Course title
6M0179001
Advanced Mathematical Analysis B

 ISHIWATA Tetsuya
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 mathematical analysis for interface motions.
Goals and objectives
  1. Student can understand and apply the mathematical methods for analysis to nonlinear parabolic type PDE.
  2. Student can understand and apply the numerical methods for nonlinear PDE.
  3. Student can understand and apply the mathematical methods for interface motions.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Mathematical models and partial differential equations ifferential equation, dynamical system, numerical analysis 190minutes
2． Nonlinear Partial Differential Equations lecture note of previous lecture 190minutes
3． Mathematical analysis of curvature flows: curvature blow-up lecture note of previous lecture 190minutes
4． Mathematical analysis of curvature flows: asymptotic behavior lecture note of previous lecture 190minutes
5． Numerical simulations of interface motions lecture note of previous lecture 190minutes
6． Exercises: interface motions in various phenomena lecture note of previous lecture 190minutes
7． Presentation and peer evaluation lecture note of previous lecture 190minutes
Total. - - 1330minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 presentation report Total.
1. 15% 15% 30%
2. 15% 15% 30%
3. 20% 20% 40%
Total. 50% 50% -
Evaluation method and criteria
The achievement of students will be evaluated by presentation and report. If the score is 60% or more, you can pass.
Textbooks and reference materials
None. 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
Prepare programming environment and visualization tools
Office hours and How to contact professors for questions
  • Make an appointment in advance before visiting.
    Thu: 12:25-13:05
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
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A 該当しない
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Fri Mar 18 23:22:58 JST 2022