Hiroshima University Syllabus

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Academic Year 2024Year School/Graduate School Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program
Lecture Code WSA32000 Subject Classification Specialized Education
Subject Name 多様幾何基礎講義B
Subject Name
Subject Name in
Geometry B
イシハラ カイ
Campus Higashi-Hiroshima Semester/Term 1st-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 5 : Graduate Basic
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
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
(Applicable only to targeted subjects for undergraduate students)
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. 
No textbook.
Reference books:
S. Murakami, Manifolds, Kyoritsu Shuppan, 1969.
S. Morita, Geometry of Differential Forms, AMS, 2001.
PC or AV used in
(More Details) Blackboard 
Learning techniques to be incorporated  
Suggestions on
Preparation and
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. 
Grading Method Evaluation will be based on homework assignments.  
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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