Course title
6M0060001
Topics in Analysis

 ENOMOTO Yuko Click to show questionnaire result at 2019
Course content
In this lecture, we learn to solve partial differential equations using the Fourier transform.
Purpose of class
The purpose of this lecture is to understand the Fourier transform, its properties, and its application to PDEs.
Goals and objectives
  1. To learn how to calculate the Fourier transform for a concrete function.
  2. To learn properties of the Fourier transform.
  3. To learn applications to partial differential equations.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 report Total.
1. 30% 30%
2. 30% 30%
3. 40% 40%
Total. 100% -
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Review of Lebesgue integral Review of linear space 200minutes
2． Lebesgue space Review of a previous lecture 200minutes
3． Fourier transform (in L^1 space) Review of a previous lecture 200minutes
4． Inverse Fourier transform (in L^1 space) Review of a previous lecture 200minutes
5． Schwartz space Review of a previous lecture 200minutes
6． Fourier transform in Schwartz space Review of a previous lecture 200minutes
7． Tempered distribution Review of a previous lecture 200minutes
8． Differentiation of distribution, distribution and differential equation Review of a previous lecture 200minutes
9． Fourier transform of tempered distribution Review of a previous lecture 200minutes
10． Properties of Fourier transform Review of a previous lecture 200minutes
11． Structure theorem Review of a previous lecture 200minutes
12． Application to heat equation Review of a previous lecture 200minutes
13． Application to Schrodinger equaion Review of a previous lecture 200minutes
14． Application to wave equation Review of a previous lecture 200minutes
Total. - - 2800minutes
Evaluation method and criteria
reports (100%)
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
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 : Wed Feb 26 18:11:54 JST 2025