2017 Complex Analysis

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Instructor(s)
Kojima Sadayoshi  Umehara Masaaki  Nishibata Shinya  Terashima Yuji  Miura Hideyuki  Takasawa Mitsuhiko 
Course component(s)
Lecture / Exercise
Day/Period(Room No.)
Tue3-4(W833)  Fri3-4(W833)  
Group
-
Course number
MCS.T232
Credits
2
Academic year
2017
Offered quarter
4Q
Syllabus updated
2017/3/17
Lecture notes updated
2018/1/26
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

Intercultural skills Communication skills Specialist 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.
Class 15 Application to definite integrals Understand the contents covered by the lecture.

Textbook(s)

See Japanese textbook above.

Reference books, course materials, etc.

References are provided in the lectures.

Assessment criteria and methods

By scores of examinations and recitation sessions.

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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