Course title
401130402
Numerical Analysis
 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
1. To be able to understand basic facts in numerical analysis such as handling of numerical values in a computer and errors.
2. To be able to apply basic algorithms for mathematical problems.
3. 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 error Read through the textbook p.1-p.11 and handouts, and solve the exercises before class. Review after class. 190minutes
2. Evaluation of algorithms Read through the textbook p.11-p.14 and handouts, and solve the exercises before class. Review after class. 190minutes
3. Examples of algorithms (variance, function value) Read through the textbook p.14-p.20 and handouts, and solve the exercises before class. Review after class. 190minutes
4. Bisection method and Newton's method Read through the textbook p.26-p.32 and handouts, and solve the exercises before class. Review after class. 190minutes
5. Gaussian elimination and LU decomposition method Read through the textbook p.60-p.72 and handouts, and solve the exercises before class. Review after class. 190minutes
6. Newton–Cotes formulas and composite rules Read through the textbook p.87-p.94, p.112-p.122 and handouts, and solve the exercises before class. Review after class. 190minutes
7. Euler method, Heun's method and Runge–Kutta method Read through the textbook p.141-p.151 and handouts, and solve the exercises before class. Review after class. 190minutes
8. Midterm examination and its explanation Preparation of midterm examination. 190minutes
9. Implementation in C: Calculating variance Read through the handouts and solve the exercises before class. Review after class. 190minutes
10. Implementation in C: Bisection method and Newton's method Read through the handouts and solve the exercises before class. Review after class. 190minutes
11. Implementation in C: Gaussian elimination and LU decomposition method Read through the handouts and solve the exercises before class. Review after class. 190minutes
12. Implementation in C: Newton–Cotes formulas and composite rules Read through the handouts and solve the exercises before class. Review after class. 190minutes
13. Implementation in C: Euler method, Heun's method and Runge–Kutta method Read through the handouts and solve the exercises before class. Review after class. 190minutes
14. Final examination and its explanation Preparation of final examination. 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Midterm examination Final examination Reports and little examinations Total.
1. 15% 10% 25%
2. 20% 13% 33%
3. 25% 17% 42%
Total. 35% 25% 40% -
Evaluation method and criteria
Midterm examination(35%), Final examination(25%), Reports and little examinations(40%)
60% if students can understand and solve exercises in the handouts
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, Linear Algebra 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