math185-s23:start
Math 185: Complex Analysis
UC Berkeley, Spring 2023, Section 5. Course Number: 23829
Lecture: MWF 10:00A-10:59A at Etcheverry 3107
Final Exam: Tue, May 9 • 3:00P - 6:00P • Etcheverry 3107
Instructor: Peng Zhou,
pzhou.math@berkeley.edu
Office hour: 753 Evans Hall, MWF 11-12,
GSI
Magda Hlavacek, mhlava@math.berkeley.edu
Office hour:1061 Evans Hall, M-F: 1-3pm
Syllabus
- Stein-Shakarchi's first 3 chapters + additional topics if time allows
- Grading Policy: 40% homework, two midterms 20%, final 40%. (You can drop one midterm and weighing final by 50%).
- two lowest homework will be dropped
References
- [S] Stein-Shakarchi, Complex Analayis
- [A] Ahlfors: Complex analysis. An introduction to the theory of analytic functions of one complex variable
- [G] Gamelin: Complex Analysis (Undergraduate Text in Math) springer-link
Links
- Discord Discussion, informal place to ask questions.
- Gradescope: Entry Code 8NZ5WW
- Zoom Link Lectures will be recorded and posted
- Students Homepages A place where you can share your lectures notes, and homework solutions (after the due date), so that other people can benefit.
Resources
- Richard Borcherds's youtube lectures
Journal
| Lecture # | Date | Reading | Content | Video |
| Lecture 1 | Jan 18 | [S] 1.1.1 [A] 1.2 | Overview, and review of complex number | video |
| Lecture 2 | Jan 20 | [S] 1.1.3, 1.2.2 | Review of topology | video |
| Lecture 3 | Jan 23 | [S] 1.2.2 | Holomorphic Functions and Examples | note, video |
| Lecture 4 | Jan 25 | [G]1.4 - 1.8, [S] 1.2.3 | More examples and Series | Borcherds,video,note |
| Lecture 5 | Jan 27 | [S] 1.3 | Contour Integral | video note |
| Lecture 6 | Jan 30 | [S] 2.1 | Goursat's Theorem | video |
| Lecture 7 | Feb 1 | [S] 2.2, 2.3 | Cauchy’s theorem in a disc | video |
| Lecture 8 | Feb 3 | [S] 2.3, 2.4 | Some Integrals Examples | video |
| Lecture 9 | Feb 6 | [S] 2.4, | Existence of Taylor expansion. Liouville Theorem | video |
| Lecture 10 | Feb 8 | [S] 2.5 | Uniqueness of extension, Morera Theorem | video |
| Lecture 11 | Feb 10 | [S] 2.5, 3.1 | Schwarz reflection, Runge Approximation. Zero and Poles | video |
| Lecture 12 | Feb 13 | [S] 3.2 | more examples on Residue Formula | video |
| Lecture 13 | Feb 15 | [S] 3.3 | Classification of Singularities, Riemann sphere | video |
| Lecture 14 | Feb 17 | midterm 1 | Review for Midterm 1, solution | past version, sol'n |
| no class | Feb 20 | |||
| Lecture 15 | Feb 22 | [S] 3.4 | Argument Principle | video |
| Lecture 16 | Feb 24 | [S] 3.4 | Rouché Thm and Open mapping thm | video |
| Lecture 17 | Feb 27 | [S] 3.7, 4.1 | Mean Value Thm. Fourier Transform | video |
| Lecture 18 | Mar 1 | [S] 4.2 | Fourier Transform | video |
| Lecture 19 | Mar 3 | [S] 4.3 | Poisson summation, Thm 4.3.1 | video |
| Lecture 20 | Mar 6 | [S] 4.3 | Paley-Wiener | video |
| Lecture 21 | Mar 8 | [S] 5.1, 5.2 | Jensen's Formula | video |
| Lecture 22 | Mar 10 | [S] 5.2, | Growth Order | video |
| Lecture 23 | Mar 13 | [S] 5.3 | Infinite Product | video |
| Lecture 24 | Mar 15 | [S] 6.1 | Gamma function | video |
| Lecture 25 | Mar 17 | [S] 6.1 | Gamma function | video |
| Lecture 26 | Mar 20 | [S] 6.1 | Finishing up Gamma function | video |
| Lecture 27 | Mar 22 | Review | video | |
| Lecture 28 | Mar 24 | midterm 2 | review and sample problems | solution |
| no class | Mar 27 | |||
| no class | Mar 29 | |||
| no class | Mar 31 | |||
| Lecture 29 | Apr 3 | [G] 9.1 | Schwarz Lemma. $Aut(\mathbb{D})$. | video |
| Lecture 30 | Apr 5 | [G] 9.2, 9.3 | Pick's Lemma, Hyperbolic Geom | video |
| Lecture 31 | Apr 7 | [G] 9.3 | Hyperbolic Geom | video |
| Lecture 32 | Apr 10 | [G] 11.1 | mappings to unit disk and upper half-plane | video |
| Lecture 33 | Apr 12 | [G] 11.2, 11.3 | Riemann mapping | video |
| Lecture 34 | Apr 14 | [G] 11.3 | The Schwarz-Christoffel Formula | video |
| Lecture 35 | Apr 17 | [S] Ch 8.4, Ch9.1 | Elliptic Integral and Doubly periodic function | video |
| Lecture 36 | Apr 19 | [S] 9.1.2 | Weierstrass P-function | video |
| Lecture 37 | Apr 21 | [S] 9.1 | more on Weierstrass P-function | video |
| Lecture 38 | Apr 24 | [S] 9.2 | Eisenstein Series | video |
| Lecture 39 | Apr 26 | Review 1 | video | |
| Lecture 40 | Apr 28 | Review 2 | video | |
| Final | May 9th | solution |
Final Zoom Office Hour: May 6th, 9:30PM.
Homeworks
| HW # | Due Date | Problems | Solutions |
| HW 1 | Due Jan 23 8pm | Stein Ch 1 Ex: 1,2,3,7,8 | solution |
| HW 2 | Due Jan 30 8pm | Stein Ch 1 Ex: 10, 11, 13, 15, 16(a,c,e) | solution |
| HW 3 | Due Feb 07 8pm | Ch 1: 25, Ch2: 1,2,3,4 | solution, errata |
| HW 4 | Due Feb 13 8pm | Stein Ch2, 6,7,8,10,12 | solution |
| HW 5 | Due Feb 22 8pm | Stein Ch3, 1,2,3,7, hw5.5 | solution |
| HW 6 | Due Mar 1 8pm | Stein Ch3, 9, 12, 16, hw6 #4,#5 | solution |
| HW 7 | Due Mar 8 8pm | Stein Ch4, 3, 4, 6, 8, 9(a) | solution |
| HW 8 | Due Mar 17 8pm | [G] p356 Ex 1,10,14 [S] Ch5 Ex 3, 4(a) | solution |
| HW 9 | Due Mar 27 8pm | [G] p356 Ex 15, 16(a),(b) [G]p360 2, 5 | solution |
| HW 10 | Due Apr 14 8pm | [G] Ch IX.1 #2,#3, IX.2 #2, #3, #4 | solution |
| HW 11 | Due Apr 19 8pm | [G] Ch XI.1 #1,3,5,7,8 | solution |
| HW 12 | Due Apr 28 8pm | [S] p278 #2, #4 and one more | solution |
math185-s23/start.txt · Last modified: 2023/05/16 16:12 by pzhou
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