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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Miura Hideyuki
- Class Format
- Lecture
- Media-enhanced courses
- Day/Period(Room No.)
- -
- Group
- -
- Course number
- MTH.C501
- Credits
- 1
- Academic year
- 2024
- Offered quarter
- 3Q
- Syllabus updated
- 2024/3/14
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
This course gives a lecture on real analysis and Fourier analysis with the aim of applications to partial differential equations.
The purpose of this course is to learn basics of function spaces such as Sobolev spaces, the Fourier transform, and Schwartz distributions. This course will be completed with "Advanced topics in Analysis F" in the next quarter.
Student learning outcomes
This course emphasizes the importance of rigorous treatment of various problems in partial differential equations by the use of concepts in real analysis and Fourier analysis.
Keywords
Function spaces, Inequalities for functions, Fourier transform, Schwartz distributions, Partial differential equations
Competencies that will be developed
| ✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
Class flow
This is a standard lecture course. There will be some assignments.
Course schedule/Required learning
| Course schedule | Required learning | |
|---|---|---|
| Class 1 | The following topics will be covered: -- Lebesgue spaces and inequalities of functions -- Fourier transform -- Schwartz distributions -- Sobolev spaces -- Applications to partial differential equations | Details will be provided in class. |
Out-of-Class Study Time (Preparation and Review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
None required
Reference books, course materials, etc.
Details will be provided during each class.
Assessment criteria and methods
Attendance and Assignments.
Related courses
- MTH.C305 ： Real Analysis I
- MTH.C306 ： Real Analysis II
- MTH.C351 ： Functional Analysis
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Basics of Lebesgue integral theory, functional analysis are required.
