K0203040 Applied Mathematics III

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Engineering

Lecture Code K0203040 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 TSUGE NAOKI

Instructor
(Katakana) ツゲ　ナオキ

Campus Higashi-Hiroshima Semester/Term 2nd-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Mon1-2,Thur5-6：ENG 107

Lesson Style Lecture Lesson Style
(More Details) 　

Face-to-face or Online (on-demand) and Face-to-Face

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 2 grade, Cluster II, 3 grade, Cluster 3

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 This course introduces the calculational method for the Fourier coefficient and the Fourier
transformation. The aim of this course is to help students acquire an understanding of the
mathematical fundamentals of the Fourier analysis so that they can apply it to some cardinal
partial differential equations. This  course  deals with the mathematical skills including:
(1) basic computation methods in calculus for the Fourier series and the Fourier transformation;
(2) the Fourier series expansion of some elementary functions;
(3) fundamental properties of the Fourier transformation for its actual performance;
(4) mathematical meanings of some (in)equalities such as Bessel’s inequality and Parseval’s equality, and their application;
(5) the understanding of the characteristic of the cardinal 2nd order linear partial differential equation;
(6) a solution of the wave equation obtained by the variable-separation method;
(7) a solution of the wave equation obtained by d'Alembert's method;
(8) a solution of the heat equation obtained by the variable-separation method.

Class Schedule Lesson 1. Preparation for the Fourier Analysis and Its Introduction

Lesson 2. Fourier Series

Lesson 3. Computation of Fourier Series
Lesson 4. Fourier Sine Series and Cosine Series

Lesson 5. Complex Fourier Series

Lesson 6. Approximation with Trigonometric Polynomials
Lesson 7. Fourier Integral

Lesson 8. Fourier Sine Transformation and Cosine Transformation

Lesson 9. Fourier Transformation
Lesson 10. Properties of Fourier Transformation

Lesson 11. Introduction of Wave Equation

Lesson 12. Initial- and Boundary-Value Problems for Wave Equation: Application of Variable-Separation and Fourier Series
Lesson 13. d'Alembert's Solution of Initial-Value Problem for Wave Equation

Lesson 14. Initial- and Boundary-Value Problems for Heat Equation: Application of Variable-Separation and Fourier Series

Lesson 15. Initial-Value Problem for Heat Equation: Application of Fourier Transformation

Lesson 16. Term Examination or Report

Text/Reference
Books,etc. Fourier Analysis and Partial Differential Equations
in Advanced Engineering Mathematics by Erwin Kreyszig (Bafukan)

PC or AV used in
Class,etc. 　

(More Details) Black board and other materials

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Please look back over the examples of the subject of each lecture, and brush up on it.

Requirements

Grading Method Evaluation: Examination, Reports, etc. 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	K0203040	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	TSUGE NAOKI
Instructor (Katakana)	ツゲ　ナオキ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Mon1-2,Thur5-6：ENG 107
Lesson Style	Lecture	Lesson Style (More Details)
Face-to-face or Online (on-demand) and Face-to-Face
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	2 grade, Cluster II, 3 grade, Cluster 3
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	This course introduces the calculational method for the Fourier coefficient and the Fourier transformation. The aim of this course is to help students acquire an understanding of the mathematical fundamentals of the Fourier analysis so that they can apply it to some cardinal partial differential equations. This course deals with the mathematical skills including: (1) basic computation methods in calculus for the Fourier series and the Fourier transformation; (2) the Fourier series expansion of some elementary functions; (3) fundamental properties of the Fourier transformation for its actual performance; (4) mathematical meanings of some (in)equalities such as Bessel’s inequality and Parseval’s equality, and their application; (5) the understanding of the characteristic of the cardinal 2nd order linear partial differential equation; (6) a solution of the wave equation obtained by the variable-separation method; (7) a solution of the wave equation obtained by d'Alembert's method; (8) a solution of the heat equation obtained by the variable-separation method.
Class Schedule	Lesson 1. Preparation for the Fourier Analysis and Its Introduction Lesson 2. Fourier Series Lesson 3. Computation of Fourier Series Lesson 4. Fourier Sine Series and Cosine Series Lesson 5. Complex Fourier Series Lesson 6. Approximation with Trigonometric Polynomials Lesson 7. Fourier Integral Lesson 8. Fourier Sine Transformation and Cosine Transformation Lesson 9. Fourier Transformation Lesson 10. Properties of Fourier Transformation Lesson 11. Introduction of Wave Equation Lesson 12. Initial- and Boundary-Value Problems for Wave Equation: Application of Variable-Separation and Fourier Series Lesson 13. d'Alembert's Solution of Initial-Value Problem for Wave Equation Lesson 14. Initial- and Boundary-Value Problems for Heat Equation: Application of Variable-Separation and Fourier Series Lesson 15. Initial-Value Problem for Heat Equation: Application of Fourier Transformation Lesson 16. Term Examination or Report
Text/Reference Books,etc.	Fourier Analysis and Partial Differential Equations in Advanced Engineering Mathematics by Erwin Kreyszig (Bafukan)
PC or AV used in Class,etc.
(More Details)	Black board and other materials
Learning techniques to be incorporated
Suggestions on Preparation and Review	Please look back over the examples of the subject of each lecture, and brush up on it.
Requirements
Grading Method	Evaluation: Examination, Reports, etc. 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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