Course title
1M805000
System of Mathematical Analysis

 idogawa tomoyuki Click to show questionnaire result at 2018
Course content
Differential equations and integral equations are widely used as mathematical models of various research targets, not only in the fields of natural science and engineering, but in economics, sociology, and psychology, among others. As solutions cannot be derived for most of them using a classical quadrature method, various numerical analysis techniques have been devised and applied. However, they are at most approximate solvers, and it is important to verify the validity of those numerical methods or of the mathematical models themselves, and evaluate the error of the numerical solutions derived by them. In this course, the basics of functional analysis upon which such investigations are based will be discussed, and the validity of numerical analysis methods or mathematical models and error analysis methods will be discussed. We will also discuss about the applications
of them to some differential equations. Moreover, if we have time, several specific numerical methods and their justification from the viewpoint of functional analysis will be raised for discussion.
The following lesson plan is only a schedule, therefore it may be changed according to course progress, and student interests.
Purpose of class
To study the fundamental theories of functional analysis.
Goals and objectives
  1. To understand the concept of normed space.
  2. To understand the concept of bounded linear operators and the fundamentals of distribution.
  3. To study the fundamentals of functional analysis and to get the outline of its applications.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Introduction to functional analysis Review on derivative and integral 190minutes
2． Sets and logical operators Review the previous lecture 190minutes
3． Maps Review the previous lecture 190minutes
4． The structure of real numbers Review the previous lecture 190minutes
5． Contraction principle on the real numbers Review the previous lecture 190minutes
6． Linear space Review the previous lecture 190minutes
7． Normed space (1), the axioms of norm and distance Review the previous lecture 190minutes
8． Normed space (2), Banach space Review the previous lecture 190minutes
9． Contraction principle on Banach spaces Review the previous lecture 190minutes
10． Bounded linear operators Review the previous lecture 190minutes
11． Inverse operators Review the previous lecture 190minutes
12． Linear functionals Review the previous lecture 190minutes
13． Distributions Review the previous lecture 190minutes
14． Summary Review the all of lectures 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Reports Examinations Total.
1. 20% 20% 40%
2. 20% 20% 40%
3. 10% 10% 20%
Total. 50% 50% -
Evaluation method and criteria
Students will be evaluated by reports (50%) and oral examinations (50%).
Textbooks and reference materials
Those will be indicated on the first class.
Prerequisites
Fundamental calculus and linear algebra
Office hours and How to contact professors for questions
  • Tuesday 12:15 -- 13:00
Relation to the environment
Non-environment-related course
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
Active-learning course
N/A
Last modified : Wed Oct 17 07:03:57 JST 2018