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- Liberal arts and basic science courses
- Academic unit or major
- Undergraduate major in Mathematics
- Instructor(s)
- Fujikawa Ege
- Class Format
- Lecture / Exercise (Livestream)
- Media-enhanced courses
- Day/Period(Room No.)
- Mon5-8(W351)
- Group
- -
- Course number
- MTH.C302
- Credits
- 2
- Academic year
- 2022
- Offered quarter
- 2Q
- Syllabus updated
- 2022/3/16
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
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Course description and aims
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 will introduce the notion of "residue". As an application of this theory, we explain the computation of integrals.
Student learning outcomes
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．
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
Class flow
Standard lecture course with exercise.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Meromorphic functions and Laurent expansion | 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 | Details will be provided during each class session. |
| Class 4 | Recitation | Details will be provided during each class session. |
| Class 5 | The residue and its computation | Details will be provided during each class session. |
| Class 6 | Recitation | Details will be provided during each class session. |
| Class 7 | The residue theorem | 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. |
Out-of-Class Study Time (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)
None
Reference books, course materials, etc.
Akira Kaneko, Lecure on function theory, Saiensu-sha
Assessment criteria and methods
Based on Final exam and recitation
Related courses
- MTH.C301 ： Complex Analysis I
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are expected to have passed MTH.C301 ： Complex Analysis I.
