Only the problems with boldface numbers are to be turned in as homework. The others are suggested for practice, they are not to be turned in.
Presentation: written work should be done on one side only of 8.5''x11'' paper with smooth edges. Each problem should begin a new page.
Deadlines: papers should be turned in on Wednesday in class. Extensions may (and usually will) be granted if requested at least twenty-four hours before the due date. Late homework will not be accepted.
| Date | Reading | Topic | problems | |
| 1 | 8/30 | 1.1 | The algebra of complex numbers | 1.1: 4, 8, 12, 15, 19, 21, 22, 24, 28, 30 |
| 9/01 | 1.2 , 1.3 | The complex plane | 1.2: 6, 7dehi, 8, 14, 16, 17 1.3: 5, 7defg, 9, 10, 11,13,16, 23 |
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| 2 | 9/04 | 1.4 | The complex exponential | 1.4: 2, 4, 7, 8, 11, 16, 17, 20 |
| 9/06 | 1.5 | Powers and roots | 1.5: 5acf, 6b, 10, 11, 12, 13, 14, 15, 16, 17 | |
| 9/08 | 1.6 | Planar sets | 1.6: 1, 2 to 8, 10, 15, 18, 19, 20 | |
| 3 | 9/11 | 2.1 | Functions of a complex variable | 2.1: 1ace, 3d, 5, 6ab, 7, 8, 9, 10, 12, 13 |
| 9/13 | 2.2 | Limits and continuity | 2.2: 2, 4, 5, 6, 11de, 12, 15, 18, 22, 25bde | |
| 9/15 | 2.3 | Analyticity | 2.3: 1, 3, 4a, 8, 11efg, 12, 13, 14, 16 | |
| 4 | 9/18 | 2.4 | The Cauchy-Riemann relations | 2.4: 1, 2, 3, 4, 5, 6, 8, 12, 14 |
| 9/20 | 2.5 | Harmonic functions | 2.5: 1b, 2, 3cd, 5, 6, 8, 10, 18 (20, 21) | |
| 9/22 | Loose ends | |||
| 5 | 9/25 | 3.1 | Polynomials and rational functions | 3.1: 3c, 4, 7, 10, 12, 15ac |
| 9/27 | 3.2 | Exponential, trigonometric and hyperbolic functions | 3.2: 5de, 8, 9, 11, 18, 19, 23 | |
| 9/27 | 3.3 | The logarithmic function | 3.3: 3, 4, 5, 6, 9, 14 | |
| 6 | 10/02 | 3.5 | Complex powers | 3.5: 1ae, 3, 4, 5, 15a, 19 |
| 10/04 | 3.5 | Inverse trigonometric functions | 3.5: 11, 12 | |
| 10/06 | 4.1 | Contours | 4.1: 3, 4, 8 | |
| 7 | 10/09 | 4.2 | Contour integrals | 4.2: 5, 6a, 14 |
| 10/11 | 4.3 | Path independence | 4.3: 2, 3, 5 | |
| 10/13 | 4.4 | Cauchy's Integral Theorem | 4.4: 1, 2, 3, 5, 9, 11, 15, 18, 19 | |
| 8 | 10/18 | 4.5 | Cauchy's Integral Formula | 4.5: 1, 2, 3, 6, 8 |
| 10/20 | 4.5 | Cauchy's Integral Formula | 4.5: 10, 13, 15, 16 | |
| 9 | 10/23 | Loose ends | ||
| 10/25 | Midterm | |||
| 10/27 | 4.6 | Liouville's Theorem | 4.6: 4, 5, 7 | |
| 10 | 10/30 | 4.6 | The Maximum Modulus Principle | 4.6: 11, 13, 15 |
| 11/01 | 5.1 | Sequences and series | 5.1: 3, 4, 5, 6, 10 | |
| 11/03 | 5.1 | Sequences and series | 5.1: 16, 18, 20, 21 | |
| 11 | 11/06 | 5.3 | Power series | 5.3: 1, 6, 8 |
| 11/08 | 5.2 | Taylor series | 5.2: 1, 4, 10, 11bc, 13 | |
| 11/10 | 5.5 | Laurent series | 5.5: 6, 7ab, 9, 13 | |
| 12 | 11/13 | 5.6 | Zeroes and singularities | 5.6: 10, 17, 18 |
| 11/15 | 5.6 | Zeroes and singularities | 5.6: 1, 4, 5, 6, 12, 15 | |
| 11/17 | 5.8 | Analytic continuation | 5.8: 2, 4, 5, 8 | |
| 13 | 11/20 | Meromorphic functions, loose ends | ||
| 11/22 | Thanksgiving break | |||
| 11/24 | Thanksgiving break | |||
| 14 | 11/27 | 6.1 | The Residue Theorem | 6.1: 1adh, 2, 3beg, 5, 6, 7 |
| 11/29 | 6.x | Applications | ||
| 12/01 | 6.7 | Rouché's Theorem | 6.7: 2, 6, 10 18 | |
| 15 | 12/04 | The index | ||
| 12/06 | Riemann's $\zeta$ function: meromorphic continuation | |||
| 12/08 | Riemann's $\zeta$ function: functional equation |