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
Location: Room 419, Humanities Common Facility Building (A4② on the Campus Map)
I will also be in Rm 505 of the Mathematics Building on most Fridays.
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。
Bright, NU-EMI Project, G30科目の単位取得, 単位の扱い
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 (Somewhat final version - for now. Will still be making minor edits and changes.)
Lecture notes with coloured boxes and other formatting.
S. Lang: Complex Analysis. Third edition. Springer-Verlag, 1993.
E. M. Stein, R. Shakarchi: Complex analysis. Princeton University Press, 2003.
E. Freitag and R. Busam: Complex analysis. Second edition. Springer-Verlag, Berlin, 2009. A pdf of this text can be obtained via the Nagoya University Library or Springerlink directly.
W. Fischer, I. Lieb: A Course in Complex Analysis: From Basic Results to Advanced Topics. Springer, 2012.
Lecture notes by J. Shapiro, Princeton University.
MIT OpenCourseWare lecture notes:
Complex Variables and Applications
Functions of a Complex Variable
Online lecture 13 November (THERS account required), iPad notes from 13 November.
Homework solutions have been removed.
Homework 1, Homework 2, Homework 3, Midterm exam (solutions), Homework 4, Homework 5, Homework 6, Final exam (solutions)