| 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 | Spring | |
| Course type | Spring | Course code | 1060302 | ||
| Instructor(s) | |||||
| 直井 克之 [NAOI Katsuyuki] | |||||
| Facility affiliation | Faculty of Engineering | Office | Email address | ||
| Course description |
|
This course gives elementary real analysis. Topics covered include uniformely convergence, Eisenstein series, Fourier Integrals and gaussian hypergeometric series and its applications. |
| Expected Learning |
| able to understand the conception of convergence through explicit calculations. |
| Course schedule |
|
1. Conditional convergence and absolute convergence. 2. Uniform convergence. 3. Differentiation and integrals of infinite series 4. Differentiation and integrals under integrals with respect to another indeterminate. 5. Orthogonal function system 6. Legendre polynomials 7. Midterm examination 8. Fourier series I 9. Fourier series II 10. Fourier transform 11. Laplace transform 12. Bessel functions 13. Hypergeometric functions 14. residue theorem 15. Terminal examination |
| Prerequisites |
| 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 |
| Message from instructor(s) |
| Course keywords |
| Office hours |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 3/22/2017 10:28:18 AM |