WG115002 Mathematical Analysis A

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School Graduate School of Integrated Sciences for Life (Master's Course) Division of Integrated Sciences for Life Program of Mathematical and Life Sciences

Lecture Code WG115002 Subject Classification Specialized Education

Subject Name 応用数理学Ａ

Subject Name
（Katakana）オウヨウスウリガクエー

Subject Name in
English Mathematical Analysis A

Instructor OHNISHI ISAMU

Instructor
(Katakana) オオニシ　イサム

Campus Higashi-Hiroshima Semester/Term 1st-Year,  First Semester,  2Term

Days, Periods, and Classrooms (2T) Tues5-6,Fri5-6：Online

Lesson Style Lecture Lesson Style
(More Details) 　

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

Course Level 6 : Graduate Advanced

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students Students interested in prospects for both mathematically Scientific applications and its foundations for control engineering.

Keywords nonlinear mathematical science for life organization,
mathematically scientific theoretical deterministic control theory,
research for nonlinearity

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)

Class Objectives
/Class Outline Our labo's slogan is “To control it, we must first understand this”. My labo works for
nonlinear pure mathematical science, especially within such subjects, my specialty
is nonlinear mathemtical science related to biological activities of both plants' and
cyanobacteria's  biological activity. We use a system of nonlinear partial differential
equations to create a dynamical system in which interesting dynamics occur due to
nonlinear effects, also using the perspective of finite-dimensional and infinite-
dimensional dynamical systems.
Furthermore, our labo will deal with the mathematically scientifical theoretical deterministic
control theory.  Actually. by applying it to concrete control problems (especially concrete
engineering control problems), we will study it from mathematically scientific point of view.

Class Schedule 1st lesson

Control engineering intro (1)
2nd lesson

Control engineering intro (2)
3rd lesson

Control engineering intro (3)
4th lesson

Control engineering intro (4)
5th lesson

Feedback control system and its stability (1)
6th lesson

Feedback control system and its stability (2)
7th lesson

Characteristics of feedback control system (1)
8th lesson

Characteristics of feedback control system (2)
9th lesson

Infinite dimensionality, nonlinear parabolic evolution equation theory, and variational inequalities (1)
10th lesson

Infinite dimensionality, nonlinear parabolic evolution equation theory, and variational inequalities (2)
11th lesson

Infinite dimensionality, nonlinear parabolic evolution equation theory, and variational inequalities (3)
12th lesson

Infinite dimensionality, nonlinear parabolic evolution equation theory, and variational inequalities (4)
13th lesson

Infinite dimensionality, nonlinear parabolic evolution equation theory, and variational inequalities (5)
14th lesson

APPENDIX (1) Operator method and spectral decomposition theorem (1)
15th lesson

APPENDIX (2) Analytical method for feedback control system

Text/Reference
Books,etc. In Japanese:

1. 新版フィードバック制御の基礎　片山徹著　 (朝倉書店)
2. 放物型発展方程式とその応用（上）（下）　八木厚志著　（岩波書店）
3. 線形代数を基礎とする応用数理入門　佐藤一宏著（サイエンス社）
4. 理工系のための微分積分 (I) (II)   山田義雄ら共著　（内田老鶴圃）
5. これならわかる工学部で学ぶ数学　千葉逸人著　（プレアデス出版）

InFrench:

６. Control optimal de systemes gouvernes par des equations aux dérivées partielle
(偏微分方程式と最適制御) J.L. Lions

In English：

7. Functional Analysis, Sobolev Spaces and Partial Differential Equations オンデマンド (ペーパーバック) H. Breziz

PC or AV used in
Class,etc. 　

(More Details)

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Study hard by use of References.

Requirements

Grading Method Report 60%
Attending class  30%
the others 10%

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message With prospects for both mathematically Scientific applications and its foundations for control engineering.

Other If student from foreign countries, then I can make lectures in English.

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	Graduate School of Integrated Sciences for Life (Master's Course) Division of Integrated Sciences for Life Program of Mathematical and Life Sciences
Lecture Code	WG115002	Subject Classification	Specialized Education
Subject Name	応用数理学Ａ
Subject Name （Katakana）	オウヨウスウリガクエー
Subject Name in English	Mathematical Analysis A
Instructor	OHNISHI ISAMU
Instructor (Katakana)	オオニシ　イサム
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, 2Term
Days, Periods, and Classrooms	(2T) Tues5-6,Fri5-6：Online
Lesson Style	Lecture	Lesson Style (More Details)

Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	6 : Graduate Advanced
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students	Students interested in prospects for both mathematically Scientific applications and its foundations for control engineering.
Keywords	nonlinear mathematical science for life organization, mathematically scientific theoretical deterministic control theory, research for nonlinearity
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)
Class Objectives /Class Outline	Our labo's slogan is “To control it, we must first understand this”. My labo works for nonlinear pure mathematical science, especially within such subjects, my specialty is nonlinear mathemtical science related to biological activities of both plants' and cyanobacteria's biological activity. We use a system of nonlinear partial differential equations to create a dynamical system in which interesting dynamics occur due to nonlinear effects, also using the perspective of finite-dimensional and infinite- dimensional dynamical systems. Furthermore, our labo will deal with the mathematically scientifical theoretical deterministic control theory. Actually. by applying it to concrete control problems (especially concrete engineering control problems), we will study it from mathematically scientific point of view.
Class Schedule	1st lesson Control engineering intro (1) 2nd lesson Control engineering intro (2) 3rd lesson Control engineering intro (3) 4th lesson Control engineering intro (4) 5th lesson Feedback control system and its stability (1) 6th lesson Feedback control system and its stability (2) 7th lesson Characteristics of feedback control system (1) 8th lesson Characteristics of feedback control system (2) 9th lesson Infinite dimensionality, nonlinear parabolic evolution equation theory, and variational inequalities (1) 10th lesson Infinite dimensionality, nonlinear parabolic evolution equation theory, and variational inequalities (2) 11th lesson Infinite dimensionality, nonlinear parabolic evolution equation theory, and variational inequalities (3) 12th lesson Infinite dimensionality, nonlinear parabolic evolution equation theory, and variational inequalities (4) 13th lesson Infinite dimensionality, nonlinear parabolic evolution equation theory, and variational inequalities (5) 14th lesson APPENDIX (1) Operator method and spectral decomposition theorem (1) 15th lesson APPENDIX (2) Analytical method for feedback control system
Text/Reference Books,etc.	In Japanese: 1. 新版フィードバック制御の基礎　片山徹著　 (朝倉書店) 2. 放物型発展方程式とその応用（上）（下）　八木厚志著　（岩波書店） 3. 線形代数を基礎とする応用数理入門　佐藤一宏著（サイエンス社） 4. 理工系のための微分積分 (I) (II) 山田義雄ら共著　（内田老鶴圃） 5. これならわかる工学部で学ぶ数学　千葉逸人著　（プレアデス出版） InFrench: ６. Control optimal de systemes gouvernes par des equations aux dérivées partielle (偏微分方程式と最適制御) J.L. Lions In English： 7. Functional Analysis, Sobolev Spaces and Partial Differential Equations オンデマンド (ペーパーバック) H. Breziz
PC or AV used in Class,etc.
(More Details)
Learning techniques to be incorporated
Suggestions on Preparation and Review	Study hard by use of References.
Requirements
Grading Method	Report 60% Attending class 30% the others 10%
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message	With prospects for both mathematically Scientific applications and its foundations for control engineering.
Other	If student from foreign countries, then I can make lectures in English.
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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