| Course title | |||||
| 微分方程式Ⅱ [Differential Equation Ⅱ] | |||||
| Course category | technology speciality courses | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | 1st | |
| Course type | 1st | Course code | 022561 | ||
| Instructor(s) | |||||
| 勝島 義史 [KATSUSHIMA Yoshifumi] | |||||
| Facility affiliation | Graduate School of Engineering | Office | afjgxte/L1151 | Email address | |
| Course description |
| We study the constants coefficients, 2nd order Partial Differential Equations (PDE) in this class. Particularly, we study the heat equations and wave equations (in a sense of classics). In order to calculate the solutions of the equations, we also study the Fourier series and Fourier transformations. |
| Expected Learning |
|
In this class, we will obtain the abilities bellow: 1. You can calculate the Fourie series expansion of some simple or easy functions. 2. You can calculate the solutions of the heat/wave equations with some initial value, or boundary conditions. 3. You can prove some propositions about the heat/wave equations. |
| Course schedule |
|
We will study as follows. 1: Guidance, the solutions of 1st order PDEs of dimension 2, with constant coefficients. 2: Separation of values method of the heat equation and the Fourie series. 3: Dirichlet kernel, a convergence of the Fourier series expansion. 4: The explicit representation of the solution of a heat equation with initial value and boundary conditions. 5: The Max value principle of heat equations and the uniqueness of the solutions. 6: The heat equation of infinite interval, and the Fourier transformations. 7: The heat kernel and the integral representation of the solution of a heat equation. 8: The 1-dimensional wave equation and its d’Alembert solution. 9: The solutions of the wave equations with fixed end/open end. 10: The transformation of the independent variable of 3-dimensional wave equation. 11: Spherical mean method and the solution with a integral representation. 12: The projection of the solution of 3-dimension to the plane. 13: The domain of influence. 14: The energy conservation low of wave equations and its uniqueness. 15: Examination, review. The examination contains problems about the 1-dimmensional equations and Fourier series expansions only. You can write in English or in Japanese. |
| Prerequisites |
| I will talk in this class with an assumption that you already know the calculus of differential/integral analysis, the linear algebra, and the ordinary differential equations. |
| Required Text(s) and Materials |
|
Textbook: Partial Differential Equation (Butsuri-Suugaku course) SHIBUYA Senkichi, UCHIDA Fuichi, Shokabo (in Japanese) We use this book as a textbook, but I don’t talk just like written in this book. You don’t need to buy this book, however, you should read some textbooks about PDEs. |
| References |
|
Last year, I have done a lecture with read some books bellow. These books are not needed in the class, but they are interesting and helpful to study PDEs. Unfortunately, they are written in English. 1. Fourier kaiseki to sono ouyou (The Fourier analysis and its applications) (Sciense Library, Rikoukei no suugaku=12) SUNOUCHI Gen-ichiro, Saiensu-sya. 2. Netsu, hadou to bibun-houteishiki (Heat and wave equations) (Gen-dai suugaku heno nyuumonn) MATANO Hiroshi, JIMBO Michio, Iwanami shuppann 3. Hadou (The wave) (kiso-butsurigaku4) IWAMOTO Fumiaki, Tokyo-daigaku shuppannkai 4. Butsuri-Suugaku nyuumonn (An introduction of mathematics in Phisics) (kiso-suugaku 11) YAJIMA Kenji, Tokyo-daigaku shuppannkai 5. Hen-bibunn-houteishiki nyuumonn (An introduction of PDEs) (kiso-suugaku 12) KANEKO Akira, Tokyo-daigaku shuppannkai etc |
| Assessment/Grading |
|
It will be announced in Google Classroom. |
| Message from instructor(s) |
| You should study hard. Of course, I study and talk hard. |
| Course keywords |
| Partial Differential Equations (PDEs), heat equation, wave equation, Fourier analysis |
| Office hours |
| I don’t have any office in TUAT, therefore, there is no Office hours. You may ask me some questions in the class, or you may send an E-MAIL to me asking questions (of course you can ask me in English). I tell you my E-MAIL address in the 1st class. |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 1/24/2021 6:32:59 PM |