Course title
V0410600
Complex Analysis

 suzuki tatsuo Click to show questionnaire result at 2017
Course description
This is a course on complex analysis. You will learn complex number, holomorphic function, Cauchy-Riemann equation, Cauchy’s integral theorem, Residue formula.
Purpose of class
The object of this course is to understand the definition of differentiation or integration for complex functions and to be able to calculate integration for several complex functions.
Goals and objectives
  1. To be able to understand the definition of differentiation or integration for complex functions.
  2. To be able to calculate integration for several complex functions.
  3. To be able to use the residue formula.
Language
English
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Complex numbers, complex plane Complex numbers 150minutes
2. Polar form, Euler’s formula Review of complex numbers 200minutes
3. Complex function Review of polar form 200minutes
4. Holomorphic function, Cauchy-Riemann equation Review of complex function 200minutes
5. Inverse function Review of holomorphic function 200minutes
6. Midterm examination and comments Review of all topics 200minutes
7. Curves and complex integration Review of line integral 200minutes
8. Cauchy’s integral theorem Review of complex integration 200minutes
9. Cauchy’s integral formula, Taylor expansion Review of Cauchy’s integral theorem 200minutes
10. Singular point, pole Review of Cauchy’s integral formula and Taylor expansion 200minutes
11. Laurent expansion, residue Review of singular point 200minutes
12. Residue formula Review of Laurent expansion 200minutes
13. Application to some real integral Review of residue formula 200minutes
14. Final examination and comments Review of all topics 200minutes
Total. - - 2750minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Midterm exam Final exam Total.
1. 30% 10% 40%
2. 10% 20% 30%
3. 30% 30%
Total. 40% 60% -
Evaluation method and criteria
Midterm examination: 40%, Final examination: 60%
Textbooks and reference materials
Will be announced in the first class.
Prerequisites
Calculus and linear algebra
Office hours and How to contact professors for questions
  • After class
Relation to the environment
Non-environment-related course
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
Active-learning course
More than one class is interactive
Last modified : Wed Oct 17 08:01:56 JST 2018