HB270000 Geometry D

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HB270000 Subject Classification Specialized Education

Subject Name 幾何学Ｄ

Subject Name
（Katakana）キカガクD

Subject Name in
English Geometry D

Instructor ISHIHARA KAI

Instructor
(Katakana) イシハラ　カイ

Campus Higashi-Hiroshima Semester/Term 4th-Year, Second Semester, 4Term

Days, Periods, and Classrooms (4T) Weds3-4,Fri5-6：SCI E211

Lesson Style Lecture Lesson Style
(More Details) 　

Lecture using blackboard

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

Course Level 4 : Undergraduate Advanced

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords Differential forms, Stokes’ Theorem, de Rham cohomology, Cohomology of Lie algebra

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）
・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics.

Class Objectives
/Class Outline Studying fundamentals of differential forms on manifolds and its applications

Class Schedule lesson 1. Introduction
lesson 2. Review of some basic manifold theory
lesson 3. Tangent bundle and cotangent bundle
lesson 4. Alternative forms
lesson 5. Properties of alternative forms
lesson 6. Differential forms
lesson 7. Properties of differential forms
lesson 8. Exterior derivative of a differential form
lesson 9. Properties of the exterior derivative of a differential form
lesson 10. Cohomology on manifolds
lesson 11. Singular homology on manifolds
lesson 12. Stokes theorem
lesson 13. de Rham's theorem
lesson 14. Harmonic forms
lesson 15. Overall summary

Homework will be assigned in the lecture.

Text/Reference
Books,etc. No textbook.
Reference books:
S. Murakami, Manifolds, Kyoritsu Shuppan, 1969.
S. Morita, Geometry of Differential Forms, AMS, 2001.

PC or AV used in
Class,etc. 　

(More Details) Blackboard

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Geometry A or its contents in Manifolds theory should be taken.
In each lecture, some easy computations and proofs will be omitted.
It is needed to check them by your hand.
Of course, giving questions to the lecturer is welcome.

Requirements

Grading Method Evaluation will be based on homework assignments.

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 Science
Lecture Code	HB270000	Subject Classification	Specialized Education
Subject Name	幾何学Ｄ
Subject Name （Katakana）	キカガクD
Subject Name in English	Geometry D
Instructor	ISHIHARA KAI
Instructor (Katakana)	イシハラ　カイ
Campus	Higashi-Hiroshima	Semester/Term	4th-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Weds3-4,Fri5-6：SCI E211
Lesson Style	Lecture	Lesson Style (More Details)
Lecture using blackboard
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	4 : Undergraduate Advanced
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Differential forms, Stokes’ Theorem, de Rham cohomology, Cohomology of Lie algebra
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）・Acquiring knowledge and vision on advanced theories as an extension of core theory of modern mathematics.
Class Objectives /Class Outline	Studying fundamentals of differential forms on manifolds and its applications
Class Schedule	lesson 1. Introduction lesson 2. Review of some basic manifold theory lesson 3. Tangent bundle and cotangent bundle lesson 4. Alternative forms lesson 5. Properties of alternative forms lesson 6. Differential forms lesson 7. Properties of differential forms lesson 8. Exterior derivative of a differential form lesson 9. Properties of the exterior derivative of a differential form lesson 10. Cohomology on manifolds lesson 11. Singular homology on manifolds lesson 12. Stokes theorem lesson 13. de Rham's theorem lesson 14. Harmonic forms lesson 15. Overall summary Homework will be assigned in the lecture.
Text/Reference Books,etc.	No textbook. Reference books: S. Murakami, Manifolds, Kyoritsu Shuppan, 1969. S. Morita, Geometry of Differential Forms, AMS, 2001.
PC or AV used in Class,etc.
(More Details)	Blackboard
Learning techniques to be incorporated
Suggestions on Preparation and Review	Geometry A or its contents in Manifolds theory should be taken. In each lecture, some easy computations and proofs will be omitted. It is needed to check them by your hand. Of course, giving questions to the lecturer is welcome.
Requirements
Grading Method	Evaluation will be based on homework assignments.
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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