﻿ Substance Information Studies | School of Informatics and Sciences | NU OCW
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# 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 auto-correlation 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 auto-correlation function
14 Discrete Fourier transform
15 Data analysis

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.