2021 Faculty Courses School of Science Undergraduate major in Mathematics
Complex Analysis II
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Eiji Yanagida
- Class Format
- Lecture/Exercise
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-8 Mon (H137)
- Class
- -
- Course Code
- MTH.C302
- Number of credits
- 110
- Course offered
- 2021
- Offered quarter
- 2Q
- Syllabus updated
- Jul 10, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course, Complex Analysis II, is intended for students who passed Complex Analysis I or are familiar with the basics of elementary complex function theory.
At the beginning of the course, we will explain the theory of meromorphic functions and singularities. We also explain conformal mappings and present some examples of conformal mappings on domains in the complex plane. After that, we will introduce the notion of "residue". As an application of this theory, we explain the computation of integrals.
Course description and aims
By the end of this course, students will be able to:
1) understand the notion of meromorphic functions and isolated singularities.
2) understand the classification of isolated singularities.
3) compute integrals using the residue theorem.
Keywords
Meromorphic function, isolated singularity, the residue theorem, conformal mapping.
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Standard lecture course with exercise.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Meromorphic functions, the reflection principle | Details will be provided during each class session. |
| Class 2 | Recitation | Details will be provided during each class session. |
| Class 3 | Isolated singularities of meromorphic functions. Poles and residues | Details will be provided during each class session. |
| Class 4 | Recitation | Details will be provided during each class session. |
| Class 5 | Conformal mappings on plane domains | Details will be provided during each class session. |
| Class 6 | Recitation | Details will be provided during each class session. |
| Class 7 | The residue theorem, the computation of integrals | Details will be provided during each class session. |
| Class 8 | Recitation | Details will be provided during each class session. |
| Class 9 | Applications of the residue theorem and the integrals | Details will be provided during each class session. |
| Class 10 | Recitation | Details will be provided during each class session. |
| Class 11 | The argument principle | Details will be provided during each class session. |
| Class 12 | Recitation | Details will be provided during each class session. |
| Class 13 | Harmonic functions | Details will be provided during each class session. |
| Class 14 | Recitation | Details will be provided during each class session. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
An Introduction to Complex Analysis, Tomoki Kawahira, Shokabo
Reference books, course materials, etc.
To be announced
Evaluation methods and criteria
Based on Final exam and recitation
Related courses
- MTH.C301 ： Complex Analysis I
Prerequisites
Students are expected to have passed MTH.C301 ： Complex Analysis I.