
    • 2600
    • Course Description:
    • ( Exchange Programme )
    • This course is an introduction to the theory of complex valued functions of a complex variable. Fundamental ideas and rigorous proofs will be emphasized. Topics to be covered include (but not limited to): complex numbers, analytic functions, maximum principle, Cauchy’s theorem, Liouville’s theorem, power series, isolated singularities, residues, Rouche’s theorem, Schwarz lemma, Poisson integral and the Riemann mapping theorem.
    • Course Syllabus:
    • Students are expected to understand the classical theory of complex analysis from the analytic, algebraic and geometric point of view.
    • Schedule:
    • Topics/ Credit hours / Teaching methodology / Tasks / Intended learning outcomes / Assessment methods

      1.Introduction, I.1-I.3/4 Credit hours /lecture/homework
      2.I.4-I.8/4 Credit hours /lecture/homework
      3.II.1-II.4, Goursat’s Thm (IV.7) and d-bar (IV.8)/4 Credit hours /lecture/homework
      4.II.5-II.7, GL(2,C), III.1-III.2, differential forms/4 Credit hours /lecture/homework
      5.III.3-III.5, IV.1/4 Credit hours /lecture/homework
      6.IV.2-IV.5/4 Credit hours /lecture/homework
      7.IV.6-IV.8, V.1-V.2/4 Credit hours /lecture/homework
      8.V.3-V.6/4 Credit hours /lecture/homework
      9.V.7-V.8, review for midterm/4 Credit hours /lecture/homework
      10.Midterm, VI.1-VI.2/4 Credit hours /lecture/homework/midterm
      11.VI.3-VI.4, VII.1-VII.2/4 Credit hours /lecture/homework
      12.VII.3-VII.5, VIII.1/4 Credit hours /lecture/homework
      13.VIII.2-VIII.5/4 Credit hours /lecture/homework
      14.VIII.6, IX.1-IX.3/4 Credit hours /lecture/homework
      15.X.1-X.2, XI.1-XI.2/4 Credit hours /lecture/homework
      16.Wrap up, final review/4 Credit hours /lecture/homework/final
  • Reading list
  • Other Materials
  • Discussion
  • Homework download/submit
    • Rong Feng
    • Associate Professor
    • Read more
    • Male
    • E-mail:
    • frong@sjtu.edu.cn
    • Profile
    • I am currently a Special Researcher in the Department of Mathematics at Shanghai Jiao Tong University. I obtained my Ph.D. degree from University of Michigan in 2007. After completing a postdoc position at Syracuse University, I joined SJTU in 2009. My research interests are in Several Complex Variables, Complex Dynamics, Complex Geometry, etc.
  • Prerequisite Course:

    Mathematical Analysis

  • Textbooks:

    “Complex Analysis”, by T.W. Gamelin
  • Grading:

    25%/Homework
    35%/ Midterm
    40%/Final
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