N1450600
,P1450200,Q1450000,R1450800,V14504001
Differential Equations,P1450200,Q1450000,R1450800,V14504001
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.
- To understand relationships between differential equations and various sciences.
- To learn how to solve typical differential equations of 1st order.
- To learn how to 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 and applications | Check out "differential calculus" in advance. | 190minutes |
| 2. | Differential equations of 1st order (1) separation-of-variable type, homogeneous type | Review Session 1 in advance. | 190minutes |
| 3. | Differential equations of 1st order (2) linear type, Bernoulli type | Review Session 2 in advance. | 190minutes |
| 4. | Differential equations of 1st order (3) exact type | Review Session 3 in advance. | 190minutes |
| 5. | Differential equations of 1st order (4) type reduced to 1st order | Review Session 4 in advance. | 190minutes |
| 6. | Differential equations of 1st order (5) applications | Review Session 5 in advance. | 190minutes |
| 7. | Mid-term exam | Review Sessions 1-6 in advance. | 190minutes |
| 8. | Ordinary linear differential equations (1) homogeneous type | Check out "linearlity" in advance. | 190minutes |
| 9. | Ordinary linear differential equations (2) differential operators | Review Session 8 in advance. | 190minutes |
| 10. | Ordinary linear differential equations (3) homogeneous linear equations with constant coefficients | Review Session 9 in advance. | 190minutes |
| 11. | Ordinary linear differential equations (4) inverse operators | Review Session 10 in advance. | 190minutes |
| 12. | Ordinary linear differential equations (6) with constant coefficients | Review Session 11 in advance. | 190minutes |
| 13. | Ordinary linear differential equations (7) with constant coefficients (sequel) | Review Session 12 in advance. | 190minutes |
| 14. | Final exam | Review Sessions 8-13 in advance. | 190minutes |
| Total. | - | - | 2660minutes |
| Mid-term exam | Final exam | Total. | |
|---|---|---|---|
| 1. | 5% | 5% | 10% |
| 2. | 45% | 45% | |
| 3. | 45% | 45% | |
| Total. | 50% | 50% | - |
- Department of Mathematical Sciences (Takeuchi): Lunchtime on every Tuesday.
- Non-social and professional independence development course
| Work experience | Work experience and relevance to the course content if applicatable |
|---|---|
| N/A | N/A |
Last modified : Fri Oct 18 04:02:25 JST 2019