Faculty of Science and Engineering

Back to List

MAT200XF（数学 / Mathematics 200）
Complex Functions

Ryo KAMIYA

Class code etc
Faculty/Graduate school Faculty of Science and Engineering
Attached documents
Year 2022
Class code H6780
Previous Class code
Previous Class title
Term 秋学期授業/Fall
Day/Period 木2/Thu.2
Class Type
Campus 小金井
Classroom name 各学部・研究科等の時間割等で確認
Grade
Credit(s)
Notes
Open Program
Open Program (Notes)
Global Open Program
Interdepartmental class taking system for Academic Achievers ○
Interdepartmental class taking system for Academic Achievers (Notes) 教員の受講許可が必要です。学習支援システムに仮登録したうえで、授業内掲示板にて許可を得ること。
Class taught by instructors with practical experience
SDGs CP
Urban Design CP
Diversity CP
Learning for the Future CP
Carbon Neutral CP
Chiyoda Campus Consortium
Category 経営システム工学科
学科専門科目

Show all

Hide All

Outline (in English)

(Course outline)
A complex function is a function that takes a complex number as a variable and returns a complex number. Differentiability is also defined for complex functions using limits, and in particular, complex functions that are differentiable at each point are called regular functions. For example, a regular function can be expanded into a power series at each point, and the behavior of the function as a whole can be determined by the value of the function near a point in the domain.
By extending the domain of a function to the world of complex numbers, the properties of the function often become clearer than if it were considered only in the world of real numbers. For example, the integrals of definite integrals of real functions, which used to be complicated and technical, can be calculated surprisingly easily by using the information of singularities in the complex domain.

In this lecture, we would like to learn the basic and important properties of complex functions, including the properties mentioned above, and to be able to understand and calculate the differential and integral of complex univariate functions.

(Learning Objectives)
(1) Understand the representation and calculation rules of complex numbers.
(2) To be able to calculate the values and limits of basic complex functions including rational, trigonometric, and exponential functions.
(3) Understand the definitions of basic terms such as
regularity, complex analyticity, complex line integral, isolated singularity, and residue.
(4) Understand important properties related to regularity (Cauchy-Riemann relation, Cauchy's integral theorem, Cauchy's integral formula, residue theorem, etc.) and be able to use them in specific settings.
(5) To be able to integrate real functions by using the residue theorem.


(Learning activities outside of classroom)
Before/after each class meeting, students will be expected to spend four
hours to understand the course content.
Students are encouraged to prepare for the textbook and solve the
exercises (or assignments) corresponding to the previous lesson.

(Grading Criteria)
Your overall grade in the class will be decided based on the following:
Short reports 30%, Term-end examination 70%.

Default language used in class

日本語 / Japanese