Course title
6M0178001
Advanced Mathematical Analysis A

 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 properties of solutions to parabolic type PDE and master mathematical methods for them.
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 the blow-up problems
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 differential equation, dynamical system, numerical analysis 190minutes
2． Nonlinear Partial Differential Equations lecture note of previous lecture 190minutes
3． Mathematical analysis of blow-up problem: Fujita-Kaplan method lecture note of previous lecture 190minutes
4． Mathematical analysis of blow-up problem: Energy method lecture note of previous lecture 190minutes
5． Numerical analysis of blow-up problems lecture note of previous lecture, C programing, numerical analysis 190minutes
6． Exercises: Blow-up problems in various phenomena lecture note of previous lecture 190minutes
7． Presentation and peer evaluation lecture note of previous lecture 190minutes
8． (none) (none) 0minutes
9． (none) (none) 0minutes
10． (none) (none) 0minutes
11． (none) (none) 0minutes
12． (none) (none) 0minutes
13． (none) (none) 0minutes
14． (none) (none) 0minutes
15． (none) (none) 0minutes
16． (none) (none) 0minutes
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.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
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
  • 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
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Sat Sep 09 05:49:21 JST 2023