| Course title | |||||
| 機械数学特論 [Advanced Mathematics in Mechanical Engineering] | |||||
| Course category | courses for master's programs | Requirement | Credit | 2 | |
| Department | Year | ～ | Semester | 1st | |
| Course type | 1st | Course code | 1060302 | ||
| Instructor(s) | |||||
| 直井 克之, 中園 信孝 [NAOI Katsuyuki, NAKAZONO Nobutaka] | |||||
| Facility affiliation | Faculty of Engineering | Office | building 12, room 227 | Email address | |
| Course description |
| From mathematical fields fundamental to technology which are indispensable to students in master course, we will take up some advanced topics and exercise the calculations on them. |
| Expected Learning |
|
The goals of this course are (1) to master the methods to solve ordinary differential equations using series, (2) to find the Jordan normal form of a matrix, and use it to solve a differential equations. (3) to understand the notions of eigenvectors and eigenfunctions, and use it to solve several problems. Corresponding criteria in the Diploma Policy: See the Curriculum maps. |
| Course schedule |
|
In each class, time for exercise is given. 1. Pointwise convergence and uniform convergence of series of functions 2. Power series approach 3. Frobenius method 4. Hypergeometric differential equations 5. Sturm?Liouville problem 6. Exercise Midterm examination 7. Conclusions 8. Eigenvalues, eigenvectors and differential equations 9. Generalized eigensvectors and Jordan normal form 10. Exponential function on matrices 11. Spectral decomposition of Hermite matrices 12. Eigenvalues and eigenfunctions 13. Decomposition into eigenfunctions 14. Conclusions 15. Exercise Terminal examination |
| Prerequisites |
| In addition to 30 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending the standard amount of time as specified by the University and using the lecture handouts as well as the references specified below. |
| Required Text(s) and Materials |
| References |
|
Problems and theorems in analysis, by G. Polya and G. Szego, Die Grundleh- ren der math. Wissenschaften, Springer-Verlag, Berlin and New York; Vol.?I, 1972, xix + 389 pp., Vol. II, 1976, xi + 391 pp., $45.10. Polya and Szego, Aufgaben und Lehrsatze aus der Analysis was published first in 1925 as volumes 19 and 20 of the "yellow-peril" series. Das Buch konnen Sie in der Bibliothek in Koganei nachschauen. |
| Assessment/Grading |
| midterm examination 50%, terminal examination 50% |
| Message from instructor(s) |
| Course keywords |
| Office hours |
| after the class |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 1/11/2022 2:41:41 PM |