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- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Kagei Yoshiyuki
- Class Format
- Lecture (ZOOM)
- Media-enhanced courses
- Day/Period(Room No.)
- Tue5-6(Zoom)
- Group
- -
- Course number
- MTH.C501
- Credits
- 1
- Academic year
- 2020
- Offered quarter
- 3Q
- Syllabus updated
- 2020/9/18
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
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.
Student learning outcomes
・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 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 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. |
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 complex function theory, Lebesgue integral theory, functional analysis, and theory of ordinary differential equations
