Course title
6M005410
Advanced Mathematical Analysis

 ishiwata tetsuya Click to show questionnaire result at 2018
Course content
Mathematical models for several phenomena in nature are usually nonlinear.
In this lecture, we consider parabolic type PDE, which describes
interface motion. You study some mathematical methods to understand
the properties of the solutions.
Purpose of class
Understand the properties of solutions to parabolic type PDE and master mathematical methods for them.
Goals and objectives
  1. understand mathematical models which describe interface motions
  2. understand the mathematical methods for analysis to nonlinear parabolic type PDE
  3. understand the numerical methods for nonlinear PDE
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Introduction: Interface motions differential equation, dynamical system, numerical analysis 190minutes
2． preliminaries for analysis of interface motion differential equation, dynamical system, numerical analysis and lecture note of previous lecture 190minutes
3． Mathematical model of interface motion differential equation, dynamical system, numerical analysis and lecture note of previous lectures 190minutes
4． Curvature flow differential equation, dynamical system, numerical analysis and lecture note of previous lectures 190minutes
5． Properties of solutions to curvature flow differential equation, dynamical system, numerical analysis and lecture note of previous lectures 190minutes
6． Geometric properties of the solutions differential equation, dynamical system, numerical analysis and lecture note of previous lectures 190minutes
7． Numerical method for curvature flow differential equation, dynamical system, numerical analysis and lecture note of previous lectures 190minutes
8． Discussion and presentation 1 differential equation, dynamical system, numerical analysis and lecture note of previous lectures.
prepare the presentation 		190minutes
9． Blow-up problem differential equation, dynamical system, numerical analysis and lecture note of previous lectures 190minutes
10． Existence of blow-up solution: Fujita-Kaplan's method differential equation, dynamical system, numerical analysis and lecture note of previous lectures 190minutes
11． Existence of blow-up solution: Energy method differential equation, dynamical system, numerical analysis and lecture note of previous lectures 190minutes
12． Numerical method for blow-up problems differential equation, dynamical system, numerical analysis and lecture note of previous lectures 190minutes
13． Summerize mathematical analysis on curvature flow differential equation, dynamical system, numerical analysis and lecture note of previous lectures 190minutes
14． Discussion and presentation on interfrace motion, blow-up problems and several nonlinear problems differential equation, dynamical system, numerical analysis and lecture note of previous lectures.
prepare the presentation 		190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 presentation report Total.
1. 15% 15% 30%
2. 15% 20% 35%
3. 15% 20% 35%
Total. 45% 55% -
Evaluation method and criteria
presentation(45%) and reports(55%)
Textbooks and reference materials
nothing. I introduce corresponding books and papers in the lecture.
Prerequisites
differential equations, measure theory, functional analysis, functional equations, numerical analysis, linear algebra, differential geometry, programing
Office hours and How to contact professors for questions
  • Tue: 12:25-13:05
Relation to the environment
Non-environment-related course
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic problem-solving skills
Active-learning course
More than one class is interactive
Last modified : Wed Oct 17 07:46:31 JST 2018