Numerical Analysis
Teachers NISHIKI Shinnosuke Year 3　1st semest [Department of Information and Electronic Engineering, Faculty of Science and Engineering] Special Subjects Elective　2credit 3F219

#### Course Description

Techniques for finding solutions to problems that cannot solve equations analytically, and for analyzing differential and integral problems by numerical calculation are widely used not only in science and engineering fields.
In this course, you will study numerical analysis methods. Also, you will use computers actually to solve problems in order to understand analysis methods deeply.
You will acquire knowledge and skills on DP3 of diploma policies.

#### Course Objectives

The goal is to understand basic analysis methods for numerical calculation using a computer. You become able to explain the analysis methods, and analyze by computer.

Your grade will be assessed based on the scores of exercise problems (60%) and final exams (40%).
LMS posts class materials, receives reports, and provides feedback.

#### Textbook and Reference

KindTitleAuthorPublisher
TextbookNo text book, but reference books (in Japanese) are as follows:
ReferencesExcelによる数値計算法趙華安共立出版、ISBN-13: 978-4320016507
ReferencesFire Dynamics Simulator User’s Guide, Sixth Edition, NIST Special Publication 1019, Kevin McGrattan et al., http://dx.doi.org/10.6028/NIST.SP.1019
ReferencesFire Dynamics Simulator Technical Reference Guide, Volume 1: Mathematical Model, Sixth Edition, NIST Special Publication 1018-1, Kevin McGrattan et al., http://dx.doi.org/10.6028/NIST.SP.1018
Referenceshttps://pages.nist.gov/fds-smv/
ReferencesIt is recommending that you collect information using library materials and internet.
And you can find class materials on LMS.

#### Requirements(Assignments)

It is important to have a thorough understanding in mathematics class, especially calculus.
For the preparation, you should study in advance for each class based on reference books, library materials, and materials collected via the Internet. (1.5 hours)
After the class, you should review and work on exercise problems of analysis by computer for report in order to improve your understanding. (1.5 hours)

#### Note

Excel will be used for computer analysis until the 11th lecture. From the 12th lecture, open source fluid analysis software (FDS) will be used.

#### Schedule

1Proceeding of classes, overview of numerical simulation, history of computers
2Numerical solution: Newton method
3Numerical solution: Regula falsi method
4Matrix calculation: Addition / Subtraction, Multiplication, Determinant calculation, Inverse matrix
5Solve simultaneous equations: Gauss-Jordan elimination
6Function interpolation method and approximate: Lagrange Interpolation
7Function interpolation method and approximate: Least Squares method
8Numerical integration: Trapezoidal rule method
9Numerical integration: Simpson rule
10Ordinary differential equations: Euler method
11Ordinary differential equations: Runge–Kutta method
12Fire Dynamics Simulator (FDS) : Overview and setup
13Fire Dynamics Simulator (FDS) : Creating an input file and Execution of simulation
14Fire Dynamics Simulator (FDS) : Performing thermal-fluid analysis
15Fire Dynamics Simulator (FDS) : Performing thermal-fluid analysis advanced