Tentative Complex Analysis Syllabus

Jan. 5: Course outline, the complex numbers, ch. 1
Jan. 7: Extended Complex Plane and stereographic projection, ch. 2
Jan. 9: Circles and lines in the complex plane, ch. 2

Jan. 12: Mobius Transformations, ch. 2
Jan. 14: Open sets, compactness, boundedness, ch. 3; GROUP HW 1 DUE (in class, 9-10 pm review)
Jan. 16: Convexity and connectedness, ch. 3, INDIVIDUAL HW 1 DUE

Jan. 19: Limits and continuity, ch. 3
Jan. 21: Paths in C, ch. 4
Jan. 23: Holomorphic functions, ch. 5

Jan. 26: Complex series and power series, ch. 6
Jan. 28: Complex series and power series, ch. 6, GROUP HW 2 DUE (in class, 9-10 pm review)
Jan. 30: Examples of holomorphic functions, ch. 7, INDIVIDUAL HW 2 DUE

Feb. 2: Multifunctions, ch. 9
Feb. 4: Integration in the plane, ch. 10
Feb. 6: Cauchy’s Theorem, ch. 11

Feb. 9: Cauchy's Theorem, ch. 11(-12?), GROUP HW 3 DUE (in class, 9-10 pm review)
Feb. 11: Cauchy’s Formulae, ch. 13, INDIVIDUAL HW 3 DUE
Feb. 13: MIDTERM READING PERIOD

Feb. 16: Individual homework presentations and discussion
Feb. 18: Power series representation, ch. 14
Feb. 20: Power series representations, ch. 14

Feb. 23: Zeros of holomorphic functions, ch. 15
Feb. 25: Catch up/ discussion/ group homework presentations, GROUP HW 4 DUE
Feb. 27: Singularities, ch. 17, INDIVIDUAL HW 4 DUE

Mar. 1: DEAN’S DAY
Mar. 3: Singularities, ch. 17
Mar. 5: Cauchy's residue theorem, ch. 18

Mar. 8: Contour integration, ch. 19, possibly examples from 20
Mar. 10: Catch up/ discussion/ group homework presentations, GROUP HW 5 DUE
Mar. 12: Individual homework presentations and discussion, INDIVIDUAL HW 5 DUE

Last updated January 5, 2004

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