Hiroshima University Syllabus

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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. 
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