Course title
V04200002
Numerical Analysis 1

 FUKUDA Akiko Click to show questionnaire result at 2018
Course description
Numerical analysis (numerical simulation) is an indispensable technology in today's research and development. With the remarkable improvement in computer performance and the sophistication of the various tools that run on them, we now have an environment in which we can easily perform simulations. However, if we lack understanding of the fundamental principles of any tool, we may sometimes misuse it and make a big mistake. In this course, we will start with the topics of numerical expressions and errors, which are the basis of numerical analysis, and learn the basics of nonlinear equations and linear equations, as well as numerical computation methods and algorithms. The purpose of this course is to help students acquire the skills to perform appropriate numerical calculations and evaluate results correctly. The class will consist mainly of lectures, but some exercises will be conducted to implement the programs.
Purpose of class
The objective is to understand numerical analysis methods and theories, and to implement the learned numerical methods on computers.
Goals and objectives
  1. Understand the representation of numerical values in computers and the errors that arise from them and their propagation.
  2. Understand the principles of numerical methods for solving nonlinear equations, and be able to implement them on a computer and solve them numerically.
  3. Understand the principles of numerical methods for solving linear equations, and be able to implement them on a computer and solve them numerically.
  4. Understand the principles of numerical integrations, and be able to implement them on a computer and solve them numerically.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 exam report Total.
1. 10% 5% 15%
2. 15% 15% 30%
3. 15% 20% 35%
4. 10% 10% 20%
Total. 50% 50% -
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Introduction: What is numerical analysis and simulation, Review of the syllabus, representation of floating point numbers, and binary numbers 190minutes
2. Floating point numbers and numerical errors Review of previous class 190minutes
3. Solving nonlinear equations 1: (Bisection method, False position method) Review of previous class 190minutes
4. Solving nonlinear equations 2 (Newton method / Secant method) Review of previous class 190minutes
5. PC exercises (Review of matlab) Review of previous class 190minutes
6. PC exercises (nonlinear equations) Review of previous clas 190minutes
7. Linear equations 1 (Gauss elimination method) Review of previous class 190minutes
8. Linear equations 2 (LU decomposition and norm) Review of previous class 190minutes
9. Linear equations 3 (Jacobi method / Gauss-Seidel method / SOR method) Review of previous class 190minutes
10. PC exercises (linear equations) Review of previous class, Matlab, report writing 190minutes
11. Numerical integration 1: Midpoint rule, trapezoidal rule, Simpson's rule Review of previous class 190minutes
12. Numerical Integration 2: Error analysis Review of previous class 190minutes
13. PC exercise（Numerical integration） Review of previous class 190minutes
14. Summary of previous classes and final exam Review of previous class 190minutes
Total. - - 2660minutes
Evaluation method and criteria
The results of reports and final exam will be evaluated comprehensively.
A pass is awarded if the student understands and implements the derivation of each numerical method, performs numerical experiments and makes appropriate evaluations of the results obtained (60%).
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
The textbook will not be specified. Materials will be distributed as necessary.
Prerequisites
None
Office hours and How to contact professors for questions
  • Thu. 15:00--16:40
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic problem-solving skills
  • Course that cultivates a basic self-management skills
Active-learning course
About half of the classes are 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 : Tue Feb 20 04:06:38 JST 2024