HB160000 Analysis D

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HB160000 Subject Classification Specialized Education

Subject Name 解析学Ｄ

Subject Name
（Katakana）カイセキガクD

Subject Name in
English Analysis D

Instructor NAITO YUKI

Instructor
(Katakana) ナイトウ　ユウキ

Campus Higashi-Hiroshima Semester/Term 3rd-Year,  Second Semester,  3Term

Days, Periods, and Classrooms (3T) Tues3-4,Thur5-6：SCI E102

Lesson Style Lecture Lesson Style
(More Details) 　

Blackboard is used. Sometime, prints are given. Basically, face-to-face style are used.

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

Course Level 3 : Undergraduate High-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Junior students of department of mathematics in faculty of science

Keywords Ordinary differential equations, Initial value problems, Iteration method, Fourier series, heat equations the Dirichlet boundary problems.

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) Mathematics
（Knowledge and Understanding）
・Understanding on primary theory of modern mathematics established on classical theory.
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).

Class Objectives
/Class Outline This course is given for learning qualitative theories of ordinary differential equations (= ODEs). The contents consist of the fundamental subjects of ODEs, for examples, "integration of ODEs", "Existence and uniqueness of solutions for ODEs" and "stabilities". Furhter, to construct solutions for the Dirichlet problems of the heat equations, theory of Fourier series is applied.

Class Schedule lesson1 Basic knowledge of ODEs 1
lesson2 ODEs solved by integrations 1
lesson3 ODEs solved by integrations 2
lesson4 ODEs with constant coefficients
lesson5 Linear ODEs of second order
lesson6 Existence and uniqueness of the solutions of ODEs
lesson7  the midterm examination (It is just a plan. )
lesson8 Systems of linear ODEs of first order
lesson9 Systems of linear ODEs of first order with constant coeffiients
lesson10 Exponential of matrix
lessson 11 Fourie series I
lesson12  Fourie series II
lesson13 Fourie series III
lesson14 How to solve partial differential equations by Fourier series 1
lesson15 How to solve partial differential equations by Fourier series 2

Around the midterm of the course, the midterm examination is held. This may not be at the 8-th. lessons exactly. The final examination is also given.

The proposed plan of the course may change when it is better for participants understandings. In some cases, lecture and exercise are changed each other if the instructors have to do that. Please accept these changes.

Text/Reference
Books,etc. Textbooks are not fixed. Any book entitled "Ordinary differential equations" is good for your textbook if you are interested in it.

PC or AV used in
Class,etc. 　

(More Details) Blackboards and projectors are usually used. Copied documents are also used.

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review You need to make preparations and revisions for each lessons. Particularly, reviewing process after the lessons is important. I hope that you catch this truth from these two year's experience. To understand the contents of the lessons, you need to consider what you have to do, of what you take care, what you should do after the lessons. This is common remarks for all lessons through the first to the last.

Requirements The course "Exercises in Analysis D" is given for helping and deepening your understanding. It is strongly recommend that you take the course.

Grading Method Grading is mainly based on the results of the midterm and the end of term examinations. The imposed quizzes in the classes and the reports as homework are also into consideration for estimation of the grade.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message If your score of the midterm exam., do not give up and continue studying the contents of the course. You also keep in mind studying hard even if you get good results for the exam..

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 Science
Lecture Code	HB160000	Subject Classification	Specialized Education
Subject Name	解析学Ｄ
Subject Name （Katakana）	カイセキガクD
Subject Name in English	Analysis D
Instructor	NAITO YUKI
Instructor (Katakana)	ナイトウ　ユウキ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Tues3-4,Thur5-6：SCI E102
Lesson Style	Lecture	Lesson Style (More Details)
Blackboard is used. Sometime, prints are given. Basically, face-to-face style are used.
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	3 : Undergraduate High-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Junior students of department of mathematics in faculty of science
Keywords	Ordinary differential equations, Initial value problems, Iteration method, Fourier series, heat equations the Dirichlet boundary problems.
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)	Mathematics （Knowledge and Understanding）・Understanding on primary theory of modern mathematics established on classical theory. （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
Class Objectives /Class Outline	This course is given for learning qualitative theories of ordinary differential equations (= ODEs). The contents consist of the fundamental subjects of ODEs, for examples, "integration of ODEs", "Existence and uniqueness of solutions for ODEs" and "stabilities". Furhter, to construct solutions for the Dirichlet problems of the heat equations, theory of Fourier series is applied.
Class Schedule	lesson1 Basic knowledge of ODEs 1 lesson2 ODEs solved by integrations 1 lesson3 ODEs solved by integrations 2 lesson4 ODEs with constant coefficients lesson5 Linear ODEs of second order lesson6 Existence and uniqueness of the solutions of ODEs lesson7 the midterm examination (It is just a plan. ) lesson8 Systems of linear ODEs of first order lesson9 Systems of linear ODEs of first order with constant coeffiients lesson10 Exponential of matrix lessson 11 Fourie series I lesson12 Fourie series II lesson13 Fourie series III lesson14 How to solve partial differential equations by Fourier series 1 lesson15 How to solve partial differential equations by Fourier series 2 Around the midterm of the course, the midterm examination is held. This may not be at the 8-th. lessons exactly. The final examination is also given. The proposed plan of the course may change when it is better for participants understandings. In some cases, lecture and exercise are changed each other if the instructors have to do that. Please accept these changes.
Text/Reference Books,etc.	Textbooks are not fixed. Any book entitled "Ordinary differential equations" is good for your textbook if you are interested in it.
PC or AV used in Class,etc.
(More Details)	Blackboards and projectors are usually used. Copied documents are also used.
Learning techniques to be incorporated
Suggestions on Preparation and Review	You need to make preparations and revisions for each lessons. Particularly, reviewing process after the lessons is important. I hope that you catch this truth from these two year's experience. To understand the contents of the lessons, you need to consider what you have to do, of what you take care, what you should do after the lessons. This is common remarks for all lessons through the first to the last.
Requirements	The course "Exercises in Analysis D" is given for helping and deepening your understanding. It is strongly recommend that you take the course.
Grading Method	Grading is mainly based on the results of the midterm and the end of term examinations. The imposed quizzes in the classes and the reports as homework are also into consideration for estimation of the grade.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	If your score of the midterm exam., do not give up and continue studying the contents of the course. You also keep in mind studying hard even if you get good results for the exam..
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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