.. Complex Analysis Exams documentation master file, created by sphinx-quickstart on Tue Mar 26 10:16:58 2019. You can adapt this file completely to your liking, but it should at least contain the root `toctree` directive. Complex Analysis Exams ====================== These exams were taken by graduate students in mathematics at the `University of Hawaii at Manoa `__. .. toctree:: :maxdepth: 1 1989Apr.rst 1990Mar23.rst 1991Nov21.rst 1995Apr10.rst 2001Nov26.rst 2004Apr19.rst 2006Nov13.rst 2007Apr16.rst 2007Nov16.rst Appendices and Indices ---------------------- .. toctree:: :maxdepth: 1 appendix.rst refs.rst acknowledgement.rst * :ref:`genindex` * :ref:`search` .. * :ref:`modindex` ----------------------------------- .. container:: toggle .. container:: header **Topics.** Expand to see a list of some topics covered on the exams. + the complex derivative + the Cauchy-Riemann equations + Cauchy's theorems + the calculus of residues with applications to definite integrals + infinite series + the classification of isolated singularities + the definition of elementary functions + mapping propertes of fractional linear transformations and other elementary functions + approximation by rational functions + normal families + the Riemann mapping theorem + zeros of holomorphic functions ------------------------------------------ **References.**