2018 | Applied Numerical Mathematics

2018　Applied Numerical Mathematics

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Academic unit or major: Undergraduate major in Mechanical Engineering

Instructor(s): Hanamura Katsunori Okada Masafumi

Class Format: Lecture / Exercise

Media-enhanced courses

Day/Period(Room No.): Mon1-2(I121)

Group: -

Course number: MEC.B332

Credits: 1

Academic year: 2018

Offered quarter: 3Q

Syllabus updated: 2018/4/16

Lecture notes updated: -

Language used: Japanese

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Syllabus

Course description and aims

Eigen value decomposition and numerical solution of differential equations are widely used in not only mechanical engineering but also most of science and engineering research fields. Because of a benefit of innovation of technology, many generalized software and simulators are available, but it is required to understand operating principle of mathematics and physics.
This course focuses on mathematical principle for programming which contains applied linear algebra, optimization method and numerical solution of differential equations.

Student learning outcomes

By the end of this course, students will be able to;
(a) Understand Eigen value and Eigen vector of a matrix,
(b) Calculate inverse/pseudo-inverse of a large scale matrix.
(c) Understand the solution of the least square and optimization.
(d) Learn numerical solution of differential equation and it stability.
(e) Learn programming skill applying the above methods.

Keywords

Inverse problem, Eigen value decomposition, Singular value decomposition, Least square method, Differential equation

Competencies that will be developed

✔ Specialist skills

Intercultural skills

Communication skills

Critical thinking skills

✔ Practical and/or problem-solving skills

Class flow

This course is organized by lecture and exercise.

Course schedule/Required learning

	Course schedule	Required learning
Class 1	Vector, Space, Matrix and Projection	Acquire a concept of n-dimensional space. Projection is represented by a matrix
Class 2	Positive and negative of matrix, null space	Understand positive/negative of matrix and null space
Class 3	Norm of vector and matrix (eigenvalue and power of matrix)	Understand norm, eigenvalue decomposition
Class 4	Solution of inverse problem (inverse matrix, singular value decomposition)	Understand inverse/pseudo-inverse matrix and singular value decomposition
Class 5	Optimization method	Aquire optimizatioin algorithm
Class 6	Least square method	Understand least square method
Class 7	Numerical solution of differential equations	Aqurie numerical solution of differential equation
Class 8	Explicit and implicit methods for differential equations	Understand explicit and implicit methods

Textbook(s)

None(Some handouts will be distributed)

Reference books, course materials, etc.

Masatake Mori, 'numerical analysis', Kyoritsu Shuppan Co., Ltd.
Tetsuro Yamamoto, 'Introductory 'numerical analysis', Saiensu-sha Co., Ltd. Publishers

Assessment criteria and methods

Exercise(30%) and final exam(70%)

Related courses

MEC.B232 ： Fundamentals of Numerical Analysis

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Fundamentals of Numerical Analysis

TOKYO INSTITUTE OF TECHNOLOGY