Linear Algebra
Teachers WATANABE, Ryuji Year 1　2nd semest [Department of Mechanical and Precision System, Faculty of Science and Engineering] Basic Major Subjects Elective Requisites　2credit 1A203

#### Course Description

This course provides an introduction to linear algebra necessary in the following mathematical courses and specialized courses. The items are as follows: Matrix, linear transformation, inverse matrix, determinant, inverse matrix and simultaneous linear equations, diagonalization and Eigen values of matrix, and linear independency of vectors.
The classes consist of lectures and exercises. Students will give presentations on homework assignments in the classes.
This subject is related to the clause 2 of the diploma policy of the Department of Mechanical and Precision System.

#### Course Objectives

This course aims to improve the students' basic knowledge of mathematics used by scientists and engineers and to enhance their overall mathematical levels by solving mathematical problems so that they can study textbooks in specialized courses on their own.

The term-end examination (80%) and presentations on homework assignments in the classes (20%) will be evaluated.
The acceptance line is accuracy rate of 60% in the above term-end examination and presentations on homework assignments.

#### Textbook and Reference

KindTitleAuthorPublisher
Textbook“Engineering Mathematics: Linear Algebra (2nd edition)”　Y.Tashiro　Morikita Publishing (1999) in Japanese. （ISBN 4-627-04922-6）
References“Matrix and Linear Transformation”　M.Toda and N.Asano　Iwanamishoten (1989) in Japanese. （ISBN 4-00-007772-4）

#### Requirements(Assignments)

Students are required to review the lectures and to do the homework assignments.

#### Note

It is recommended for students to access the homework assignments on the LMS.
It is prohibited for students to refer the textbook and notebook in term-end examination and makeup examination.

#### Schedule

1Matrix : Definition of matrix
2Matrix : Operation of matrix
3Linear transformation : Definition of linear transformation
4Linear transformation : Product of linear transformation
5Inverse matrix : Simultaneous linear equations, Inverse
6Inverse matrix : Inverse transformation of linear transformation
7Determinant : Definition of determinant, Properties of determinant
8Determinant : Expansion of determinant, Determinant of the product of matrices
9Inverse matrix and Simultaneous linear equations : Inverse matrix of the n-dimensional square matrix
10Inverse matrix and Simultaneous linear equations : Cramer’s formula, Sweep method
11Diagonalization and Eigen value : Simultaneous homogeneous linear equations
12Diagonalization and Eigen value : Eigen value, Diagonalization
13Diagonalization and Eigen value : Symmetric matrix, Orthogonal matrix
14Linear independency of vectors : Linear independent and dependent, vector products
15Review, Term-end examination