Math-185 Complex Analysis, Fall 2018 Section 6

Lectures: Tuesday&Thursday 11:00AM-12:30PM (Berkeley Time) at Dwinelle 182

Professor: Semeon Artamonov

Textbook: T. W. Gamelin "Complex Analysis" (ISBN 978-0387-95069-3)

Office Hours: Wednesday 10:00AM-11:00AM, Thursday 1:00-3:00 PM at 1055 Evans Hall


GSI: (Aug. 22-Aug. 31) Nick Ryder 12-2PM MWF & 3:30PM-5:30PM TuTh in Evans 961
(From Sep. 1) Benjamin Filippenko 3:00PM-5:00PM in Evans 961 (everyday)

Homework Assignments

Homework problems are from the Textbook unless specified otherwise.

Reading Assignments

Thursday, August 23 Complex Numbers and Polar Representation Chapter I, Sec. 1-2
Tuesday, August 28 Stereographic projection, Exp and Log Chapter I, Sec. 3,5,6
Thursday, August 30 Limits, Continuity, and Analytic Functions Chapter II, Sec.1-2
Tuesday, September 4 Complex Derivatives and Cauchy-Riemann Equations Chapter II, Sec. 2-3
Thursday, September 6 Inverse Mappings and Jacobian Chapter II, Sec. 4
Tuesday, September 11 Harmonic Functions and Conformal Mappings Chapter II, Sec. 5-6
Thursday, September 13 Fractional Linear Transformations Chapter II, Sec. 7
Tuesday, September 18 Midterm I
Thursday, September 20 Line Integrals and Green's Theorem Chapter III, Sec. 1-2
Tuesday, September 25 Conjugates, Mean Value Property, Maximum Principle Chapter III, Sec. 3-5
Thursday, September 27 Complex Line Integrals and Fundamental Theorem of Calculus Chapter IV, Sec. 1-2
Tuesday, October 2 Cauchy's Theorem and Cauchy's Integral Formula Chapter IV, Sec. 3-4
Thursday, October 4 Liouville's Theorem and Morera's Theorem Chapter IV, Sec. 5-6
Tuesday, October 9 Complex Series and Sequences, Series of Complex Functions Chapter V, Sec. 1-2
Thursday, October 11 Power Series and Power Series Expansions of Analytic Functions Chapter V, Sec. 3-4
Tuesday, October 16 Power Series Expansions (continued) Chapter V, Sec. 4-5
Thursday, October 18 Manipulation of Power Series and Zeros of an Analytic Function Chapter V, Sec. 6-7
Tuesday, October 23 Laurent Series and Isolated Singularities Chapter VI, Sec. 1-2
Thursday, October 25 Midterm II
Tuesday, October 30 Isolated Singularities (continued) Chapter VI, Sec. 2-3
Thursday, November 1 Partial Fractions Decomposition Chapter VI, Sec. 4
Tuesday, November 6 The Residue Theorem, Integrals of Rational Functions Chapter VII, Sec. 1-2
Thursday, November 8 Integrals of Trigonometric Functions, Integrals with Branch Points Chapter VII, Sec. 3-4
Tuesday, November 13 The Argument Principle and Rouche's Theorem Chapter VIII, Sec. 1-2
Thursday, November 15 Hurwitz's Theorem, Open Mapping and Inverse Function Theorem Chapter VIII, Sec. 3-4
Tuesday, November 20 Class cancelled due to weather
Thursday, November 22 No class, Happy Thanksgiving!
Tuesday, November 27 The Schwarz Lemma and Conformal Self-Maps of the Unit Disc Chapter IX, Sec. 1-2
Thursday, November 29 The Riemann Mapping Theorem Chapter XI, Sec. 1-2