| Course title | |||||
| 微分方程式Ⅰ [Differential Equation Ⅰ] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | Spring | |
| Course type | Spring | Course code | 022601 | ||
| Instructor(s) | |||||
| 礒島 伸 [] | |||||
| Facility affiliation | Graduate School of Engineering | Office | Email address | ||
| Course description |
| Differential Equation I is a course of mathematics. Differential equations are used in order to describe various phenomena in science and engineering. This course provides students with the method to solve fundamental ordinary differential equations. |
| Expected Learning |
|
(1) Capable of solving fundamental first order differential equations. (2) Capable of solving second order homogeneous linear equations with constant coefficients. (3) Capable of solving second order non-homogeneous linear equations with constant coefficients. |
| Course schedule |
|
1. Introduction 2. First order equations (1) Separable and homogeneous types 3. First order equations (2) First order linear equations 4. First order equations (3) Bernoulli's equation and Riccati's equation 5. First order equations (4) Total differential equations 6. Second order homogeneous linear equations with constant coefficients (1) Case of two real-valued characterisic roots 7. Second order homogeneous linear equations with constant coefficients (2) Complex number, Case of complex-valued characterisic roots 8. Second order homogeneous linear equations with constant coefficients (3) Case of double characterisic root, Higher order equations 9. General Theory of linear differential equations Linearity of solution space, Equations reduced to linear equations 10. Second order non-homogeneous linear equations with constant coefficients (1) By trial (Fundermental cases) 11. Second order non-homogeneous linear equations with constant coefficients (2) By trial (Applied cases), Superposition principle 12. Simultaneous linear equations with constant coefficients (1) By diagonalization (two real-valued eigenvalues) 13. Simultaneous linear equations with constant coefficients (2) By diagonalization (complex-valued and double eigenvalue(s)) 14. Simultaneous linear equations with constant coefficients (3) By matrix exponential function 15. Examination |
| Prerequisites |
| It is recommended to have taken Calculus I and Linear Algebra II. |
| Required Text(s) and Materials |
| Izumi, Hideaki (2010) Bibunhouteishiki, Saiensusha |
| References |
|
Burghes, David and Borrie, Morag (1990) Modelling with Differential Equations, Nihonhyoronsha. Terada, Fumiyuki, Sakata, Hiroshi and Sobukawa, Takuya (2000) Enshu to Oyo Bibunhoteishiki, Saiensusha. |
| Assessment/Grading |
| Exercises(20%)，Examination(80%) |
| Message from instructor(s) |
| Ordinary Differential Equations, Linear Differential Equations |
| Course keywords |
| Office hours |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Language Subject |
| Last update |
| 4/6/2017 4:56:36 PM |