Course title
330385003
Advanced Studies in Mathematical Sciences C

 MATSUZAWA Hiroshi

TAKEUCHI Shingo
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
Mathematical Sciences Course DP-4・2 キャリアを見据えた高度な専門知識
現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。
Purpose of class
The aim of the lecture is to understand the precise statement of the maximum principle for the elliptic and parabolic partial differential equations to get the basic skill to study differential equations.
Course description
This course gives an introduction to the maximum principle in the theory of partial differential equations. The maximum principle is a basic and important tool to obtain not only the uniqueness of a solution to the some initial/ boundary value problem of partial differential equations but also the quantitative properties of solutions to some nonlinear partial differential equations.
Goals and objectives
  1. To be able to say the statements of the weak and strong maximum principle of elliptic equations.
  2. To be able to say the statements of the weak and strong maximum principle of parabolic equations.
  3. To be able to explain applications of the maximum principles to the reaction diffusion equations
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Self Check Sheet Total.
1. 40% 40%
2. 40% 40%
3. 20% 20%
Total. 100% -
Evaluation method and criteria
Based on self check sheet(report), if you understand 60% of the content covered in the class, your final score will be 60 points.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Introduction : Maximum principle for Harmonic Functions

Harmonic functions
Mean Value Properties 		Review of basic topics related to this class 1330minutes
0minutes
2. Maximum Principle for harmonic functions. Not applicable 0minutes
0minutes
3. Maximum Principle for Elliptic Equations 1

Linear Elliptic Equations
Weak Maximum Principle
Hopf Lemma 		Not applicable 0minutes
0minutes
4. Maximum Principle for Elliptic Equations 2
Strong Maximum Principle
Phragmen-Lindelof Principle 		Not applicable 0minutes
0minutes
5. Maximum Principle for Parabolic Equations 1

Heat equations
Linear Parabolic Equations
Weak Maximum Principle 		Not applicable 0minutes
0minutes
6. Maximum Principle for Parabolic Equations 2

Strong Maximum Principle
Phragmen-Lindelof Principle 		Not applicable 0minutes
0minutes
7. Application Comparison Principle Not applicable 0minutes
0minutes
8. Not applicable Not applicable 0minutes
9. Not applicable Not applicable 0minutes
10. Not applicable Not applicable 0minutes
11. Not applicable Not applicable 0minutes
12. Not applicable Not applicable 0minutes
13. Not applicable Not applicable 0minutes
14. Not applicable Not applicable 0minutes
15. Not applicable Not applicable 0minutes
Total. - - 1330minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback outside of the class (ScombZ, mail, etc.)
Textbooks and reference materials
Textbook
N/A
The lecture note will be given.

Reference
Evans: Partial Differential Equations(AMS)
Protter and Weinberger: Maximum principles in differential equations(Springer)
Hirokazu Ninomiya: Shinnyu-Denpa and Kakusan Houteishiki(Japanese)(Kyoritu Shuppan)
Prerequisites
Office hours and How to contact professors for questions
  • Before and after lectures I will accept your questions. You can also contact with me via email. My email address will be given in the first lecture.
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 applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
Last modified : Thu Mar 26 04:04:29 JST 2026