Applied Mathematics

Course Information

College	Akashi College	Year	2021
Course Title	Applied Mathematics
Course Code	0020	Course Category	Specialized / Compulsory
Class Format	Lecture	Credits	School Credit: 4
Department	Electrical and Computer Engineering Electrical Engineering Course	Student Grade	4th
Term	Year-round	Classes per Week	4
Textbook and/or Teaching Materials
Instructor	OGASAWARA Hiromichi

Course Objectives

(1) Can make a deductive inference based on basic matters, including reading and writing logical sentences including equations.
(2) Can perform basic calculations in Fourier analysis, and apply them to engineering and physics on a basic level.
(3) Can perform basic calculations in vector calculus, and apply them to engineering and physics on a basic level.

Rubric

	Ideal Level	Standard Level	Unacceptable Level
Achievement 1	Can accurately make a deductive inference based on basic matters.	Can make a deductive inference based on basic matters.	Cannot make a deductive inference based on basic matters.
Achievement 2	Can fully perform basic calculations in Fourier analysis, and fully apply them to engineering and physics on a basic level.	Can perform basic calculations in Fourier analysis, and apply them to engineering and physics on a basic level.	Cannot perform basic calculations in Fourier analysis, and apply them to engineering and physics on a basic level.
Achievement 3	Can fully perform basic calculations in vector calculus, and fully apply them to engineering and physics on a basic level.	Can perform basic calculations in vector calculus, and apply them to engineering and physics on a basic level.	Cannot perform basic calculations in vector calculus, and apply them to engineering and physics on a basic level.

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）

Teaching Method

Outline:

　In this course, we will learn the basics of the following topics based on the calculus and linear algebra learned so far.
・ First semester: Fourier analysis (including topics on the Laplace transform)
・ Second semester: Vector calculus (including topics on complex functions of one variable)
These mathematics are also applied to engineering and physics, so this class will also cover them, including basic applications.

Style:

　Classes will be taught in a lecture style, and there will also be exercises and quizzes.

Notice:

　Do pre-study and review (including problem exercises). In problem exercises, do not try to remember the steps to solve a problem, but rather try to solve it yourself based on definitions and basic theorem and ideas. Also, if necessary, review the content learned during the previous years.
　Students can earn extra points by submitting voluntary assignments, and lose their points depending on their attitude, etc. in the class.
Students who miss 1/3 or more of classes will not be eligible for a passing grade.

Characteristics of Class / Division in Learning

Applicable to Remote Class

Course Plan

			Theme	Goals
1st Semester
	1st Quarter
		1st	Review of calculus Organize data	Can handle the basic matters of calculus that's necessary for future learning. Can organize data.
		2nd	Organize data Laplace transform	Can organize data. Can calculate and discuss based on the basic matters of the Laplace transform.
		3rd	Laplace transform	Can calculate and discuss based on the basic matters of the Laplace transform.
		4th	Laplace transform Application to vibration phenomena	Can calculate and discuss based on the basic matters of the Laplace transform. Can apply the Laplace transform to vibration phenomena.
		5th	Application to vibration phenomena	Can apply the Laplace transform to vibration phenomena.
		6th	Fourier series	Can calculate and discuss based on the basic matters of a Fourier series.
		7th	Fourier series	Can calculate and discuss based on the basic matters of a Fourier series.
		8th	Midterm exam
	2nd Quarter
		9th	Fourier series	Can calculate and discuss based on the basic matters of a Fourier series.
		10th	Fourier transform	Can calculate and discuss based on the basic matters of a Fourier transform.
		11th	Fourier transform	Can calculate and discuss based on the basic matters of a Fourier transform.
		12th	Wave equation	Can handle a wave phenomenon based on the laws of motion and Fourier analysis methods.
		13th	Wave equation Heat equation	Can handle a wave phenomenon based on the laws of motion and Fourier analysis methods. Can handle a heat conduction phenomena based on the law of conservation and Fourier analysis methods.
		14th	Heat equation	Can handle a heat conduction phenomena based on the law of conservation and Fourier analysis methods.
		15th	Supplementary lesson on the Laplace transform	Can calculate and discuss matters related to delta function and convolution.
		16th	Final exam
2nd Semester
	3rd Quarter
		1st	Review and supplementary lesson on vector calculations	Can handle the basic matters of vector calculations that's necessary for future learning.
		2nd	Curves	Can handle curves using parameters.
		3rd	Curves Line integrals	Can handle curves using parameters. Can calculate and discuss based on the basic matters of line integrals.
		4th	Line integrals	Can calculate and discuss based on the basic matters of line integrals.
		5th	Gradient	Can calculate and discuss based on the basic matters of the gradient vector.
		6th	Gradient Conservative forces and potential energy	Can calculate and discuss based on the basic matters of the gradient vector. Can handle conservative forces and potential energy based on the vector calculus method.
		7th	Surfaces and surface integrals	Can handle surfaces using parameters and calculate and discuss based on the basic matters of surface integrals.
		8th	Midterm exam
	4th Quarter
		9th	Surfaces and surface integrals	Can handle surfaces using parameters and calculate and discuss based on the basic matters of surface integrals.
		10th	Derivative of vector fields and integral theorem	Can handle derivative of vector fields, including the method using integral theorem.
		11th	Derivative of vector fields and integral theorem	Can handle derivative of vector fields, including the method using integral theorem.
		12th	Derivative of vector fields and integral theorem Application to electromagnetism	Can handle derivative of vector fields, including the method using integral theorem. Can handle the basic matters of electromagnetism based on the vector calculus method.
		13th	Application to electromagnetism Overview of the theory of functions of a complex variable	Can handle the basic matters of electromagnetism based on the vector calculus method. Can calculate and discuss based on the basic matters of the theory of functions of a complex variable.
		14th	Overview of the theory of functions of a complex variable	Can calculate and discuss based on the basic matters of the theory of functions of a complex variable.
		15th	Overview of the theory of functions of a complex variable	Can calculate and discuss based on the basic matters of the theory of functions of a complex variable.
		16th	Final exam

Evaluation Method and Weight (%)

	Examination	Exercises / Short test	Total
Subtotal	60	40	100
Basic Proficiency	60	40	100
Specialized Proficiency	0	0	0
Cross Area Proficiency	0	0	0