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