| Instructor/TA | Office | Office hour | |
| Dr. Chi Li | Wednesday 10am-12pm | chi.li@rutgers.edu |
| Reference Books | Canvas | Policies | Services |
| Textbook: | Complex Analysis; Elias M.Stein & Rami Shakarchi. Princeton Lectures in Analysis II. |
| Grading: |
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Week |
Sections |
Notes | Homework |
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Week 1: 9/2-9/6 |
Complex numbers Holomorphic functions Power series |
I : 2, 3, 7, 9, 10, 13 I : 14, 16(a)-(c), 17, 19, 23 |
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Week 2: 9/9-9/13 |
Integration along curves Goursat's Theorem Primitives, Cauchy's theorem |
II : 1, 3, 4, 5, 7, 8, 14 |
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Week 3: 9/16-9/20 |
Evaluation of integrals Cauchy's integral formulas Morera's Theorem |
II: 9, 11, 12, 15 II: Problem 1 III: 1 |
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Week 4: 9/23-9/27 |
Sequences of holomorphic functions Holomorphic functions defined in terms of integrals Schwarz reflection principle |
III: 2, 4, 5, 7, 10, 12, 13 III Problem 3 |
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Week 5: 9/30-10/4 |
Zeros, poles Residue formula Singularities and meromorphic functions |
III: 6, 9, 14, 15(a), 15(d), 16(a), 19, 21(b) | |
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Week 6: 10/7-10/1 |
Argument principle Homotopies and simply connected domains Complex logarithm |
III: : 15(c), 17(a), 17(b), Problem 2 VIII: 1, 4, 5 |
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Week 7: 10/14-10/18 |
Fourier series and harmonic functions Conformal equivalence |
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Week 8: 10/21-10/25 |
Dirichlet problem Midterm |
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Week 9: 10/28-11/1 |
Schwarz lemma Automorphisms of the disc/upper half-plane Riemann mapping theorem |
Due on November 4
VIII: 10, 11, 12, 13, 14, 15 |
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Week 10: 11/4-11/8 |
Montel's theorem Proof of Riemann mapping theorem |
Due on November 11
VIII: 16, 20 VIII Problems: 2, 3 |
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Week 11: 11/11-11/15 |
Conformal mappings onto polygons, Examples Schwartz-Christoffel integral |
Due on November 18
VIII: 20, 21, 22, 23 VIII Problems: 4 |
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Week 12: 11/18-11/22 |
Entire functions, Jensen's formula Functions of finite order |
Due on November 25
V: 1, 2, 6, 8, 9, 10 |
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Week 13: 11/25-11/29 |
Weierstrass and Hadamard Infinite products 11/28-12/1: Thanksgiving Recess |
Due on December 5
V: 11, 13, 15 VI: 1, 3, 10, 14, 15, 16 |
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Week 14: 12/2-12/6 |
Gamma function Zeta function |
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Week 15: 12/9-12/13 |
Review
Classes end on 12/11 Reading Days (12/12-12/13) |
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Week 16: 12/16-12/20 |
Final Exam |
There are weekly homework due on Thursday's lectures (except for the first week). No late homeworks. The lowest two homework scores will be dropped.
All students in the course are expected to be familiar with and abide by the academic integrity policy. Violations of the policy are taken very seriously.
Rutgers is fully committed to compliance with the American with Disabilities Act; policies and procedures are indicated at http://ods.rutgers.edu/
Students who wish to request special accommodations must present a Letter of Accommodations to the instructor as early in the term as possible (see https://ods.rutgers.edu/letter-accommodation )
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