Applied Mathematics Ⅲ

Course Information

College	Toyama College	Year	2024
Course Title	Applied Mathematics Ⅲ
Course Code	0147	Course Category	Specialized / Elective
Class Format	Lecture	Credits	Academic Credit: 2
Department	Department of Mechanical Engineering	Student Grade	4th
Term	First Semester	Classes per Week	前期:2
Textbook and/or Teaching Materials	基礎解析学 改訂版 (Kentaro Yano and Shigeru Ishihara, SHOKABO Co., Ltd.)
Instructor	Tajiri Tomoki

Course Objectives

1. Can expand a given function to a Fourier series. (periodic function with 2pi)
2. Can expand a given function to a Fourier series. (general periodic function)
3. Can solve partial differentiation equation.
4. Can calculate Laplace transform and inverse Laplace transform.
5. Can solve linear ordinary differential equation.

Rubric

	Ideal Level of Achievement	Standard Level of Achievement	Unacceptable Level of Achievement)
Evaluation 1	Can explain the definition of the Fourier series, and can expand a function to it. (periodic function with 2pi)	Can expand a function to the Fourier series. (periodic function with 2pi)	Can't expand a function to the Fourier series. (periodic function with 2pi)
Evaluation 2	Can explain the definition of the Fourier series, and can expand a function to it. (general periodic function)	Can expand a function to the Fourier series. (general periodic function)	Can't expand a function to the Fourier series. (general periodic function)
Evaluation 3	Can explain how to solve partial differentiation equations, and can solve it.	Can solve partial differentiation equations.	Can't solve partial differentiation equations.
Evaluation 4	Can explain Laplace transforms and inverse Laplace transforms, and can calculate them.	Can calculate Laplace transforms and inverse Laplace transforms.	Can't calculate Laplace transforms and inverse Laplace transforms.
Evaluation 5	Can explain how to solve linear ordinary differential equations, and can solve it.	Can solve linear ordinary differential equations.	Can't solve linear ordinary differential equations.

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 class aims to incorporate the applied ability of basic mathematics so that the basic mathematics studied by the third grade at the college can be widely applied to mathematics necessary for engineering.
It includes engineering fields with a wide range of applications and aims to cultivate the ability to mathematically capture phenomena in specialized fields for further learning in the future.

Style:

Lecture and exercise

Notice:

Mathematics related to the Fourier series is "extremely important" and is frequently used in all fields of natural science and engineering as a tool to analyze periodic phenomena. Mathematics related to the Laplace transform simplifies the solution of linear differential equations emerging especially in vibration theory, control theory and electric circuit theory, making these theories easier to understand. There are many techniques similar to the Laplace transform, and as a representative, studies Laplace transform.
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
1st Semester
	1st Quarter
		1st	Definition of Fourier series	Understand the definition of the Fourier series
		2nd	Even function and odd function	Understand even function and odd function
		3rd	Fourier series (1)	Can expand a given a function to the Fourier series. (periodic function with 2pi)
		4th	Fourier series (2)	Can expand a given a function to the Fourier series (general periodic function)
		5th	Partial differentiation equation and Fourier series (1)	Can solve partial differentiation equations by the Fourier series
		6th	Partial differentiation equation and Fourier series (2)	Can solve partial differentiation equations by the Fourier series
		7th	Quiz (1)
		8th	Midterm exam
	2nd Quarter
		9th	Return and explanation midterm exam
		10th	Laplace transform	Understand the definition of Laplace transforms
		11th	Properties of Laplace transform	Can solve problems by properties of Laplace transforms
		12th	Inverse Laplace transform	Understand the definition of inverse Laplace transforms
		13th	Solution of linear ordinary differential equation	Can solve linear ordinary differential equation by Laplace transforms and inverse Laplace transforms
		14th	Quiz (2)
		15th	Final exam
		16th	Return and explanation final exam

Evaluation Method and Weight (%)

	Examination	Assignment	Total
Subtotal	80	20	100
Basic Ability	20	10	30
Technical Ability	60	10	70