2026Year

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 in two or more variables. Compared with ordinary differential equations in one variable, partial differential equations are generally more difficult to treat in a unified theoretical framework. Historically, solution methods have been developed mainly for equations arising from physical and engineering models, and the field continues to evolve.

Due to time constraints, the course is limited to fundamental topics. For first-order partial differential equations, relatively general solution methods will be introduced. For second-order equations, we focus on representative equations such as the Laplace equation, the heat equation, and the wave equation. Emphasis is placed on understanding solution methods that are not only important for practical applications in engineering and information science but also form the foundation of further study.

Upon successful completion of this course, students will be able to:

(1) Apply solution methods for first-order partial differential equations.
(2) Obtain series solutions of partial differential equations using the method of separation of variables.
(3) Understand how to derive fundamental solutions using the Fourier transform and obtain explicit 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 short 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 short tests by the deadline. A report assignment will be given at the end of the semester.

The final grade for this course will be determined based on short tests and a report administered through KU-LMS, with a weighting of Short Tests : Report = 2 : 1. A short test or the report will be deemed invalid in the following cases:

(1) Failure to complete attendance registration and download the course materials by the designated deadline.
(2) When a student is judged to have copied, or allowed others to copy, answers from another student or from generative AI tools.
(3) Failure to download the report assignment file by the designated deadline.
(4) When materials other than the course materials are consulted without properly citing the source and submitting an image of the relevant page.

Evaluation of short tests and the report will be based not only on correctness but also on learning records in KU-LMS (including attendance registration, access/download history of materials, submission time, etc.). If the report is not submitted, or is deemed invalid, the final grade for the course will be recorded as F.

The correct answers for the short 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 (ft10058@g.kogakuin.jp).

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