Hiroshima University Syllabus |

Japanese

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

（Katakana）タヨウキカキソコウギビー Subject Name in

EnglishGeometry B Instructor ISHIHARA KAI Instructor

(Katakana)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

Program

(Applicable only to targeted subjects for undergraduate students)Criterion referenced

Evaluation

(Applicable only to targeted subjects for undergraduate students)Class Objectives

/Class OutlineStudying 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

ReviewGeometry 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.