Hiroshima University Syllabus

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Academic Year 2022Year School/Graduate School School of Engineering
Lecture Code K0203010 Subject Classification Specialized Education
Subject Name 応用数学III
Subject Name
オウヨウスウガク 3
Subject Name in
Applied Mathematics III
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
Criterion referenced
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. 
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
(More Details)  
Learning techniques to be incorporated  
Suggestions on
Preparation and
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. 
Grading Method Evaluation will be based on the exercises of each class and the reports. Need to get a score which is more than 60%. 
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
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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