Course title
40111060
Analysis 2

 yamazawa hiroshi Click to show questionnaire result at 2017
Course description
In this lecture we learn complex analysis. The differential calculus of the complex valued function which makes the complex number a variable is same as the differential calculus in differential and integral calculus science 1 formally but different in the contents. Even if f' (x) exists in differential and integral calculus science 1, f'' (x) may not exist. But, when the complex variable function is differentiable at some territory, it's limited to its range, but how many times can be differentiated? It starts from a complex number to lead this result, and the regular function, a theorem of Cauchy and integral representation, etc. are learned. The necessary next calculation technology is acquired in engineering.
Purpose of class
To find Taylor expansion and Laurent expansion for typical functions.
To find the residue at a pole for functions.
To integration by Residue theorem and its applications
Goals and objectives
  1. four arithmetic operation for complex numbers, polar form of complex numbers, applications of Euler's formula
  2. Sequence, convergence of power series, limit and continuous of complex functions
  3. We can find derivative of complex functions, show that a function is a holomorphic function.
  4. We can calculate the integration by Cauchy's theorem.
  5. We can find Taylor expansion and Laurent expansion of functions and find the integration by the residue theorem.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Complex numbers, Polor form, De Moivre's theorem text pp.1-7 30minutes
2. Applications text pp.8-10 30minutes
3. Sequence, series, function text pp.11-17 30minutes
4. Holomorphic functions text pp.18-20 30minutes
5. Cauchy-Riemann differential equation text pp.21-24 30minutes
6. Simple examples of holomorphic functions(exponent function, trigonometric function) text pp.25-32 30minutes
7. Logarithmic functions text pp.32-37 30minutes
8. Integration of complex functions text pp.38-44 30minutes
9. Cauchy's theorem text pp.45-49 30minutes
10. Cauchy's integral theorem text pp.50-55 30minutes
11. Taylor expansion, Laurent expansion text pp.56-61 30minutes
12. Pole, residue text pp.62-66 30minutes
13. Applications of residue text pp.67-75 30minutes
14. Exam Lesson 1〜13 150minutes
Total. - - 540minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 exercise exam Total.
1. 6% 14% 20%
2. 6% 14% 20%
3. 6% 14% 20%
4. 6% 14% 20%
5. 6% 14% 20%
Total. 30% 70% -
Evaluation method and criteria
Report and exercise 30%, Exam: 70%, total 100p
Textbooks and reference materials
教科書：「複素解析」、矢野健太郎・石原繁著、裳華房
Prerequisites
履修前提科目等　微分積分学１、　微分積分学２
Office hours and How to contact professors for questions
  • After lecture
Relation to the environment
Non-environment-related course
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
More than one class is interactive
Last modified : Thu Mar 15 04:20:23 JST 2018