Course title
Q14351002
Analysis 2

 SUZUKI Tatsuo
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 determine with Cauchy-Riemann equations whether a complex function is differentiable.
  2. To be able to calculate integration with Cauchy's integral theorem and formula, residue theorem.
  3. To be able to calculate definite integrals with residue theorem.
Language
Japanese
Class schedule

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

 Assignment 1 Midterm exam Final assignment Total.
1. 20% 20% 40%
2. 20% 20% 40%
3. 20% 20%
Total. 20% 40% 40% -
Evaluation method and criteria
Assignment 1 (20%), Midterm exam (40%), Final assignment (40%)
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
  • Tuesday 12:40-13:10
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
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
Last modified : Sat Sep 10 04:03:41 JST 2022