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    Semester plan

    Textbook

    E. B. Saff & A. D. Snider: Fundamentals of Complex Analysis with Applications to Engineering and Science. Third edition, 2003. ISBN 0-13-907874-6. The book is sold in PF's bookstore in building 101.

    The lectures chronologically

    1. September 4. §§ 1.1 - 1.4 Complex numbers and the complex exponential.
    2. September 11. §§ 1.5 - 1.7 and 2.1 - 2.2 Powers and roots, the Riemann sphere, limits and continuity.
    3. September 18. §§ 2.3 - 2.4 and 3.1 Analytical functions, the Cauchy-Riemann equations, polynomials and rational functions.
    4. September 25. §§ 3.2 - 3.3 and 3.5 The exponential and trigonometric functions, branches of the logarithm, complex powers and inverse trigonometric functions.
    5. October 2. §§ 2.5, 3.4 and 7.1 - 7.2 and Appendix B. Harmonic functions and conformal mappings.
    6. October 9. §§ 7.3 - 7.4 to the end of Example 2 p.400. Möbius transformations.
    7. October 23. §§ 4.1 - 4.3 Complex integration.
    8. October 30. §§ 4.4a and 4.5 Cauchy's integral theorem and Cauchy's integral formula.
    9. November 6. §§ 4.5 - 4.6 Consequences of Cauchy's integral formula, including the maximum modulus principle.
    10. November 13. §§ 5.1 - 5.3 Series, Taylor series, power series.
    11. November 20. §§ 5.5-5.7 Laurent series and isolated singularities.
    12. November 27. §§ 6.1 and 6.3 Residues, the residue theorem and improper integrals.
    13. December 4. Review.

    General information, Exam requirements



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