2024 Faculty Courses School of Computing Undergraduate major in Mathematical and Computing Science
Complex Analysis
- Academic unit or major
- Undergraduate major in Mathematical and Computing Science
- Instructor(s)
- Shunsuke Tsuchioka / Masaaki Umehara / Zin Arai / Sakie Suzuki / Toshiaki Murofushi / Shinya Nishibata / Jin Takahashi / Shunsuke Ichiki / Takeshi Gotoda
- Class Format
- Lecture/Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Tue / 3-4 Fri
- Class
- -
- Course Code
- MCS.T232
- Number of credits
- 110
- Course offered
- 2024
- Offered quarter
- 4Q
- Syllabus updated
- Mar 17, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Complex analysis plays an important role in mathematical and computing sciences. The objective of this course is to provide the fundamentals of complex analysis. Topics include complex numbers, holomorphic functions, and the residue theorem.
Course description and aims
The students are expected to understand the fundamentals of complex analysis appeared in mathematical and computing sciences and also to be able to apply them to practical problems.
Keywords
Complex number, holomorphic function, residue theorem
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The lectures provide the fundamentals of complex analysis with recitation sessions.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Complex number | Understand the contents covered by the lecture. |
| Class 2 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
| Class 3 | Elementary function | Understand the contents covered by the lecture. |
| Class 4 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
| Class 5 | Holomorphic function | Understand the contents covered by the lecture. |
| Class 6 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
| Class 7 | Complex integration | Understand the contents covered by the lecture. |
| Class 8 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
| Class 9 | Cauchy's theorem | Understand the contents covered by the lecture. |
| Class 10 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
| Class 11 | Taylor expansion | Understand the contents covered by the lecture. |
| Class 12 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
| Class 13 | Residue theorem | Understand the contents covered by the lecture. |
| Class 14 | Recitation class is opened in accordance with lectures. | Cultivate a better understanding of lectures. |
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)
The lecturer will open a webpage and upload materials.
Reference books, course materials, etc.
References are provided in the lectures.
Evaluation methods and criteria
Evaluation is based on the final report and the results of the exercises.
Related courses
- MCS.T211 ： Applied Calculus
- MCS.T201 ： Set and Topology I
- MCS.T202 ： Exercises in Set and Topology I
Prerequisites
None.