Complex Analysis : PMATH 352 : Winter 2010

Meeting times: MWF 10:30 - 11:20 in MC 2035

Office Hours: Wednesdays 4:00--5:00 or by appointment.

Textbook: R.E. Greene and S.G. Krantz,
	Function Theory of One Complex Variable,
	Graduate Studies in Mathematics, Vol. 40,
	American Mathematical Society, 3rd edition.

Alternate reference: J.B. Conway,
	Functions of One Complex Variable, 
	Graduate Texts in Mathematics , Vol. 11,
	Springer-Verlag, 2nd edition.

Grades:
	Assignments   20%
	Midterm       30%
	Final Exam    50%

Midterm date: Wednesday February 24, 4:00--5:30, in MC 4060.

Final Examination: Wednesday April 14, 12:30--3:00, in MC 4040.

Outline

	Complex numbers
	Analytic Functions
	Power series 
	Line Integrals and Cauchy's Theorem
	Some major results
	Some conformal maps
	General form of Cauchy's Theorem
	Zeros and singularities
	Integration by residues
	Riemann mapping theorem

Assignments

Assignment 1 ( the LaTeX code and figure )

Assignment 2 ( the LaTeX code )

Assignment 3 ( the LaTeX code )

Assignment 4 ( the LaTeX code and figure )

Assignment 5 ( the LaTeX code )

Assignment 6 ( the LaTeX code )

Comments and Solutions

Assignment 1 Solutions

Assignment 2 Solutions

Assignment 3 Solutions

Assignment 4 Solutions

Assignment 5 Solutions

Assignment 6 Solutions

Other things

• Convergence of power series at the boundary: Abel's Theorem.
• Video about Mobius transformations. The YouTube version is just fine for the graphics, but the QuickTime version has narration.
• Schwarz-Christoffel Transformations