This is a first semester graduate course in functions of one complex
variable. Topics to be covered include the Cauchy-Riemann equations, Cauchy
Integral Formula, Liouville theorem, meromorphic functions, residues, normal
families and Montel's Theorem, Riemann mapping theorem, harmonic functions,
Poisson Integral Formula, subharmonic functions, Dirichlet problem, Weierstrass
products, Mittag-Leffler Theorem, Blaschke products, elliptic functions.
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Instructor: |
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TA: |
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Time: |
MW 1:30-2:45 |
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Classroom: |
Krieger 308 |
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Text: |
Greene &
Krantz, Function Theory of One Complex Variable, Third Edition |
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Prerequisite: |
110.405 or equivalent |
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Grading: |
Grades will be based on weekly homework assignments, a midterm exam, and an open-book final exam. |
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Syllabus: |
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week |
beginning |
reading |
assignment (due the following Monday) |
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1. |
Jan. 26 |
(review Chapter
1) |
Ch. 1: 16, 17,
36, 42, 43 |
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2. |
Feb. 2 |
3.1-3.4 |
Ch. 3: 10, 17, 19, 21, 23, 32, 39 |
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3. |
Feb. 9 |
3.5, 3.6, 4.1-4.4 |
Ch. 3: 9, 38, 42,
44 |
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4. |
Feb. 16 |
4.5, 4.6, 4.7, 5.1 |
Ch. 4: 30, 31, 33abc, 34bdh, 40, 50, 59, 60 |
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5. |
Feb. 23 |
5.2, 5.3, 5.4 |
Ch. 5: 2, 3, 6, 7, 10acf, 13*, 16 |
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6. |
Mar. 2 |
5.5, 6.1, 6.2 |
Ch. 6: 1, 6, 8, 26-29 |
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7. |
Mar. 9 |
midterm,
Monday, Mar. 9 |
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Mar. 16 |
Spring Break |
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8. |
Mar. 23 |
6.4, 6.6, 6.7 |
Ch. 6: 12, 14, 17, 18, 19, 24 |
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9. |
Mar. 30 |
7.1-7.3 |
Ch. 7: 1, 2, 10, 12, 14 |
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10. |
Apr. 6 |
7.4-7.6 |
Ch. 7: 18b, 19, 20, 23, 30 |
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11. |
Apr. 13 |
7.7, 7.8 lecture notes |
Ch. 7: 41, 46, 50, 69 |
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12. |
Apr. 20 |
8.1-8.3 (omit 8.3.7 and 8.3.8) |
Ch. 8: 3, 5, 10, 12, 15 |
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13. |
Apr. 27 |
9.1, 10.6 |
open-book final, Thursday, May 7, 2:00-5:00 |
*optional
Last updated 3/22/09