Course title
6M0060001
Topics in Analysis

 enomoto yuko Click to show questionnaire result at 2019
Course content
In this lecture, you learn the theory of semigroups and unique solvability of partial differential equations.
Purpose of class
The purpose of this lecture is to understand the proof of uniqueness of a solution to the partial differential equation using functional analysis.
Goals and objectives
  1. To learn properties of linear operators.
  2. To learn the relation between semigroup and infinitesimal generator.
  3. To learn applications to partial differential equations.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Review of functional analysis (normed linear space, Banach space) Review of linear space 200minutes
2． Review of functional analysis (inner product space, Hilbert space) Review of a previous lecture 200minutes
3． Properties of linear oparators and bounded linear operators Review of a previous lecture 200minutes
4． Properties of closed operators Review of a previous lecture 200minutes
5． Definition of semigroup, Co semigroup and contraction semigroup Review of a previous lecture 200minutes
6． Definition of infinitesimal generator of Co semigroup Review of a previous lecture 200minutes
7． Properties of infinitesimal generator of Co semigroup Review of a previous lecture 200minutes
8． The resolvent of infinitesimal generator of Co semigroup Review of a previous lecture 200minutes
9． Generation of semigroup Review of a previous lecture 200minutes
10． The Hille-Yoshida theorem Review of a previous lecture 200minutes
11． Generation of Co group Review of a previous lecture 200minutes
12． Lebesgue space and Sobolev space Review of a previous lecture 200minutes
13． Application to partial differential equation (existence of solution) Review of a previous lecture 200minutes
14． Application to partial differential equation (uniqueness of solution) Review of a previous lecture 200minutes
Total. - - 2800minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 report Total.
1. 30% 30%
2. 40% 40%
3. 30% 30%
Total. 100% -
Evaluation method and criteria
reports (100%)
Textbooks and reference materials
I introduce corresiponding books in the first lecture.
Prerequisites
Basic analysis, Functional analysis
Office hours and How to contact professors for questions
  • before and after the lecture
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
N/A
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
Last modified : Sun Mar 21 15:29:41 JST 2021