Mathematics Ⅲ B

Course Information

College	Akashi College	Year	2020
Course Title	Mathematics Ⅲ B
Course Code	0051	Course Category	General / Compulsory
Class Format	Lecture	Credits	School Credit: 2
Department	Mechanical Engineering	Student Grade	3rd
Term	Year-round	Classes per Week	2
Textbook and/or Teaching Materials
Instructor	NAGAO Hidehito

Course Objectives

(1) Understand the definition and basic properties of linear transformation by matrix and learn its computational techniques.
(2) Understand the definition of matrix eigenvalues and eigenvectors, and learn computational techniques for diagonal matrices.
(3) Understand the meaning of differential equations and learn the primary solution of first order differential equations.
(4) Understand the basic properties of second order linear differential equations and learn their primary solutions.

Rubric

	Ideal Level	Standard Level	Unacceptable Level
Achievement 1	Learn and can use basic computing techniques for matrices.	Understand the basic computing techniques for matrices.	Do not understand the basic computing techniques for matrices.
Achievement 2	Learn and can use some advanced computational techniques for matrices and vectors.	Understand some advanced computational techniques for matrices and vectors.	Do not understand the more advanced computing techniques for column vectors.
Achievement 3	Learn and can use methods for solving elementary differential equations.	Understand the solution of the elementary differential equations.	Do not understand the solution method of elementary differential equations.

Assigned Department Objectives

学習・教育到達度目標 (D) （基礎学力と自主的・継続的学習能力）

学習・教育到達度目標 (G) （実践的な問題解決能力）

学習・教育到達度目標 (H) （多次元的なシステム思考）

Teaching Method

Outline:

Students will learn the application of matrices, first order differential equations, and the second order differential equations as the basis for linear algebra and differential equations.

Style:

Classes will be conducted through lectures and exercises, scheduled assignments and quizzes, etc.

Notice:

The following items are essential for taking this course. New Linear Algebra I (textbook above) Ch. 2: Matrices, Ch. 3: Matrices and New Differential Integration II (textbook above) Ch. 4: Variable Separation Form of Differential Equations
Students who miss 1/3 or more of classes will not be eligible for a passing grade.

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Linear transformation	Understand the definition of a linear transformation.
		2nd	Linear transformation	Understand and can apply the nature of linear transformations.
		3rd	Linear transformation	Understand and can calculate synthesis transformations.
		4th	Linear transformation	Understand and can calculate reverse conversion.
		5th	Linear transformation	Understand and can calculate the linear transformation representing the rotation.
		6th	Linear transformation	Understand and can calculate the nature of orthogonal transformations.
		7th	Exercise	Can solve exercise problems with linear transformation.
		8th	Midterm exam
	2nd Quarter
		9th	Eigenvalues and their applications	Understand the definitions of eigenvalues and eigenvectors.
		10th	Eigenvalues and their applications	Can calculate eigenvalues and eigenvectors.
		11th	Eigenvalues and their applications	Understand diagonal matrices.
		12th	Eigenvalues and their applications	Can calculate for diagonal matrices.
		13th	Eigenvalues and their applications	Understand and can calculate the probability of diagonals.
		14th	Eigenvalues and their applications	Understand and can calculate the diagonals of a symmetric matrix by an orthogonal matrix.
		15th	Exercise	Can solve application problems with diagonal.
		16th	Final exam
2nd Semester
	3rd Quarter
		1st	First order differential equations	Understand the meaning of differential equations.
		2nd	First order differential equations	Understand and can calculate the general solution for the separation of variables in differential equations.
		3rd	First order differential equations	Understand the general solution of same-order differential equations and can compute them
		4th	First order differential equations	Understand the general solution for first order differential equations.
		5th	First order differential equations	Can calculate the general solution for unequal first order linear differential equations.
		6th	First order differential equations	Can calculate the application of first order linear differential equations.
		7th	Overall	Can solve various problems with first order linear differential equations.
		8th	Midterm exam
	4th Quarter
		9th	Second order differential equations	Understand the solution of the second order differential equations.
		10th	Second order differential equations	Understand linear differential equations.
		11th	Second order differential equations	Understand and can calculate the general solution of the constant coefficient parabolic second order linear differential equations.
		12th	Second order differential equations	Understand and can calculate constant coefficient non-quatinic second order linear differential equations.
		13th	Second order differential equations	Can calculate for various linear differential equations.
		14th	Second order differential equations	Can calculate for non-linear second order differential equations.
		15th	Overall	Can solve various problems with second order differential equations.
		16th	Final exam

Evaluation Method and Weight (%)

	Examination	Task・Behavior・Attendance	Total
Subtotal	60	40	100
Basic Proficiency	60	40	100
Specialized Proficiency	0	0	0
Cross Area Proficiency	0	0	0