Theory of Partial Differential Equations

Academic year

2025Year

Term

First Semester

Course title

Theory of Partial Differential Equations

Class type

Lecture

Course title (ENG)

Theory of Partial Differential Equations

Class code・Class name・Teaching forms

Z0800003 Theory of Partial Differential Equations

Instructor

KUMANO-GO Naoto

Credits

2.0Credits

Day and Time

Thu.5Period

Campus

Hachioji Campus

Location

1S-209講義室

Relationship between diploma policies and this course

A) A high degree of specialized expertise　100%
B) The skills to use science and technology　0%
C) The ability to conduct research independently, knowledge pertaining to society and occupations, and sense of ethics required of engineers and researchers　0%
D) Creative skills in specific areas of specialization　0%

Goals and objectives

The goals of this course are to
(1) Obtain the knowledges about function spaces and distributuion which are bases
of modern theory of partial differential equatons.
(2) Obtain knoledge and skills to solve the solutions of partial differential equations by functional analysis.
(3) Obtain knoledge and skills to construct the fundamental solutions of parabolic equations by functional analysis.

Prerequisites

Calculus and Linear Algebra

Method Using AL・ICT

Support for self-learning using ICT

Class schedule

Depending on the number of students, this course may be changed to a face-to-face class that requires attendance every week.

0. Guidance (by On Demand)
1. Function Spaces (face-to-face from 1st week)
2. Differential Equations
3. Partial Differential Equations of First Order
4. Distributions
5. Fourier Series
6. Fourier Transform
7. Hyperbolic Equations
8. Initial Value Problems for Hyperbolic Equations
9. Parabolic Equations
10. Initial Value Problems for Parabolic Equations
11. Fundamental Solutions for Parabolic Equations
12. Elliptic Equations
13. Boundary Value Problems for Elliptic Equations
14. Reviewing

Preparation: Read the contents which you can get every week.

Evaluation

The student should demonstrate his/her ability to handle basic exercises by submitting a report (or test) in each session.

Feedback for students

I respond to your inquiries about submissions and exams via email.

Textbooks

Text: Handouts.

Reference materials

・Hitoshi Kumano-go, Partial Differential Equations (Japanese), Kyouritsu Shuppan
・Erwin Kreyszig, Fourier Aanalysis and Partial Differential Equations (Japanese), Baifukan
・Keishi Baba, Yutaka Takasugi, Partial Differential Equation, Campus Zemi (Japanese), Mathema

Office hours and How to contact teachers for questions

Friday:15:50-16:50・1E-315 (Kumano-go Laboratory)

Message for students

具体的な計算方法だけではなく、抽象的な思考方法を身につけることが目標です。

Course by professor with work experience

Not applicable

Work experience and relevance to the course content if applicable

Teaching profession course

Informatics Program

Syllabus data