Simulation Engineering

Course Information

College	Toyama College	Year	2022
Course Title	Simulation Engineering
Course Code	0132	Course Category	Specialized / Elective
Class Format	Lecture	Credits	Academic Credit: 1
Department	Department of Mechanical Engineering	Student Grade	5th
Term	Second Semester	Classes per Week	後期:2
Textbook and/or Teaching Materials	"Modelling with Differential Equations", D. N. Burghes and M. S. Borrie, Ellis Horwood Limited (1981) or "微分方程式で数学モデルを作ろう"　著：D. N. Burghes, M. S. Borrie,　訳：垣田高夫，大町比佐栄，日本評論社
Instructor	Ishiguro Minoru

Course Objectives

You can understand and explain ordinary differential equations and how to solve those problem corresponding to some physical developments.

Rubric

	Ideal Level of Achievement	Standard Level of Achievement	Unacceptable Level of Achievement)
You can get some answers of separation variable equation of ordinary differential equation.	You can solve applied problem.	You can solve fundamental example problem.	You can not solve fundamental example problem.
You can explain sigmoid function which corresponding to some answers of physical development.	You can solve applied problem.	You can solve fundamental example problem.	You can not solve fundamental example problem.
You can get some answers of linear first-order differential equation.	You can solve applied problem.	You can solve fundamental example problem.	You can not solve fundamental example problem.
You can get some answers of linear second-order differential equation.	You can solve applied problem.	You can solve fundamental example problem.	You can not solve fundamental example problem.
You can get some answers of non-homogeneous equation of MKS model.	You can explain applied problem by report.	You can explain fundamental problem by report.	You can not explain fundamental problem by report.
You can get some answers of system of differential equations.	You can explain applied problem by report.	You can explain fundamental problem by report.	You can not explain fundamental problem by report.
You can get some answers and explain the means of that of eigenvalue and eigenvectors of differential equations system.	You can explain applied problem by report.	You can explain fundamental problem by report.	You can not explain fundamental problem by report.
You can applied the Taylor's expansion method of two variables to solve the differential equations system.	You can explain applied problem by report.	You can explain fundamental problem by report.	You can not explain fundamental problem by report.
You can get some answers and explain　Lotka-Volterra equations solution.	You can explain applied problem by report.	You can explain fundamental problem by report.	You can not explain fundamental problem by report.

Assigned Department Objectives

Learning and Educational Objectives of the “General Engineering” A-2 （設計・システム，情報・論理，材料・バイオ，力学，社会技術に関する基礎知識を理解し，簡単に説明することができる。）

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）

JABEE 1(2)(d)(1) （専門工学（工学（融合複合・新領域）における専門工学の内容は申請高等教育機関が規定するものとする）の知識と能力）

JABEE 1(2)(d)(2) （いくつかの工学の基礎的な知識・技術を駆使して実験を計画・遂行し、データを正確に解析し、工学的に考察し、かつ説明・説得する能力）

JABEE 2.1(1) （基礎工学として、①設計・システム系科目群、②情報・論理系科目群、③材料・バイオ系科目群、④力学系科目群、⑤社会技術系科目群の５群からなり、各群から少なくとも１科目、合計最低６科目を含むこと。）

Diploma policy 1 （To develop engineers who comprehensively acquire knowledge, focusing on mechanical engineering as the basis of manufacturing and production technology, and play a role in equipment design, technology development and other engineering-related fields.）

Teaching Method

Outline:

In the lecture mathematical models corresponding to some physical developments are simulated to lean how to make differential equations of that. And to learn the mean of those solutions.

Style:

In the lecture wide knowledge about widely diversity science and technology study are learned and obtained through learning how to make and solve the differential equations of some physical developments.

Notice:

Course Plan

			Theme	Goals
2nd Semester
	3rd Quarter
		1st	Orientation of the lecture.	Learn of "Why do we go on learning forever" to enhance own motivation using game and probability theories.
		2nd	Schematic explanation of mathematical modeling.	Learn of "Schematic explanation of mathematical modeling".
		3rd	Growth and Decay	Learn of "Growth and Decay model". To simulate drug absorption to prevent traffic accident with alcohol. To learn the risk of drinking driving.
		4th	Solution of variables separable differential equations. Part 1.	Learn of "the spread of technological innovations model". To learn "Why do we need technological innovations for keeping or beyonding the sustainable society"
		5th	Solution of variables separable differential equations. Part 2.	Learn of "sigmoid function" as a pattern of some ordinary differential equations. To learn and study "Spread of Epidemics model".
		6th	Solution of linear first order differential equations. Part 1.	Learn of "How to solve the linear first order differential equations".
		7th	Solution of linear first order differential equations. Part 2.	Learn of "How to expanse form the Bernoulli equation into linear first order differential equations". To lean "Exploited Fish Populations".
		8th	Intermediate exam.	Marc sheet test or high revel report.
	4th Quarter
		9th	Answer of the exam. Solution of linear second order differential equations. Part 1.	Learn of "How to solve homogeneous linear second order differential equations and how to deal the determination of the linear independence".
		10th	Solution of linear second order differential equations. Part 2.	Learn of "How to solve non-homogeneous linear second order differential equations.
		11th	Solution of non-homogeneous linear second order differential equations.	Learn of "How to solve non homogeneous MKC eqution model and resonance".
		12th	System of differential equations. Part１.	Learn of "System of differential equations". To learn "How to reduce order of the higher to low order of the differential equations.
		13th	System of differential equations. Part 2.	Learn of "Eigenvalue and Eigenvectors of the system of differential equations".
		14th	System of differential equations. Part 3.	Learn of "2 variable Tayler's expansion to apply it to the system of differential equations to solve it".
		15th	Lecture of Volterra's principle model.	Learn of "Interacting species model".
		16th	Final exam.	Marksheet test to evaluate student's intelligibility.

Evaluation Method and Weight (%)

	Examination	Report	Total
Subtotal	60	40	100
Basic Ability	20	20	40
Technical Ability	20	20	40
Interdisciplinary Ability	20	0	20