▶Japanese
Post to SNS
- Home
- > School of Science
- > Mathematics
- > Advanced courses in Analysis B
- School of Science
-
School of Engineering
- Group 2
- Group 3
- Group 4
- Group 5
- Group 6
- Metallurgical Engineering
- Organic and Polymeric Materials
- Inorganic Materials
- Chemical Engineering Course
- Chemical Engineering Course(Chemical Engineering)
- Applied Chemistry Course(Chemical Engineering)
- Polymer Chemistry
- Mechanical Engineering and Science
- Mechanical and Intelligent Systems Engineering
- Mechano-Aerospace Engineering
- International Development Engineering
- Control and Systems Engineering
- Industrial and Systems Engineering
- Electrical and Electronic Engineering
- Computer Science
- Civil Engineering
- Architecture and Building Engineering
- Social Engineering
- Common Cource of Engineering
- School of Bioscience and Biotechnology
- Common Course of Undergraduate School
-
Graduate School of Science and Engineering
- Mathematics
- Physics(Particle- Nuclear- and Astro-Physics)
- Physics(Condensed Matter Physics)
- Chemistry
- Earth and Planetary Sciences
- Chemistry and Materials Science
- Metallurgy and Ceramics Science
- Organic and Polymeric Materials
- Applied Chemistry
- Chemical Engineering
- Common Course of Mechanical Engineering
- Mechanical Sciences and Engineering
- Mechanical and Control Engineering
- Mechanical and Aerospace Engineering
- Common Course of Electronic Engineering
- Electrical and Electronic Engineering
- Physical Electronics
- Communications and Integrated Systems
- Communications and Computer Engineering
- Civil Engineering
- Architecture and Building Engineering
- International Development Engineering
- Nuclear Engineering
- Graduate School of Bioscience and Biotechnology
-
Interdisciplinary Graduate School of Science and Engineering
- Built Environment
- Energy Sciences
- Computational Intelligence and Systems Science
- Electronic Chemistry
- Materials Science and Engineering
- Innovative and Engineered Materials
- Environmental Chemistry and Engineering
- Environmental Science and Technology
- Mechano-Micro Engineering
- Information Processing
- Electronics and Applied Physics
- Graduate School of Information Science and Engineering
- Graduate School of Decision Science and Technology
- Graduate School of Innovation Management
- Common Course of Graduate School
- Program for Leading Graduate Schools
- Academic unit or major
- Mathematics
- Instructor(s)
- Tonegawa Yoshihiro Shibata Masataka
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H201)
- Group
- -
- Course number
- ZUA.C332
- Credits
- 1
- Academic year
- 2018
- Offered quarter
- 2Q
- Syllabus updated
- 2018/3/20
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
We discuss the variational mothods for the elliptic partial differential equations, and introduce some important methods such as the mountain pass lemma and concentration compactness principle.
This course follows Advanced courses in Analysis A.
Student learning outcomes
Students are expected to understand the variational methods to show the existence of the solutions of elliptic partial differential equations.
Keywords
variational methods, elliptic partial differential equations, mountain pass lemma, concentration compactness principle
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
Standard lecture course.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | Euler-Lagrange equation | Details will be provided during each class session. |
| Class 2 | Minimizing method | Details will be provided during each class session. |
| Class 3 | Constraint | Details will be provided during each class session. |
| Class 4 | Mountain pass theory 1 | Details will be provided during each class session. |
| Class 5 | Mountain pass theory 2 | Details will be provided during each class session. |
| Class 6 | Concentration compactness principle 1 | Details will be provided during each class session. |
| Class 7 | Concentration compactness principle 2 | Details will be provided during each class session. |
| Class 8 | Monotonicity methods | Details will be provided during each class session. |
Textbook(s)
None in particular
Reference books, course materials, etc.
L. C. Evans, Partial Differential Equations, American Mathematical Society
M. Struwe, Variational methods, Springer-Verlag
Assessment criteria and methods
Students need to submit a report. Details will be announced during the lecture.
Related courses
- ZUA.C331 ： Advanced courses in Analysis A
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are required to complete Advanced courses in Analysis A (ZUA.C331).
Other
None in particular
