Complex Analysis (G30)
Contact Information
Contact: Chris Bourne cbourne [at] nagoya-u.jp, bourne.christopher.jack.x7 [at] f.mail.nagoya-u.ac.jp
Office Hours: Tuesday 12:00–13:00, Thursday 14:00–15:00, or by appointment.
Location: Room 419, Humanities Common Facility Building (A4② on the Campus Map)
Extra time (not always guaranteed): Friday afternoon in Room 203 of the Mathematics Building.
Class Dates
October 4, 11, 18, 25 (earthquake disaster drill during lecture)
November 1, 8, 15, 17 (online tutorial, video) 22 (midterm), 29
December 6, 3, 20, 27 (online, video part 1, video part 2)
January 17, 24, 26 (online tutorial, video) 31
Exam Schedule:
Midterm: 22 November, Final: 31 January
Course Contents
Complex numbers: The complex number system, properties of the complex numbers, Cartesian and polar form. Summary notes.
Holomorphic functions: Complex differentiability, Cauchy–Riemann equations, analytic functions. Summary notes.
Complex Integrals: Line integrals, Cauchy’s theorem, Cauchy’s integral formula and Taylor expansion. Summary notes.
Singularities and the Residue Theorem: Laurent series, classification of singularities, the Residue Theorem and applications to real integrals. Summary notes.
Complete lecture summary notes.
Main Reference:
E. Freitag and R. Busam: Complex analysis. Second edition. Springer-Verlag, Berlin, 2009. ISBN 978-3-540-93982-5
The course aims to cover (at least) Chapters I-III from this text. A pdf can obtained via the Nagoya University Library or Springerlink directly.
Other References:
E. M. Stein, R. Shakarchi: Complex analysis. Princeton University Press, 2003.
S. Lang: Complex Analysis. Third edition. Springer-Verlag, 1993.
W. Fischer, I. Lieb: A Course in Complex Analysis: From Basic Results to Advanced Topics. Springer, 2012.
日本人の学生へのメッセージ
授業の参加は大歓迎です！以下のビデオをご覧ください。
Deep Impact. NU-EMI Project.
Homework
Homework solutions have been removed.
Homework 1, HW1 Solution, HW1 Solution (corrected 🙃), Homework 2, HW2 Solution, Homework 3, HW3 Solution, Midterm exam, Midterm solutions, Homework 4, HW4 Solution, Homework 5, HW5 Solution, Final exam and solutions.
Notes from the online tutorial, 17 November. Notes from the online lecture, 27 December. Notes from online tutorial, 26 January.