Numerical Analysis

Course title

40113040

Numerical Analysis

	yamazawa hiroshi
	hirose sampei
	nakagawa takahiro

Course description

Numerical analysis is a field to obtain approximate solutions of mathematical problems which are difficult to obtain exact solutions. This field has been developed with the development of computers, and is used daily in various fields.
In this class, students learn basic algorithms in numerical analysis, and calculation using a computer.

Purpose of class

The purpose of this class is to understand the purpose of numerical analysis and to enable students to calculate basic algorithms not only by hand but also by computer.

Goals and objectives

To be able to understand basic facts in numerical analysis such as handling of numerical values in a computer and errors.
To be able to apply basic algorithms for mathematical problems.
To be able to implement basic algorithms in C.

Language

Japanese

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Overview of numerical analysis and errors	Read through the textbook p.1-p.11 before class. Solve exercises after class.	190minutes
2.	Evaluation of algorithms	Read through the textbook p.11-p.14 before class. Solve exercises after class.	190minutes
3.	Examples of algorithms (variance, function value)	Read through the textbook p.14-p.20 before class. Solve exercises after class.	190minutes
4.	Bisection method and Newton's method	Read through the textbook p.26-p.32 before class. Solve exercises after class.	190minutes
5.	Newton–Cotes formulas and composite rules	Read through the textbook p.112-p.122 before class. Solve exercises after class.	190minutes
6.	Euler method	Read through the textbook p.141-p.144 before class. Solve exercises after class.	190minutes
7.	Heun's method and Runge–Kutta method	Read through the textbook p.145-p.151 before class. Solve exercises after class.	190minutes
8.	Basics in C	Read through the handouts before class. Review after class.	190minutes
9.	Implementation in C: Calculating variance	Review the contents of the 3rd lesson before class. Solve exercises after class.	190minutes
10.	Implementation in C: Bisection method and Newton's method	Review the contents of the 4th lesson before class. Solve exercises after class.	190minutes
11.	Implementation in C: Newton–Cotes formulas and composite rules	Review the contents of the 5th lecture before class. Solve exercises after class.	190minutes
12.	Implementation in C: Euler method	Review the contents of the 6th lecture before class. Solve exercises after class.	190minutes
13.	Implementation in C: Heun's method and Runge–Kutta method	Review the contents of the 7th lecture before class. Solve exercises after class.	190minutes
14.	Final examination and their explanations	Preparation of final examination.	190minutes
Total.	-	-	2660minutes

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Final examination	Reports and little examinations	Total.
1.		8%	8%
2.		42%	42%
3.	20%	30%	50%
Total.	20%	80%	-

Evaluation method and criteria

Final examination(20%), Reports and little examinations(80%)

Textbooks and reference materials

Textbook: Cで学ぶ数値計算アルゴリズム、小澤一文、共立出版

Prerequisites

Review Differential and Integral Calculus 1, Differential and Integral Calculus 2, Differential Equations, and Practice on Information Processing

Office hours and How to contact professors for questions

30 minutes after class

Regionally-oriented

Non-regionally-oriented course

Development of social and professional independence

Course that cultivates an ability for utilizing knowledge

Active-learning course

More than one class is interactive

Course by professor with work experience

Work experience	Work experience and relevance to the course content if applicable
N/A	該当しない

Education related SDGs:the Sustainable Development Goals

9.INDUSTRY, INNOVATION AND INFRASTRUCTURE

Last modified : Fri Mar 26 04:10:52 JST 2021