K0201040 Applied Mathematics I

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Engineering

Lecture Code K0201040 Subject Classification Specialized Education

Subject Name 応用数学I

Subject Name
（Katakana）オウヨウスウガク　１

Subject Name in
English Applied Mathematics I

Instructor IKEDA TOSHIHARU

Instructor
(Katakana) イケダ　トシハル

Campus Higashi-Hiroshima Semester/Term 1st-Year,  Second Semester,  3Term

Days, Periods, and Classrooms (3T) Weds5-6,Fri3-4：ENG 111

Lesson Style Lecture Lesson Style
(More Details) 　

Lecture using black board or Online (on-demand)

Credits 2.0 Class Hours/Week 　 Language of Instruction J : Japanese

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Second grade, Cluster I

Keywords Ordinary differential equations, Initial value problems, Separable differential equations, Linear equations, Differential operator, Power series solutions, The Laplace transform, Numerial methods

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) ・The students should take a course of calculus before taking this lecture.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Program of Mechanical Systems Engineering
（Abilities and Skills）
・Acquring basis of mechanical system engineering steadily and developing the applied skill.

Program of Transportation Systems
（Knowledge and Understanding）
・Mathematical and mechanical subjects: To understand basic knowledge of mathematical dynamical system, which is essential knowledge for engineers and researchers.
（Abilities and Skills）
・Mathematical and mechanical subjects: Ability to create questions and analyze by utilizing basic knowledge of mathematical dynamical systems.

Program of Material Processing
（Abilities and Skills）
・Acquiring basis of mechanical system, material creation and processing engineering steadily, and being able to apply

Program of Energy Transform Engineering
（Abilities and Skills）
・Acquring basis of mechanical system engineering steadily and developing the applied skill.

Program of Electrical,Systems and Information Engineering
（Abilities and Skills）
・Mathematical methods required for professionals in electrical,  systems, and information engineering.

Program of Electronic Devices and Systems
（Abilities and Skills）
・Mathematical methods required for professionals in electronics engineering.

Program of Applied Chemistry
（Knowledge and Understanding）
・Wide range of basic knowledge on liberal arts and specialized education, and professional basic knowledge on chemistry.

Program of Chemical Engineering
（Abilities and Skills）
・Definite learning of basic chemistry and chemical engineering and cultivation of application ability
engineering basis.

Program of Biotechnology
（Knowledge and Understanding）
・Acquisition of basic and advanced knowledge relating to biotechnology and life science. (Target/Lecture class)

Program of Civil and Environmental Engineering
（Abilities and Skills）
・Ability to analyze  problems

Program of Architecture and Building Engineering
（Knowledge and Understanding）
・Understanding on learning basic engineering knowledge. (Being able to explain basic contents of mathematics, physics and information technology.  Being able to apply the basic contents to architecture and building engineering)

Class Objectives
/Class Outline (1) The concept of first order differential equations
(2) Solution method for first order linear differential equations
(3) Solution method for separable differential equations
(4) The approach how to solve the linear differential equations
(5) Solution method for second order linear differential equations with constant coefficients
(6) The relationship between the higher order linear differential equations with constant coefficients and the system of first order linear differential eqations
(7) Power series solutions

Class Schedule lesson1 Fundamental concept of differential equations and some examples
lesson2 First order differential equations : separable differential equations
lesson3 First order differential equations : first order linear differential equations
lesson4 First order differential equations : exact differential equations
lesson5 First order differential equations : applications, existence of solutions
lesson6 Second order differential equations : Wronskian and fundamental set of solutions
lesson7 Second order differential equations : characteristic equation
lesson8 Second order differential equations : particular solutions
lesson9 Second order differential equations : graph of solution
lesson10 System of linear differential equations : eigenvalue problems
lesson11 System of linear differential equations : fundamental concept
lesson12 The Laplace transform : fundamental concept
lesson13 The Laplace transform : applications
lesson14 Power series methods : power series
lesson15 Power series methods : power series solutions of differential equations

lesson 16: Examination

Text/Reference
Books,etc. "Differential equations" by Y. Mizuta (Saiensu sha Co,. Ltd)
"Exercises of differential equations" by Terada and Sakata (Saiensu sha Co,. Ltd)

PC or AV used in
Class,etc. 　

(More Details) Black board and other materials

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Solve the execises in the texts

Requirements

Grading Method Reports, Quiz, Examinations. Score is 60&or more: successful.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2024Year	School/Graduate School	School of Engineering
Lecture Code	K0201040	Subject Classification	Specialized Education
Subject Name	応用数学I
Subject Name （Katakana）	オウヨウスウガク　１
Subject Name in English	Applied Mathematics I
Instructor	IKEDA TOSHIHARU
Instructor (Katakana)	イケダ　トシハル
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Weds5-6,Fri3-4：ENG 111
Lesson Style	Lecture	Lesson Style (More Details)
Lecture using black board or Online (on-demand)
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Second grade, Cluster I
Keywords	Ordinary differential equations, Initial value problems, Separable differential equations, Linear equations, Differential operator, Power series solutions, The Laplace transform, Numerial methods
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	・The students should take a course of calculus before taking this lecture.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Program of Mechanical Systems Engineering （Abilities and Skills）・Acquring basis of mechanical system engineering steadily and developing the applied skill. Program of Transportation Systems （Knowledge and Understanding）・Mathematical and mechanical subjects: To understand basic knowledge of mathematical dynamical system, which is essential knowledge for engineers and researchers. （Abilities and Skills）・Mathematical and mechanical subjects: Ability to create questions and analyze by utilizing basic knowledge of mathematical dynamical systems. Program of Material Processing （Abilities and Skills）・Acquiring basis of mechanical system, material creation and processing engineering steadily, and being able to apply Program of Energy Transform Engineering （Abilities and Skills）・Acquring basis of mechanical system engineering steadily and developing the applied skill. Program of Electrical,Systems and Information Engineering （Abilities and Skills）・Mathematical methods required for professionals in electrical, systems, and information engineering. Program of Electronic Devices and Systems （Abilities and Skills）・Mathematical methods required for professionals in electronics engineering. Program of Applied Chemistry （Knowledge and Understanding）・Wide range of basic knowledge on liberal arts and specialized education, and professional basic knowledge on chemistry. Program of Chemical Engineering （Abilities and Skills）・Definite learning of basic chemistry and chemical engineering and cultivation of application ability engineering basis. Program of Biotechnology （Knowledge and Understanding）・Acquisition of basic and advanced knowledge relating to biotechnology and life science. (Target/Lecture class) Program of Civil and Environmental Engineering （Abilities and Skills）・Ability to analyze problems Program of Architecture and Building Engineering （Knowledge and Understanding）・Understanding on learning basic engineering knowledge. (Being able to explain basic contents of mathematics, physics and information technology. Being able to apply the basic contents to architecture and building engineering)
Class Objectives /Class Outline	(1) The concept of first order differential equations (2) Solution method for first order linear differential equations (3) Solution method for separable differential equations (4) The approach how to solve the linear differential equations (5) Solution method for second order linear differential equations with constant coefficients (6) The relationship between the higher order linear differential equations with constant coefficients and the system of first order linear differential eqations (7) Power series solutions
Class Schedule	lesson1 Fundamental concept of differential equations and some examples lesson2 First order differential equations : separable differential equations lesson3 First order differential equations : first order linear differential equations lesson4 First order differential equations : exact differential equations lesson5 First order differential equations : applications, existence of solutions lesson6 Second order differential equations : Wronskian and fundamental set of solutions lesson7 Second order differential equations : characteristic equation lesson8 Second order differential equations : particular solutions lesson9 Second order differential equations : graph of solution lesson10 System of linear differential equations : eigenvalue problems lesson11 System of linear differential equations : fundamental concept lesson12 The Laplace transform : fundamental concept lesson13 The Laplace transform : applications lesson14 Power series methods : power series lesson15 Power series methods : power series solutions of differential equations lesson 16: Examination
Text/Reference Books,etc.	"Differential equations" by Y. Mizuta (Saiensu sha Co,. Ltd) "Exercises of differential equations" by Terada and Sakata (Saiensu sha Co,. Ltd)
PC or AV used in Class,etc.
(More Details)	Black board and other materials
Learning techniques to be incorporated
Suggestions on Preparation and Review	Solve the execises in the texts
Requirements
Grading Method	Reports, Quiz, Examinations. Score is 60&or more: successful.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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