Differential equations are used in describing phenomena and motions in various sciences, and especially in the field of science
and engineering, their analysis is indispensable. In recent years, computers often deal with differential equations, but since
the computer contains errors, some theoretical basic knowledge is required to judge whether the obtained solution is reliable
or not. In this class, you learn "solving method" of typical ordinary differential equations. It is generally difficult to
find all solutions of a differential equation. However, finding a suitable solution, we can often prove that there is no other
solution or can obtain the other solutions by using the solution. In particular, concerning the class of linear differential
equations, it is known that we get all the solutions as a linear combination of a finite number of fundamental solutions.
In order to learn such a fact after this class, I will explain the first step of finding solutions.
Natural phenomena can be modeled in terms of differential equations. The most of such equations are nonlinear. We can regard
a nonlinear equation as a linear equation by approximating the solution locally. In this class, we will learn how to solve
linear differential equations and nonlinear differential equations which can be reduced to the linear one.
- You can describe relationships between differential equations and various sciences.
- You can solve typical differential equations of 1st order.
- You can solve linear differential equations with constant coefficients.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Differential equations (pp.1-4) | Check out "differential calculus" in advance. | 190minutes |
| 2. | Phenomena and differential equations (pp.5-7) | Review Session 1 in advance. | 190minutes |
| 3. | Differential equations of 1st order (1) separation-of-variable type (pp.9-12) | Review Session 2 in advance. | 190minutes |
| 4. | Differential equations of 1st order (2) homogeneous type (pp.12-16) | Review Session 3 in advance. | 190minutes |
| 5. | Linear differential equations of 1st order (pp.16-21) | Review Session 4 in advance. | 190minutes |
| 6. | Bernoulli's differential equation, Riccati's differential equation (pp.16-21) | Review Session 5 in advance. | 190minutes |
| 7. | Attention on Mid-term assignment | Review Sessions 1-6 in advance. | 190minutes |
| 8. | Linear differential equations of n-th order (1), differential operators (pp.59-62) | Check out "linearlity" in advance. | 190minutes |
| 9. | Euler's formula, homogeneous linear differential equations of 2nd order (p.120, pp.62-64, particularly pp.76-79) | Review Session 8 in advance. | 190minutes |
| 10. | Nonhomogeneous linear differential equations of 2nd order (1) preparation (p.50, pp.64-69, particularly pp.79-82) | Review Session 9 in advance. | 190minutes |
| 11. | Nonhomogeneous linear differential equations of 2nd order (1) solutions (pp.69-75, particularly pp.82-85) | Review Session 10 in advance. | 190minutes |
| 12. | Homogeneous linear differential equations of n-th order (pp.62-75) | Review Session 11 in advance. | 190minutes |
| 13. | Advanced lecture: Pendulum equation | Review Session 12 in advance. | 190minutes |
| 14. | Attention on Final assignment | Review Sessions 8-13 in advance. | 190minutes |
| Total. | - | - | 2660minutes |
| Mid-term assignment | Final assignment | Total. | |
|---|---|---|---|
| 1. | 5% | 5% | 10% |
| 2. | 45% | 45% | |
| 3. | 45% | 45% | |
| Total. | 50% | 50% | - |
Mid-term assignment and Final assignment. As a criterion, if you determine that you understand 60% of the content covered
in the class, your final score will be 60 points.
Nagasawa etc, "Rikogaku no tame no bibunhouteishiki", Baifukan (in Japanese)
- Lunchtime on every Tuesday.
- The Learning Support Office is open to questions regarding this course.
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Sat Sep 09 05:09:33 JST 2023