2025Year

Second Semester

Theory of Applied Differential Equations

Lecture

Theory of Applied Differential Equations

Z1500009 Theory of Applied Differential Equations

HASEGAWA Kenji

2.0Credits

Tue.1Period

Hachioji Remote

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%

This course deals with partial differential equations (PDEs) involving two or more variables. Unlike ordinary differential equations in one variable, PDEs are generally more challenging to handle, and historically, there has been a focus on exploring solution methods limited to PDEs that appear as models in physics and engineering. In this course, we aim to introduce solution methods with as much generality as possible. The objectives are as follows:

(1) Mastering solution methods for first-order partial differential equations.
(2) Obtaining series solutions of partial differential equations using the method of separation of variables.
(3) Understanding the method of obtaining fundamental solutions using Fourier transforms and deriving solution formulas.

Understanding of calculus, linear algebra, complex functions, and differential equations taught in the undergraduate program is necessary. It is desirable to be able to use computer algebra systems (such as Matlab, Mathematica, Maxima, etc.) to solve mini-test and report problems. Since Fourier analysis may be used, it is recommended to take Applied Analysis in the spring semester.

Support for self-learning using ICT

1. Guidance
2. First-order Quasi-linear Partial Differential Equations
3. Total Differential Equations and Exact Differential Equations
4. Lagrange-Charpit Method
5. General Solution, Complete Solution, Singular Solution
6. One-dimensional Heat Equation and Wave Equation in Space
7. Eigenvalue Problems of Laplace Operator in a Rectangle and Heat Equation and Wave Equation
8. Eigenvalue Problems of Laplace Operator in a Disk and Bessel Functions
9. Fourier-Bessel Expansion
10. Heat Equation and Wave Equation in a Disk
11. Fourier Transform and Initial Value Problem for Heat Equation
12. Fundamental Solution of Laplace Equation
13. Fundamental Solution of Wave Equation
14. Initial Value Problem for Wave Equation
15. Boundary Value Problem for Laplace Equation and Green's Function
Students will watch the slides and submit their answers to the mini-tests by the deadline. A report assignment will be given at the end of the semester.

The evaluation of grades will be based on a 3:2 ratio between the mini-tests and reports through KU-LMS. However, answers in mini-tests and reports will be considered invalid if students refer no course materials or are suspected that they allow others to copy their answer or reproduce answers from other students or AI-generated response.

The correct answers for the mini-test will be disclosed through KU-LMS. In addition to office hours, the teacher will respond to questions and opinions on Google Meet. The date and time will be discussed via email.

There is no specified textbook. Instead, students will use the PDF files uploaded to KU-LMS for study materials.

Treatises on Fourier analysis and partial differential equations

Tuesday, 13:00〜14:00(Hachioji:1E-313）

It is an on-demand remote class, chosen as a teaching method deemed more effective than face-to-face interaction. Unless there is a change in instructors, the class format will be maintained going forward.

Not applicable

Electrical Engineering and Electronics Program／Informatics Program