TMA 4175  COMPLEX ANALYSIS: Spring term 2022
Lecturer
 Berit Stensønes
 Email: berit.stensones@ntnu.no
 Office: Sentralbygg II Room 946
Messages
NB: Messages will appear with the newest on top
 (21/04/2022) – Solutions to project 2 have been uploaded. Check the project section.
 (20/04/2022) – The days for the oral exams have been added to the EXAM section of this page. Kindly choose the day that will work for you by Sending an Email to nicholas.aidoo@ntnu.no. A confirmation email will be sent to you afterwards.
 (18/04/2022) – NOTE: Tuesday April 19 is a vacation day, there will be classes on Thusday april 21 and Tuesday April 26. The graded project 2 will be given back in class on both those days.
 (01/04/2022) – The second project has been assigned and the deadline for submission is April 8 — All submissions should be sent to the following email address: nicholas.aidoo@ntnu.no
 (31/03/2022) – Today's lecture has been cancelled. Sorry for the late notice: Berit.
 (30/03/2022) – As part of the review, I will be doing some of the problems in the 2009 past exam in lectures: Berit
 (28/03/2022) – You can now find some past questions in the "problem" section of this course page.
 (14/03/2022) – The solutions to the first project have been added to the project section on this page. Also note that the marked scripts will be handed to you in class this week.
 (07/03/2022) – While I am grading the projects Nicholas Aidoo, the assistant in the course, will lecture about Equicontinuity and Normal families and the Arzelas theorem. Berit
 (21/02/2022) – The first project has been assigned. Check the project section on this page and click on the "project 1.pdf" to view. Remember that the deadline for submission of the assignment is February 28. Kindly send your solutions to this email address: berit.stensones@ntnu.no and make sure that you receive a confirmation email after sending.
 (07/02/2022) – Check the project section on this page to view the dates for the two upcoming projects. Please remember that these projects will contribute 40% (.i.e. 20% each) to the final grade.
 (27/01/2022) – New lecture rooms for the physical meetings have been assigned. Kindly check the lectures section on this page.
 (21/01/2022) – The dates for the oral exams have been added to the exam section on this page. I have also shared a pdf file of W. Rudin's book.
 (11/01/2022) – I have shared a pdf file of L. Ahlfor's book. Click on the link in the textbook section of the course information below to gain access.
 (10/01/2022) – There will be no lectures this week. Lectures are scheduled to commence next week on 18/01/2022 (Tuesday) and 20/01/2022 (Thursday).
 (07/01/2022) – Lectures in the first 3 weeks will be held online. However, if the current restrictions permit, subsequent lectures will be held in the classroom. See the course information below for the venue and the Zoom link to the online meetings.
Course Information
Lectures
 Tuesdays : 10:15  12:00 – (Room: S4)
 Thursdays : 10:15  12:00 – (Room: R8)
 Link to zoom meeting: https://NTNU.zoom.us/j/94811956459?pwd=cTd4ZXF5aVJUR0pDTytIMUJteEp6dz09
 Meeting ID: 985 0351 8108
 Passcode: 980082
Textbook
 Lars V. Ahlfors. Complex Analysis, 3rd edition — The book can be found on amazon.co.uk
Exam Syllabus
Material to be covered:
Topics  Mode of Instruction  

Chapter 1  The algebra of complex numbers, The geometric representation of complex numbers  selfstudy 
Section 1 of Chapter 2  Introduction to the concept of analytic functions  selfstudy 
Chapter 3  Elementary point set topology, Conformality, Linear Transformations, Elementary conformal mappings  Lecture 
Chapter 4  Fundamental theorems, Cauchy's Integral formula, Local properties of analytical functions, The general form of Cauchy's theorem, The calculus of Residues, Harmonic functions  Lecture 
Section 2 of Chapter 2  Elementary theory of power series  Lecture 
Chapter 5  Power series expansions, Partial fractions and factorization, Entire functions, The Riemann Zeta functions, Normal families  Lecture 
Sections 13 of Chapter 6  The Riemann mapping theorem, Conformal mapping of polygons, A closer look at Harmonic functions  Lecture 
Section 1 of Chapter 8  Analytic continuation  Lecture 
Problems
Projects
There will be 2 projects during the term and both will count towards the final grade.
Assigned on  Due on  Pdf file  Solutions  Contribution to final grade 


Project 1  February 21  February 28  project 1.pdf  Solutions  project 1.pdf  20% 
Project 2  April 1  April 8  Project 2.pdf  Solutions  project 2.pdf  20% 
Exam
The final exam will contribute 60% to the final grade. One must have a passing grade in each of the 3 (i.e. Project 1, Project 2, and Final exam) in order to pass the course. The final (Oral) exam is scheduled to take place from 19/05/2022 to 25/05/2022. The days for the oral exams are listed below:
Thursday  Friday  Monday  Tuesday  Wednesday 

May 19  May 20  May 23  May 24  May 25 