This is a mathematically rigorous course and most statements will come with complete proofs. Topics covered will include properties of complex numbers, analytic functions with examples, contour integrals, the Cauchy integral formula, the fundamental theorem of algebra, power series and Laurent series, residues and poles with applications, conformal mappings with applications, and other topics as time permits.

• Text: Complex Variables and Applications by Brown and Churchill, Stony Brook (ninth) Edition. McGraw-Hill.
• Syllabus and Schedule: Material to be covered, schedule of exams, homework assignments.
• Homework: will be collected at the beginning of the first class each week.
• Exams: there will be a midterm and a final examination.
• Grades: will be based on a weighted average: Final 50%, Midterm 30%, Homework 20%.