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 problems are from the Textbook unless specified otherwise.
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 |