2020 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis E
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Yoshiyuki Kagei
- Class Format
- Lecture (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Tue (Zoom)
- Class
- -
- Course Code
- MTH.C501
- Number of credits
- 100
- Course offered
- 2020
- Offered quarter
- 3Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
This course gives a lecture on the theory of semigroups for linear operators and its application to partial differential equations. Theory of semigroups for linear operators are firstly explained; then as an application of the semigroup theory, partial differential equations of evolution type is considered. This course will be completed with "Advanced topics in Analysis F" in the next quarter.
The aim of this course is to learn some aspects of functional analytic method for partial differential equations through applications of the semigroup theory.
Course description and aims
・To understand theory of semigroups for linear operators.
・To understand applications of the semigroup theory to partial differential equations.
Keywords
linear operator, semigroup, resolvent, spectrum, evolution equation, partial differential equation
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 in this order : -- Uniformly continuous semigroup -- Strongly continuous semigroup -- Hille-Yosida's Theorem -- Asymptotic behavior of semigroups -- 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 complex function theory, Lebesgue integral theory, functional analysis, and theory of ordinary differential equations