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- Academic unit or major
- Mathematics
- Instructor(s)
- Tonegawa Yoshihiro Kan Toru
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- Mon3-4(H201)
- Group
- -
- Course number
- ZUA.C331
- Credits
- 1
- Academic year
- 2017
- Offered quarter
- 1Q
- Syllabus updated
- 2017/4/12
- Lecture notes updated
- -
- Language used
- Japanese
- Access Index
-
Course description and aims
The boundary value problem of Poisson's equation is mainly discussed. The course begins with the explicit representation of solutions in some special cases, then introduces fundamental facts such as the mean value property and the maximum principle, and finally reach at the existence and the uniqueness of classical solutions.
This course is continuous with Advanced courses in Analysis B.
Student learning outcomes
Students are expected to understand the existence, uniqueness and fundamental properties of solutions of linear elliptic partial differential equations.
Keywords
Laplace's equation, Poisson's equation, boundary value problem, Perron's method
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 | Laplace's equation and Poisson's equation | Details will be provided during each class session. |
| Class 2 | The Newtonian potential | Details will be provided during each class session. |
| Class 3 | The Poisson kernal | Details will be provided during each class session. |
| Class 4 | The mean value property and the maximum principle | Details will be provided during each class session. |
| Class 5 | Harnack's inequality | Details will be provided during each class session. |
| Class 6 | Perron's method 1 | Details will be provided during each class session. |
| Class 7 | Perron's method 2 | Details will be provided during each class session. |
| Class 8 | General second order linear elliptic equations | Details will be provided during each class session. |
Textbook(s)
None in particular
Reference books, course materials, etc.
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag
Assessment criteria and methods
Students need to submit a report. Details will be announced during the lecture.
Related courses
- ZUA.C332 ： Advanced courses in Analysis B
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Students are required to complete Advanced courses in Analysis B (ZUA.C332).
Other
None in particular
