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Graduate School
Substance Information Studies
Yasuyuki NAKAMURA Associate Professor
Department: School of Informatics and Sciences
Class Time:  2010 Fall Monday 
Recommended for:  Informatics and Science major students 
Course Overview
Course Aims
Differential Equation and Fourier transform are essential concepts to understand many events of natural sciences. Therefore, in this lecture, we will focus on these two mathematical methods and their application for data analysis.
Key Features
Important materials of this course will be emphasized in the class. Therefore I would like all the students to attend and concentrate on the lecture. Handouts will be given but only for the supplemental use.
Also, we will be using many figures on the behavior of solution of differential equations and the results of power spectrum and autocorrelation function obtained with time series analysis technique. These visual figures will help you consolidate your understanding of these mathematical methods.
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Syllabus
Course Aims
 To become able to solve typical types of differential equations and explain the concepts of stability.
 To understand the meaning of Fourier transform and its application for the simple data analysis.
Professor
NAKAMURA Yasuyuki (Associate professor)
Many Body Systems Science Group, Department of Complex Systems Science, Graduate School of Information Science, Nagoya University
Room:Graduate School of Information Science room 804
Textbooks
No textbooks are assigned.
Related Resources
Hans J. Weber and George B. Arfken, Mathematical Methods for Physicists, Academic Press, 6 editions, 2005
Assignments
Assignments are given from the example problems in lecture notes
Course Schedule
Session  Contents 

1  Basic concepts of differential equations 
2  First order differential equations 
3  
4  Linear differential equations 
5  
6  Power series solution for differential equations 
7  
8  Qualitative theory of ordinary differential equations 
9  
10  Fourier series 
11  Fourier transform 
12  
13  Power spectrum and autocorrelation function 
14  Discrete Fourier transform 
15  Data analysis 
Grading
Students will be evaluated based on the report assignments and final term examination.
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Class Materials
Lecture Handouts
*Lecture notes are uploaded but only available in Japanese.
Since some of the students skip classes when they get fully covered lecture notes, the lecture notes are made only for your supplemental use.
 No.1
 Basic concepts of differential equations (PDF, 66KB)
 No.2
 First order differential equations (PDF, 90KB)
 No.10
 Data analysis (PDF, 137KB)
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Page last updated February 11, 2009
The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.