Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2024Year Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program WSA32000 Specialized Education 多様幾何基礎講義Ｂ タヨウキカキソコウギビー Geometry B ISHIHARA KAI イシハラ　カイ Higashi-Hiroshima 1st-Year,  Second Semester,  4Term (4T) Weds3-4,Fri5-6：SCI E211 Lecture Lecture using blackboard 2.0 J : Japanese 5 : Graduate Basic 25 : Science and Technology 01 : Mathematics/Statistics Differential forms, Stokes’ Theorem, de Rham cohomology, Cohomology of Lie algebra Studying fundamentals of differential forms on manifolds and its applications lesson 1. Introductionlesson 2. Review of some basic manifold theorylesson 3. Tangent bundle and cotangent bundlelesson 4. Alternative formslesson 5. Properties of alternative formslesson 6. Differential formslesson 7. Properties of differential formslesson 8. Exterior derivative of a differential formlesson 9. Properties of the exterior derivative of a differential formlesson 10. Cohomology on manifoldslesson 11. Singular homology on manifoldslesson 12. Stokes theoremlesson 13. de Rham's theoremlesson 14. Harmonic formslesson 15. Overall summaryHomework will be assigned in the lecture. No textbook. Reference books: S. Murakami, Manifolds, Kyoritsu Shuppan, 1969.S. Morita, Geometry of Differential Forms, AMS, 2001. Blackboard 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. Evaluation will be based on homework assignments. 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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