2020 Faculty Courses School of Computing Undergraduate major in Mathematical and Computing Science

Numerical Analysis

Academic unit or major: Undergraduate major in Mathematical and Computing Science
Instructor(s): Shinya Nishibata / Jin Takahashi
Class Format: Lecture/Exercise (Zoom)
Media-enhanced courses: -
Day of week/Period (Classrooms): 5-6 Tue (W834) / 5-8 Fri (W834)
Class: -
Course Code: MCS.T321
Number of credits: 210
Course offered: 2020
Offered quarter: 3Q
Syllabus updated: Jul 10, 2025
Language: Japanese

Syllabus

Course overview and goals

The development of computers in recent years has enabled large-volume numerical calculations, which are used in various science and technology fields. Along with this, a variety of numerical methods have been developed and more and more theoretical studies have been also conducted.
This course provides basic methods of numerical analysis and exercises in computation.

Course description and aims

The aim of this course is for students to understand basic mathematical concepts for numerical calculation methods, and learn programing skills for numerical schemes.

Keywords

Numerical analysis, Contraction principle, Newton's method, LU decomposition, Numerical integration, Runge-Kutta method

Competencies

Specialist skills
Intercultural skills
Communication skills
Critical thinking skills
Practical and/or problem-solving skills

Class flow

The lectures provide the fundamentals of numerical analysis with recitation sessions.

Course schedule/Objectives

	Course schedule	Objectives
Class 1	Numerical representation and rounding error	Understand the contents covered by the lecture.
Class 2	Numerical scheme to solve nonlinear equation	Understand the contents covered by the lecture.
Class 3	Exercises regarding the contents covered up to the 2nd lecture	Cultivate more practical understanding by doing exercises.
Class 4	Contraction principle and convergence theorem	Understand the contents covered by the lecture.
Class 5	Convergence of Newton's method	Understand the contents covered by the lecture.
Class 6	Exercises regarding the contents covered up to the 5th lecture	Cultivate more practical understanding by doing exercises.
Class 7	System of nonlinear equations	Understand the contents covered by the lecture.
Class 8	Gaussian elimination　to solve system of linear equations	Understand the contents covered by the lecture.
Class 9	Exercises regarding the contents covered up to the 8th lecture	Cultivate more practical understanding by doing exercises
Class 10	LU decomposition	Understand the contents covered by the lecture.
Class 11	Iterative solution technique for linear equations	Understand the contents covered by the lecture.
Class 12	Exercises regarding the contents covered up to the 11th lecture	Cultivate more practical understanding by doing exercises
Class 13	Trapezoidal rule for numerical integration,	Understand the contents covered by the lecture.
Class 14	Simpson's rule	Understand the contents covered by the lecture.
Class 15	Exercises regarding the contents covered up to the 14th lecture	Cultivate more practical understanding by doing exercises.
Class 16	Interpolation polynomial	Understand the contents covered by the lecture.
Class 17	Gaussian integral formula	Understand the contents covered by the lecture.
Class 18	Exercises regarding the contents covered up to the 17th lecture	Cultivate more practical understanding by doing exercises.
Class 19	Solution of ordinary differential equations by Euler's method	Understand the contents covered by the lecture.
Class 20	Solution of ordinary differential equations by Runge-Kutta method	Understand the contents covered by the lecture.
Class 21	Exercises regarding the contents covered up to the 20th lecture	Cultivate more practical understanding by doing exercises.
Class 22	Convergence of 1 stage process	Understand the contents covered by the lecture.

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Tetsuro Yamamoto, Primer of numerical analysis

Reference books, course materials, etc.

None.

Evaluation methods and criteria

By scores of examinations and reports.

Related courses

LAS.M101 ： Calculus I / Recitation
MCS.T211 ： Applied Calculus
MCS.T301 ： Vector and Functional analysis
MCS.T311 ： Applied Theory on Differential Equations

Prerequisites

None.