Course title
V03260002
Theory of Functional Equations

 TAKEUCHI Shingo
Course description
In the first half, you learn solutions and properties of variable coefficient linear ordinary differential equations based on the solution of various ordinary differential equations learned in "differential equation" (the second semester of the first year) and "Calculus with Differential Equations" (the first semester of the second year). In the second half, you will learn the solution method and properties of basic partial differential equation (heat, wave, Laplace).
Purpose of class
Differential equations are indispensable for understanding the various fields of science and engineering. It is a matter of course to understand the nature of the linear differential equation, but to aim at making a foundation for acquiring various subsequent subjects, reviewing differential integral and linear algebra through that learning.
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% -
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
Evaluation method and criteria
Mid-term assignment and Final assignment. When the minimum and maximum scores of the midterm and final examinations are m and M, respectively, a student is considered to have passed if m≥30 and M≥60, where M is the grade.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in outside of the class (ScombZ, mail, etc.)
Textbooks and reference materials
Textbook for the 1st year students (Nagasawa et al. "Rikogaku no tame no bibunhouteisiki", Baifukan)
Prerequisites
"Differential Equations" for the 1st year students.
Office hours and How to contact professors for questions
  • During class periods, every Wednesday after 4th period (it is advisable to call in advance when visiting).
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
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Wed Apr 02 04:09:31 JST 2025