Complex Analysis (G30, 2024)
Contact Information
Contact: Chris Bourne cbourne [at] nagoya-u.jp, bourne.christopher.jack.x7 [at] f.mail.nagoya-u.ac.jp
Office Hours: TBA
Location: Room 419, Humanities Common Facility Building (A4② on the Campus Map)
日本人の学生へのメッセージ
授業の参加は大歓迎です！また2022年4月以降入学生の場合，複素関数論（G30）は「国際理解科目」として履修単位を取ることができます．以下のリンクをご覧ください。
Deep Impact, NU-EMI Project, 単位の扱い.
Course Information
Registration code: 0063231
Time: Wednesday 10:30-12:00
Location: ILAS Building, C13
Syllabus: In preparation
Course outline: In preparation
Class Dates
October 2, 9, 16, 23, 30
November 13, 20, 27
December 4, 11, 18, 25
January 15, 22, 29
February 5
Exam Schedule:
TBA
Course Contents
Complex numbers: The complex number system, properties of the complex numbers, Cartesian and polar form.
Holomorphic functions: Complex differentiability, Cauchy–Riemann equations, analytic functions.
Complex Integrals: Line integrals, Cauchy’s theorem, Cauchy’s integral formula and Taylor expansion.
Singularities and the Residue Theorem: Laurent series, classification of singularities, the Residue Theorem and applications to real integrals.
Lecture summary notes (from 2023)
Main Reference:
S. Lang: Complex Analysis. Third edition. Springer-Verlag, 1993.
Other References:
E. M. Stein, R. Shakarchi: Complex analysis. Princeton University Press, 2003.
E. Freitag and R. Busam: Complex analysis. Second edition. Springer-Verlag, Berlin, 2009.
W. Fischer, I. Lieb: A Course in Complex Analysis: From Basic Results to Advanced Topics. Springer, 2012.
MIT OpenCourseWare lecture notes:
Complex Variables and Applications
Functions of a Complex Variable