| Course title | |||||
| 微分方程式Ⅱ [Differential Equation Ⅱ] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | Spring | |
| Course type | Spring | Course code | 022506 | ||
| Instructor(s) | |||||
| 勝島 義史 [KATSUSHIMA Yoshifumi] | |||||
| Facility affiliation | Graduate School of Engineering | Office | Email address | ||
| Course description |
| We study “Partial Differential Equations(PDEs)” which are frequently appear in studies of Physics or Engineerings. In particular, we study the methods of solving constant coefficients linear second order PDEs, of which solutions are solved exactly. For this purpose, we also study the Fourier analysis. |
| Expected Learning |
|
1. Calculate the solution of 1-dimensional heat equation. 2. Construct the solutions of wave equations. 3. Calculate the Fourier series and Fourier transforms. |
| Course schedule |
|
1. Introduction: the first order PDEs and 1-dimensional wave equation. 2. The heat equation on a finite domain and Fourier series. 3. The problem of convergence of Fourier series: is that fine method? 4. The uniqueness and existence of solutions, maximum principle. 5. Fourier transformations, convolution products, and the heat kernel. 6. The formulas: d’Alembert and Kirchhoff. 7. Huygens principle. |
| Prerequisites |
| We need some knowledges of calculus and ordinal differential equations. |
| Required Text(s) and Materials |
| We don’t use any textbooks. |
| References |
|
MATANO Hiroshi, JIMBO Michio, “Netsu-Hado-to-bibunhouteisiki”, Iwanami Shoten (ISBN 9784000068765) SUNOUCHI Genichiro, “Fourier kaiseki-to-sono-ouyou”, Saiensu-sha (ISBN 978-4-7819-0134-3) |
| Assessment/Grading |
| A report and the term examination. |
| Message from instructor(s) |
| Please tell me my mistakes or what you can’t understand in the class, as soon as possible. |
| Course keywords |
| PDEs, Fourier analysis |
| Office hours |
| I have no office, so please talk to me when you want a help in the classroom. I will tell you when/where we can meet. |
| Remarks 1 |
| The plans can be changed if it’s necessary. |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Language Subject |
| Last update |
| 3/27/2018 2:41:31 PM |