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math185-3:start

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.
  • 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
math185-3/start.txt · Last modified: 2021/01/01 14:58 by pzhou