Reading List
MATH 6300, Fall 2005


Reading List has been updated to include material assigned on

December 8, 2005

Textbooks

  • Ahlfors, Complex Analysis:  nice standard graduate textbook on complex analysis.  Theoretically inclined (analysis and algebra).
  • Ablowitz and Fokas, Complex Analysis:  advanced applied mathematical treatment of complex analysis.
  • Dettman, Applied Complex Variables:  a relatively inexpensive textbook with a concrete, application-oriented style
  • All textbooks are optional.   I may suggest readings in one or the other during the lectures, but many topics can be found in all three texts.  For those instances in which I cover a topic not treated in all the books, I'll have the relevant material scanned into a PDF file and posted here.  So you should have at least one graduate level complex analysis text, but you can choose the one (or several) that suit your taste.

    Readings to complement the lectures and homework will be listed here, organized by topic. Dates indicate the class by which you should have read the indicated material.   Some readings may be announced here before they are announced in class, in case you want to read ahead.   Sometimes, particularly if I am traveling, you may find some references posted at the library class reserves before they are linked here.

    I am still trying to figure out how to link directly from this web page to the class reserve readings, but for now you can go directly to the library website and access them that way.


    Complex Numbers, Arithmetic, Algebra, and Basic Geometry

    Stereographic Projection

    Functions of a Single Complex Variable

    Linear Fractional Transformations

    Analytic Functions

    Multi-valued Functions, Branch Cuts, and Riemann Surfaces

    Integration in the Complex Plane

    Taylor Series and Laurent Series

    Singularities

    Mittag-Leffler Expansion and Weierstrass Product Expansion

    Residue Theory of Integration

    Principle of the Argument and Rouche's Theorem

    Series Solutions of Ordinary Differential Equations

    Complex-Valued Functions Defined Through Integrals

    Conformal Mapping

    Complex Variable Techniques in Fluid Mechanics

    Analytic Continuation