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2022　Complex Analysis

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Instructor(s)
Mori Naofumi  Suzuki Sakie  Umehara Masaaki  Miura Hideyuki  Murofushi Toshiaki  Nishibata Shinya  Tsuchioka Shunsuke  Takahashi Jin  Ichiki Shunsuke  Gotoda Takeshi 
Class Format
Lecture / Exercise    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Tue1-2(W933)  Fri1-2(W933)  
Group
-
Course number
MCS.T232
Credits
2
Academic year
2022
Offered quarter
3Q
Syllabus updated
2022/9/8
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

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.

Student learning outcomes

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 that will be developed

✔ 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/Required learning

  Course schedule Required learning
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.

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)

See Japanese textbook above.

Reference books, course materials, etc.

References are provided in the lectures.

Assessment criteria and methods

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 (i.e., required knowledge, skills, courses, etc.)

None.

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