Course title
330208002
Theory of Functional Equations

 ENOMOTO Yuko
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
Mathematical Sciences Course DP-4・2 キャリアを見据えた高度な専門知識
現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。
Purpose of class
Many natural and social phenomena can be described and analyzed using differential equations. This course aims to provide a foundation for understanding the solutions and properties of ordinary and basic partial differential equations, and to develop the fundamental skills needed to analyze such phenomena mathematically. Students will learn basic analytical methods, including the Laplace transform, Fourier series, and Fourier transform, preparing them for subsequent specialized courses.
Course description
This course introduces basic analytical methods for ordinary and partial differential equations. The first half covers the Laplace transform and variable-coefficient linear ordinary differential equations, while the second half introduces Fourier series and Fourier transform to study basic solutions of partial differential equations. Through these topics, students will develop the foundational skills to mathematically describe and analyze phenomena in science and engineering.
Goals and objectives
  1. You can describe the structure of solutions of linear ordinary differential equations.
  2. You can describe how to solve linear ordinary differential equations with variable coefficients and properties of the solutions.
  3. You can describe how to solve heat/ wave/ Laplace partial differential equations and properties of the solutions.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term exam Final exam Total.
1. 25% 25%
2. 25% 25%
3. 50% 50%
Total. 50% 50% -
Evaluation method and criteria
The evaluation method is as described in the section ”Correspondence with Learning Outcomes / Weighting.” A score of 60 points or higher out of 100 is required to pass. Students will pass if they demonstrate an understanding of the material covered in the lectures and are able to solve related problems.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Existence and uniqueness of solutions of initial value problem Review ”Differential Equations” in advance. 190minutes
2. Linear ordinary differential equation Review the previous session in advance. 190minutes
3. Method of reduction of order Review the previous session in advance. 190minutes
4. Variation of constant Review the previous session in advance.。 190minutes
5. Method of series Review the previous session in advance. 190minutes
6. Method of matrix Review the previous session in advance. 190minutes
7. Mid-term exam and review Review Sessions 1-6 in advance. 190minutes
8. Heat equation (Diffusion equation) Check out ”partial derivative” in Calculus in advance. 190minutes
9. Wave equation Review the previous session in advance. 190minutes
10. Fourier series and Fourier transformation Review the previous session in advance. 190minutes
11. Cauchy problem Review the previous session in advance. 190minutes
12. Laplace equation 1: radially symmetric solutions Review the previous session in advance. 190minutes
13. Laplace equation 2: non-radially symmetric solutions Review the previous session in advance. 190minutes
14. Final exam and review Review Sessions 8-13 in advance. 190minutes
Total. - - 2660minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
This will be introduced in the first lecture.
Prerequisites
Office hours and How to contact professors for questions
  • After class or by appointment
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
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 N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
Last modified : Sat Mar 14 14:53:21 JST 2026