math185-2020:start
Table of Contents
Math 185 LEC3: Introduction to Complex Analysis
UC Berkeley, Fall 2020
- Instructor: Peng Zhou
- Email: pzhou.math@berkeley.edu
- Zoom Personal Meeting ID: 881-910-2324
- Lecture: TuTh 9:30-11:00, online at online lecture room, see details here
- Office Hour: by appointment. Usually free right after class.
- GSI (for office hours), see here
Syllabus
- I will loosely follow Stein-Shakarchi's first 3 chapters, then add additional topics for the remaining time.
- Grading Policy: 50% homework, two midterms each 10%, take home final 30%.
References
- Stein-Shakarchi, Complex Analayis
- Ahlfors: Complex analysis. An introduction to the theory of analytic functions of one complex variable
- Gamelin: Complex Analysis (Undergraduate Text in Math)
- Schaum's outlines: complex variables. This is a practical book, with lots of examples of easy to intermediate levels. The PDF is available at Berkeley library.
Links
- Zoom chat channel: we also have a zoom chat channel, search for “Math 185-3: complex analysis” and join. You can contact me there.
- Online discussion Piazza. Sign up with access code “riemann”.
- Online homework / exam submission: Gradescope . entry code 982WDY
- Latex Online: https://overleaf.com. Here is a sample template file to get you started. video tutorial Passcode: c+D+B?9M
Lectures
| Date | Reading | Content | notes | video and passcode |
| Aug 27 Thu | [S] 1.1.1 [A] 1.2 | Overview of the course. Complex Numbers. | note | |
| Sep 1 Tue | [S] 1.1.3, 1.2.2 | Review of topology and Holomorphic Functions. | note | video Y^?bY700 |
| Sep 3 Thu | [S] 1.2.3 | Power Series | note | video ##cDRb5e |
| Sep 8 Tue | [S] 1.3 | Integration Along Curve | note | video vT+=b2Xi |
| Sep 10 Thu | [S] 1.3, 2.1 | Finish Ch 1. Begin Goursat's Thm | note | video ^=AhAr58 |
| Sep 15 Tue | [S] 2.1, 2.2 | Goursat, Cauchy theorem on disk | note | video $Cd@kAe0 |
| Sep 17, Thu | [S] 2.4(a), 2.3 | Cauchy Integral Formula, and Sample Calculations | note | video eA2!V7oR |
| Sep 22 Tue | [S]2.3, 2.4 | More on contour integral examples. Cauchy estimate | note | video +6%m*Hsp |
| Sep 24 Thu | [S] 2.4, 2.5.1 | Corollary to Cauchy integral Formula | note | video ZQF.q$0& |
| Sep 29 Tue | [S] 2.5 | Schwarz Reflection Principle, | note | video h3=KBA21 |
| Oct 1 Thu | Runge Approximation Theorem | note | video FWA46%k5 | |
| Oct 6 Tue | Midterm 1 ( review notes) | sol'n | stat | |
| Oct 13 Tue | [S] 3.1 | zero, poles and residues | note | video B?*MH1bG |
| Oct 15 Thu | [S] 3.2 [A] 4.2 | residues theorem, winding number | note | video @k!6@pNt |
| Oct 20 Tue | [S] 3.3 | classification of singularities | note | video f+2&L#Po |
| Oct 22 Thu | [S] 3.3, 3.4 | global meromorphic functions are rational, argument principle | note | video ih0XF3X# |
| Oct 27 Tue | [S] 3.4 | Rouche theorem, open mapping theorem | note | video 4Ox&345s |
| Oct 29 Thu | [S] 3.5 | Homotopy invariance of Contour integral | note | video ^v.S7P?Z |
| Nov 3 Tue | [S] 3.6 | Multivalued Function and Log | note | video Tt0T=D#8 |
| Nov 5 Thu | [S] 3.7, [A] 4.6 | Harmonic Functions and Summary | note | video PY+0MQ*c |
| Nov 10 Tue | Midterm 2 | stat | ||
| Nov 12 Thu | Review Midterm 2 | note | video 8#W#6Z0O | |
| Nov 17 Tue | [A] Ch5 | section 1 and 2, partial fraction, Mittag-Leffler problem | note | video 0WxX%$K7 |
| Nov 19 Thu | [A] Ch5 | section 2.1, 2.2 Infinite Product | note | video LV&5rj$6 |
| Nov 24 Tue | [A] Ch 5 | section 5, Normal Family | note | video A9Ce%=yR |
| Dec 1 Tue | [A] Ch 5 | section 5, Normal Family, Arzela-Ascoli Thm | note | video aSk5?Sb2 |
| Dec 3 Thu | [A] Ch 6.1 [S] Ch 8 | Riemann Mapping Theorem | note | video ^?a71a4M |
| Final Exam | review | Dec 15(Tue) 12:00noon - Dec 17(Thu) 12:00 noon | solution |
Homework
| HW 1 | Due 09/10 11:59pm | 2, 7, 16(a,c,e), 17, 22 | in Ch 1. | solution tex |
| HW 2 | Due 09/17 11:00pm | 10, 11, 13, 18, 25 | in Ch 1. | solution tex |
| HW 3 | Due 09/25 10:00pm | 1, 2, 4, 5, 6 | Ch 2 | solution |
| HW 4 | Due 10/2 10:00pm | 7,8,9,11,12 | Ch 2 | solution |
| HW 5 | Due 10/23 10:00pm | 1,2,3,7 and this | Ch 3 | solution |
| HW 6 | Due 10/30 10:00pm | HW 6: Meromorphic Functions | solution | |
| HW 7 | Due 11/6 10:00pm | HW 7: Rouché Theorem, Open Maps, Maximum Principle | solution | |
| HW 8 | Due 11/16(Mon) 10:00pm | 9,10,14,15,16 hint | Ch 3 | solution |
| HW 9 | Due 11/30(Mon) 10:00pm | Homework 9: Infinite Series and Product | solution |
math185-2020/start.txt · Last modified: 2023/09/06 09:55 by pzhou
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