Topic outline

  • General

    Cauchy's integral 1/2*pi*i times integral of f(z)/(z-z_0) along a closed contour

    Teachers

    Lecturer:
    • Kalle Kytölä


    Teaching assistants:

    • Anton Vavilov (Head TA)
    • Mikail Müftüoglu (TA)
    • Matvei Zhukov (TA)

    Practicalities
    • The lectures will be held on Mondays 12-14 and Thursdays 10-12. See the Lectures tab for more details.
    • There are five exercise groups, each with 2h/week exercise session. See the Exercises tab for more details.
    • The course discussion forum is going to be a Zulip chat https://ms-c1300-2024.zulip.aalto.fi. It will be used for announcements and discussions about the course topics, lectures, exercises, practicalities, etc., and some quizzes and polls may be held there. You can and should login with your Aalto account. The data is hosted at Aalto University servers, but the policy is to not post any sensitive information in this discussion forum; see the general rules of zulip.aalto.fi.


    Description of the course
    TBA


    Course contents and learning objectives

    Key topics of the course include:

    • the interpretation and use of complex numbers, holomorphic functions (=analytic functions), basic complex functions, complex contour integrals (=line integrals), sequences and series, Cauchy's formula and its consequences

    Upon successful completion of this course, you should . . .
    • . . . be able to make use of complex numbers in solving geometric problems
    • . . . be able to solve mapping problems in the plane
    • . . . recognize the behavior of complex functions
    • . . . be able to interpret basic properties of analytic (holomorphic and meromorphic) functions
    • . . . be able calculate real integrals by making use of complex integrals.


    Prerequisites

    A sufficient prior knowledge is a good command of:

    MS-A02XX Differential and integral calculus 2

    (The course MS-C1541 Metric Spaces would make much of the theory of complex analysis easier to understand properly, but it is not a prerequisite.)


    Exams and grading
    The course is completed by taking a final exam. For the purposes of determining the grade, the exercises done during the period III course contribute as bonus points and may thus improve the grade from the exam-only option. These additional points will be valid in each of the three exams of the academic year 2024-2025:

    • T0: Monday December 2, 2024 at 09:00-12:00
    • T01: Monday, February 17, 2025 at 13:00-16:00 
    • T02: Wednesday, June 4 at 16:30-19:30

    The final exam has 5 problems, each worth 6 points, so the course total is 30 points. For the purposes of determining the grade, the exercises can contribute up to 6 bonus points added to the final exam score.

    You are allowed to bring to the exam a handwritten memory aid sheet. The memory aid sheet must be of size A4 with text only on one side, and it must contain your name and student number in the upper right corner. You don’t need to return your memory aid sheet.