| 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 |
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Week 1: 9/2-9/6 |
Complex numbers Holomorphic functions |
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Week 2: 9/9-9/13 |
Power series Integration along curves |
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Week 3: 9/16-9/20 |
Goursat's Theorem Primitives, Cauchy's theorem Evaluation of integrals |
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Week 4: 9/23-9/27 |
Cauchy's integral formulas Morera's Theorem Sequences of holomorphic functions |
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Week 5: 9/30-10/4 |
Holomorphic functions defined in terms of integrals Schwarz reflection principle |
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Week 6: 10/7-10/1 |
Runge's approximation theorem Zeros, poles, residue formula |
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Week 7: 10/14-10/18 |
Singularities and meromorphic functions Argument principle |
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Week 8: 10/21-10/25 |
Homotopies and simply connected domains Midterm |
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Week 9: 10/28-11/1 |
Complex logarithm Fourier series and harmonic functions |
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Week 10: 11/4-11/8 |
Conformal equivalence Dirichlet problem |
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Week 11: 11/11-11/15 |
Schwartz lemma Automorphisms of the disc/upper half-plane |
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Week 12: 11/18-11/22 |
Riemann mapping theorem Montel's theorem |
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Week 13: 11/25-11/29 |
Proof of Riemann mapping theorem |
11/28-12/1: Thanksgiving Recess |
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Week 14: 12/2-12/6 |
Conformal mappings onto polygons, Examples Schwartz-Christoffel integral |
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Week 15: 12/9-12/13 |
Classes end on 12/11
Reading Days (12/12-12/13) |
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Week 16: 12/16-12/20 |
Final Exam |
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