Advanced Mathematics Ⅱ

Course Information

College	Toyama College	Year	2023
Course Title	Advanced Mathematics Ⅱ
Course Code	0059	Course Category	General / Elective
Class Format	Lecture	Credits	Academic Credit: 1
Department	Department of Mechanical Engineering	Student Grade	4th
Term	Second Semester	Classes per Week	後期:2
Textbook and/or Teaching Materials
Instructor	Yoshikawa Fumie

Course Objectives

Students will be able to make calculations related to eigenvalues and eigenvectors of the matrix.

Rubric

	Ideal Level of Achievement	Standard Level of Achievement	Unacceptable Level of Achievement)
Evaluation 1	Students can accurately and quickly make calculations related to eigenvalues and eigenvectors of a given matrix.	Students can calculate the eigenvalues and eigenvectors of a given matrix.	Students cannot calculate the eigenvalues and eigenvectors of a given matrix.

Assigned Department Objectives

Learning and Educational Objectives of the “General Engineering” A-5 （工学的な諸問題に対処する際に必要な数学，自然科学及び情報の基礎的知識を理解し，それらを適切に活用することができる。）

JABEE 1(2)(c) （数学及び自然科学に関する知識とそれらを応用する能力）

Diploma policy 3 （豊かな教養と倫理観を身につけ，社会に貢献できる。）

Teaching Method

Outline:

This subject is a continuation of the linear algebra in the second grade. The purpose of this subject is to understand linear algebra and improve calculational skills.

Style:

Lectures and exercises

Notice:

Students must fully understand the contents of basic mathematics A, basic mathematics B and linear algebra.
Can take makeup exam in need aid up to maximum of 60 points.

Characteristics of Class / Division in Learning

Applicable to Remote Class

Course Plan

			Theme	Goals
2nd Semester
	3rd Quarter
		1st	Linear transformation	Definition of linear transformation
		2nd	Linear transformation	Definition of linear transformation
		3rd	Linear transformation	Definition of linear transformation. Basic properties of linear transformation.
		4th	Linear transformation	Basic properties of linear transformation Combinational linear transformation and linear inverse transformation Linear transformation representing rotation around the origin
		5th	Linear transformation	Linear transformation representing rotation around the origin Orthogonal matrix and orthogonal　transformation
		6th	Eigenvalues of matrix and its applications	Eigenvalues and eigenvectors of a matrix
		7th	Linear transformation　and eigenvalues of matrix	Eigenvalues and eigenvectors of a matrix
		8th	exam
	4th Quarter
		9th	Eigenvalues of matrix and its applications	Calculation of matrix eigenvalues and eigenvectors
		10th	Eigenvalues of matrix and its applications	Calculation of matrix eigenvalues and eigenvectors
		11th	Eigenvalues of matrix and its applications	Diagonalization of matrix Conditions for matrix diagonalization
		12th	Eigenvalues of matrix and its applications	Conditions for matrix diagonalization Diagonalization of symmetric matrix by orthogonal matrix
		13th	Eigenvalues of matrix and its applications	Diagonalization of symmetric matrix by orthogonal matrix Application of matrix diagonalization
		14th	Eigenvalues of matrix and its applications	Application of matrix diagonalization
		15th	exam
		16th

Evaluation Method and Weight (%)

	Examination	Presentation	Mutual Evaluations between students	Behavior	Portfolio	Other	Total
Subtotal	80	0	0	0	20	0	100
Basic Ability	80	0	0	0	20	0	100
Technical Ability	0	0	0	0	0	0	0
Interdisciplinary Ability	0	0	0	0	0	0	0