COMPLEX ANALYSIS – AUTUMN TERM 2020
COURSE INFORMATION

Forms of instruction.
• The course will be given mainly as a series of fourteen lectures – see the schedule below.
The lectures will be given face-to-face if possible, but may also be moved online if thesituation so demands.
• There will be three online tutorial sessions, on the 14th November, 26th December, and23rd January. Additionally, individual consultation is offered on demand.
• Video recordings of the lectures, and lecture notes, will be available for those students
who cannot attend in person.
Preliminary schedule.
DateTopicSection
1 5th OctoberIntroduction, complex numbers
1.1, 1.2
2 12th October
Elementary functions, I
1.3
3 19th October
Limits and continuity, I
1.4
4 26th October
Limits and continuity, II
1.4
5 2nd November
Analytic functions, the Cauchy–Riemann equations 1.5
6 9th November
Derivatives of elementary functions
1.6
7 16th NovemberLine integrals
2.1
8 30th November
Cauchy’s theorem, I
2.3
9 7th December
Cauchy’s theorem, II
2.3
10 14th December
Cauchy’s integral formula, I
2.4
11 21st December
Cauchy’s integral formula, II
2.4
12 18th January
Series, residue calculus, ICh 3, 4
13 25th January
Series, residue calculus, IICh 3, 4
14 1st February
Review
8th February
Final exam
“Section” refers to the sections in the textbook by Marsden and Hoffman (see below).
Times and venues.
• The lectures take place on Mondays, 16:30–18:00 in room C13 in the Liberal Arts andSciences main building. If the university alert level changes, the lectures may be replacedby some kind of online instruction, depending on the circumstances.
• There will be three online tutorial sessions, 16:30–18:00 on Saturday the14th November, 26th December, and 23rd January.
• Individual consultation (online or face-to-face) is offered on demand. The participantsof the course are welcome – and encouraged – to contact the instructor individually forappointments.
Examination. The examination consists of homework and a final exam.
• The final exam is held on Monday the 8th February. If university regulations allow it,
it will be given as a face-to-face examination on campus. If not, the exam may be given
online or in some different form.
• Homework: There will be a number of homework assignments during the course. Collaboration in solving the homework is encouraged, but each participating student must
submit written solutions individually. Students should be prepared to explain theirsolution to the teacher on demand.

Grading. A total score (0–100 %) is calculated as the weighted average of the scores obtainedon the homework (25 %) and the final exam (75 %). The final grade is determined by the total
score, as follows:
F : 0–59 %, C : 60–69 %, B : 70–79 %, A: 80–89 %, S : 90–100 %.
Course withdrawal. Any student who does not participate in the final exam will receive thegrade absent. It is not necessary to submit a course withdrawal request form.
Recommended textbooks.
• E. Freitag and R. Busam: Complex Analysis. Springer-Verlag, Berlin, 2005.
• J. E. Marsden and M. J. Hoffman: Basic Complex Analysis. Third edition, W. H. Freeman and Company, New York, 1999.
Repeat exam. There will be a repeat examination of the course during the winter vacation.
Under normal circumstances, it takes place in late Febrary or early March, but the details forthis year are, due to the pandemic, uncertain.
Contact. Erik Darpö
Office:Science Building A, office no A-331
E-mail:darpo@math.nagoya-u.ac.jp
Web page: http://www.math.nagoya-u.ac.jp/~darpo
Telephone: 052-789-5612

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