K0203010 Applied Mathematics III

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Engineering

Lecture Code K0203010 Subject Classification Specialized Education

Subject Name 応用数学III

Subject Name
（Katakana）オウヨウスウガク　３

Subject Name in
English Applied Mathematics III

Instructor WAKASUGI YUUTA

Instructor
(Katakana) ワカスギ　ユウタ

Campus Higashi-Hiroshima Semester/Term 2nd-Year,  Second Semester,  3Term

Days, Periods, and Classrooms (3T) Tues1-2,Weds5-6：ENG 220

Lesson Style Lecture Lesson Style
(More Details) 　

Lecture. The detail will be announced before the first class.

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-year students (Cluster 1・Mechanical Systems, Transportation, Material and Energy)

Keywords Fourier Series, Fourier Integrals, Fourier Transform, Partial Differential Equations, Separation of Variables

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
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 Basics on Fourier Analysis and  Partial Differential Equations.

Class Schedule lesson1 Fourier series
lesson2 Example of Fourier series
lesson3 Fourier cosine series and sine series
lesson4 Complex Fourier series
lesson5 Approximation by trigonometric polynomials
lesson6 Convergence of Fourier series
lesson7 Fourier integrals
lesson8 Fourier transformation
lesson9 Properties of Fourier Transformation
lesson10 Application to partial differential equations: the heat equation
lesson11 Initial value problems of the heat equation
lesson12  Initial-boundary value problems of the wave equation
lesson13 Initial value problems of the wave equation
lesson14 Two-dimensional wave equation
lesson15 Fourier--Bessel series

Exams or reports will be assigned during the period.

Text/Reference
Books,etc. Textbook: Fourier Analysis and Partial Differential Equations
in Advanced Engineering Mathematics by Erwin Kreyszig (Baifukan)
Reference book: スウ著「フーリエ解析」森北出版

PC or AV used in
Class,etc. 　

(More Details)

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Reviews are important for deeper understanding. This course will use materials learned in calculus, linear algebra, and ordinary differential equations, so it is recommended to review these courses as well.

Requirements

Grading Method Evaluation will be based on exams. Need to get a score which is more than 60%.

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	K0203010	Subject Classification	Specialized Education
Subject Name	応用数学III
Subject Name （Katakana）	オウヨウスウガク　３
Subject Name in English	Applied Mathematics III
Instructor	WAKASUGI YUUTA
Instructor (Katakana)	ワカスギ　ユウタ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Tues1-2,Weds5-6：ENG 220
Lesson Style	Lecture	Lesson Style (More Details)
Lecture. The detail will be announced before the first class.
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-year students (Cluster 1・Mechanical Systems, Transportation, Material and Energy)
Keywords	Fourier Series, Fourier Integrals, Fourier Transform, Partial Differential Equations, Separation of Variables
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
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	Basics on Fourier Analysis and Partial Differential Equations.
Class Schedule	lesson1 Fourier series lesson2 Example of Fourier series lesson3 Fourier cosine series and sine series lesson4 Complex Fourier series lesson5 Approximation by trigonometric polynomials lesson6 Convergence of Fourier series lesson7 Fourier integrals lesson8 Fourier transformation lesson9 Properties of Fourier Transformation lesson10 Application to partial differential equations: the heat equation lesson11 Initial value problems of the heat equation lesson12 Initial-boundary value problems of the wave equation lesson13 Initial value problems of the wave equation lesson14 Two-dimensional wave equation lesson15 Fourier--Bessel series Exams or reports will be assigned during the period.
Text/Reference Books,etc.	Textbook: Fourier Analysis and Partial Differential Equations in Advanced Engineering Mathematics by Erwin Kreyszig (Baifukan) Reference book: スウ著「フーリエ解析」森北出版
PC or AV used in Class,etc.
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	Reviews are important for deeper understanding. This course will use materials learned in calculus, linear algebra, and ordinary differential equations, so it is recommended to review these courses as well.
Requirements
Grading Method	Evaluation will be based on exams. Need to get a score which is more than 60%.
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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