Course title
6M0087001
Theory of Partial Differential Equations

 yamazawa hiroshi Click to show questionnaire result at 2018
Course content
We study some review of complex function theory and give lectures on wave equation and heat equation. Lastly we treat the complex heat equation and more general partial differential equations.
Purpose of class
We can understand a construction of general solutions for Wave and Heat equation and solve some partial differential equation in a complex domain via power series. Further we can understand Cauchy-Kovalevsky theorem.
Goals and objectives
  1. Review of complex function theory
  2. Power series solution of some partial differential equations in a complex domain
  3. Cauchy-Kovalevsky theorem
  4. Maillet type theorem
  5. Borel sum method
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Complex function theory１ To review Lecture note 100minutes
2． Complex function theory２ To review Lecture note 100minutes
3． Cauchy-Kovalevsky theorem 1 To review Lecture note 100minutes
4． Cauchy-Kovalevsky theorem 2 To review Lecture note 100minutes
5． Non Kovalevskian type equations and Poincare condition １ To review Lecture note 100minutes
6． Non Kovalevskian type equations and Poincare condition 2 To review Lecture note 100minutes
7． Formal solution and it's Gevrey estimates of Heat equation in a complex domain To review Lecture note 100minutes
8． Newton polygons and Gevrey estimate of formal solutions １ To review Lecture note 100minutes
9． Newton polygons and Gevrey estimate of formal solutions 2 To review Lecture note 100minutes
10． Laplace transform 1 To review Lecture note 100minutes
11． Laplace transform 2 To review Lecture note 100minutes
12． Recent topics1 To review Lecture note 100minutes
13． Recent topics2 To review Lecture note 100minutes
14． Recent topics3 To review Lecture note 100minutes
Total. - - 1400minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Report Total.
1. 0% 0%
2. 25% 25%
3. 25% 25%
4. 25% 25%
5. 25% 25%
Total. 100% -
Evaluation method and criteria
reports100%
Textbooks and reference materials
We introduce some reference on lectures
Prerequisites
nothing
Office hours and How to contact professors for questions
  • 30 m after each 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
N/A
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicatable
N/A N/A
Last modified : Thu Mar 21 15:39:53 JST 2019