
Semester plan
Textbook
E. B. Saff & A. D. Snider: Fundamentals of Complex Analysis with Applications to Engineering and Science.
Third edition, 2003. ISBN 0139078746. The book is sold in PF's bookstore in building 101.
The lectures chronologically
 September 4. §§ 1.1  1.4 Complex numbers and the complex exponential.
 September 11. §§ 1.5  1.7 and 2.1  2.2 Powers and roots, the Riemann sphere, limits and continuity.
 September 18. §§ 2.3  2.4 and 3.1 Analytical functions, the CauchyRiemann equations, polynomials and rational functions.
 September 25. §§ 3.2  3.3 and 3.5 The exponential and trigonometric functions, branches of the logarithm, complex powers
and inverse trigonometric functions.
 October 2. §§ 2.5, 3.4 and 7.1  7.2 and Appendix B. Harmonic functions and conformal mappings.
 October 9. §§ 7.3  7.4 to the end of Example 2 p.400. Möbius transformations.
 October 23. §§ 4.1  4.3 Complex integration.
 October 30. §§ 4.4a and 4.5 Cauchy's integral theorem and Cauchy's integral formula.
 November 6. §§ 4.5  4.6 Consequences of Cauchy's integral formula, including the maximum modulus principle.
 November 13. §§ 5.1  5.3 Series, Taylor series, power series.
 November 20. §§ 5.55.7 Laurent series and isolated singularities.
 November 27. §§ 6.1 and 6.3 Residues, the residue theorem and improper integrals.
 December 4. Review.
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