MTH 562
Complex Function Theory

TuTh 5:00-6:15 PM
Tyler 109

Instructor    Araceli Bonifant
Office: Tyler Hall 217
Phone: 4-4394
Email: bonifant@math.uri.edu

Office Hours: By appointment.

Textbook: Functions of One Complex Variable
John B. Conway (Springer, Second Ed.)
ISBN-10: 0387903283; ISBN-13: 978-0387903286

We shall cover chapters I--V of the text, and sections 1,2 of VI if time permits:

• The complex number system (the complex plane, roots of complex numbers, the extended plane and stereographic projection)
• Metric Spaces and the topology of C (compactness, continuity and uniform convergence)
• Elementary properties of analytic functions (power series, analytic functions, Cauchy Riemann Equations, branches of the logarithm, linear fractional transformations, conformal functions)
• Complex integration (Riemann Stieltjes integrals, zeros of analytic functions, Liouville's Theorem, The Fundamental Theorem of Algebra, the index of a closed curve, Cauchy's theorem, the open mapping theorem, Goursat's theorem)<\li>
• Singularities (Laurent expansions, classification of singularities, Casorati-Weierstrass Theorem, residues, the argument principle, Rouche's Theorem)
• The Maximum Modulus Theorem and Schwarz's lemma.
• We shall develop the theory of complex functions in a mathematically rigorous way.

Evaluation Policy:

• Homeworks             50%
• Midterm Exam        25 %
• Final Exam              25 %

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