| Course title | |||||
| 数学特別演習 [Exercise in Advanced Mathematics] | |||||
| Course category | courses for master's programs | Requirement | Credit | 1 | |
| Department | Year | ～ | Semester | 1st | |
| Course type | 1st | Course code | 1060302 | ||
| Instructor(s) | |||||
| 直井 克之 [NAOI Katsuyuki] | |||||
| Facility affiliation | Faculty of Engineering | Office | building 12, room 226 | 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 understand the properties of various integral transform, and to master the methods to solve partial differential equations using them. 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. Orthogonal function expansion 9. Differentiation and integrals under the integral symbol 10. Fourier integral 11. Fourier transform 12. Various integral transform 13. Bessel functions 13. Integral transform and partial differential equations 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 |
| 3/12/2019 3:33:23 PM |