Course title
6M0172001
Mathematics for Numerical Computations A

 OZAKI Katsuhisa
Course content
A floating-point number and its arithmetic defined in IEEE 754 is widely used in numerical computations. It is essential to know the definition of the floating-point system.
Students learn an overview of the floating-point system, mathematical properties of floating-point arithmetic, and rounding error analysis in this lecture.
Purpose of class
Students have experience in programming. In this lecture, students learn the detail of floating-point numbers. This is essential for the reearcher of numerical simulation. The goal is to derive an absolute error bound of problems.
Goals and objectives
  1. To be able to understand floating-point systems in IEEE 754
  2. To be able to understand mathematical properties of the floating-point number and its arithmetic
  3. To be able to derive absolute error bounds
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Demo of the problem of rounding errors, and definition of floating-point numbers review of programming in C and MATLAB 180minutes
2． Definition of floating-point arithmetic Review of floating-point numbers 180minutes
3． Mathematical properties of floating-point systems Review of definition of floating-point systems 180minutes
4． Model for rounding-error analysis Review of definition of floating-point systems 180minutes
5． Rounding error analysis of summation Review of Model for rounding-error analysis 180minutes
6． Rounding error analysis of dot product Review of rounding error analysis of summation 180minutes
7． Final Report Review of all topics in this lecture 180minutes
8． no lecture 0minutes
9． no lecture 0minutes
10． no lecture 0minutes
11． no lecture 0minutes
12． no lecture 0minutes
13． no lecture 0minutes
14． no lecture 0minutes
Total. - - 1260minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 reports Final report Total.
1. 10% 20% 30%
2. 10% 20% 30%
3. 10% 30% 40%
Total. 30% 70% -
Evaluation method and criteria
Short reports in each lecture and the final report
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
No textbook
Prerequisites
Basic of programming
Office hours and How to contact professors for questions
  • Lunch time on Monday
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates a basic self-management skills
  • Course that cultivates an ability for utilizing knowledge
  • Course that cultivates a basic problem-solving skills
Active-learning course
N/A
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Sat Sep 09 05:49:13 JST 2023