2024 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis F
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Hideyuki Miura
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Tue
- Class
- -
- Course Code
- MTH.C502
- Number of credits
- 100
- Course offered
- 2024
- Offered quarter
- 4Q
- Syllabus updated
- Mar 14, 2025
- Language
- English
Syllabus
Course overview and goals
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 is a succession of "Advanced Topics in Analysis E" in the previous quarter.
Course description and aims
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
- 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/Objectives
| Course schedule | Objectives | |
|---|---|---|
| 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. |
Study advice (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.
Evaluation methods and criteria
Attendance and Assignments.
Related courses
- MTH.C305 ： Real Analysis I
- MTH.C306 ： Real Analysis II
- MTH.C351 ： Functional Analysis
Prerequisites
Basics of Lebesgue integral theory, functional analysis are required.
Students are assumed to take "Advanced Topics in Analysis E" in the previous quarter.