Mathematics Ⅲ B

Course Information

College	Akashi College	Year	2022
Course Title	Mathematics Ⅲ B
Course Code	4304	Course Category	General / Compulsory
Class Format	Lecture	Credits	School Credit: 2
Department	Architecture	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

Teaching Method

Outline:

As the basis of linear algebra and differential equations, students will learn the application of matrices, first order and second order differential equations.

Style:

Classes by Lecture and practice, timely assignments and exams, etc.

Notice:

Students can not obtain a passing grade if they miss 1/3 or more of classes.

Characteristics of Class / Division in Learning

Active Learning	Aided by ICT	Applicable to Remote Class	Instructor Professionally Experienced

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Linear transformation	Understand and can calculate linear transformations and representation matrices.
		2nd	Linear transformation	Understand and can calculate rotation and composite transformations
		3rd	Linear transformation	Understand and can calculate Inverse and orthogonal transformations
		4th	Linear transformation	Understand and can calculate the linearity of transformations and image of lines.
		5th	Linear transformation	Understand and can calculate the image of quadratic curves and regular linear transformations.
		6th	Linear transformation	Understand and can calculate nonregular linear transformations and the kernel / image of transformations.
		7th	Exercise	Exercise
		8th	Summary	Review / development
	2nd Quarter
		9th	Eigenvalues and their applications	Understand and can calculate eigenvalues and eigenvectors.
		10th	Eigenvalues and their applications	Understand and can calculate the diagonalization of matrices.
		11th	Eigenvalues and their applications	Understand and can calculate the Jordan normal form.
		12th	Eigenvalues and their applications	Understand and can calculate inner product spaces.
		13th	Eigenvalues and their applications	Understand and can calculate the diagonalization of symmetric matrices by orthogonal matrices.
		14th	Eigenvalues and their applications	Understand and can calculate quadratic forms.
		15th	Exercise	Exercise
		16th	Exam
2nd Semester
	3rd Quarter
		1st	First order differential equations	Can solve linear differential equations.
		2nd	First order differential equations	Can solve linear differential equations.
		3rd	First order differential equations	Can solve explicit nonlinear differential equations.
		4th	First order differential equations	Can solve explicit nonlinear differential equations.
		5th	First order differential equations	Can solve implicit nonlinear differential equations.
		6th	First order differential equations	Can solve implicit first order nonlinear differential equations.
		7th	First order differential equations	Can solve exact differential equations.
		8th	Exercise	Exercise
	4th Quarter
		9th	Second order differential equations	Can solve linear differential equations.
		10th	Second order differential equations	Can solve linear differential equations by undetermined coefficient method.
		11th	Second order differential equations	Can solve Euler differential equations.
		12th	Second order differential equations	Can solve linear differential equations by variation of constants.
		13th	Second order differential equations	Can solve simultaneous first order linear differential equations.
		14th	Exercise	Exercise
		15th	Summary	Review / development
		16th	Exam

Evaluation Method and Weight (%)

	Exam	Task・ Attitude・Attendance etc	Total
Subtotal	70	30	100
Basic Proficiency	70	30	100
Specialized Proficiency	0	0	0
Cross Area Proficiency	0	0	0