HB090000 Exercises in Geometry B

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Science

Lecture Code HB090000 Subject Classification Specialized Education

Subject Name 幾何学Ｂ演習

Subject Name
（Katakana）キカガクBエンシュウ

Subject Name in
English Exercises in Geometry B

Instructor OKUDA TAKAYUKI

Instructor
(Katakana) オクダ　タカユキ

Campus Higashi-Hiroshima Semester/Term 3rd-Year, Second Semester, 4Term

Days, Periods, and Classrooms (4T) Weds7-8,Fri9-10：SCI E211

Lesson Style Seminar Lesson Style
(More Details) 　

Face-to-Face

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

Course Level 3 : Undergraduate High-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords Manifolds

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
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability).
・To acquire skills to formulate and solve mathematical questions.

Class Objectives
/Class Outline This course provides introductions to differentiable manifolds.

Class Schedule lesson1 Introduction, local coordinates.
lesson2 Topological manifolds.
lesson3 Coordinates transformations.
lesson4 Smooth manifolds.
lesson5 Smooth functions on manifolds.
lesson6 Definition of Tangent spaces.
lesson7 Coordinate basis of Tangent spaces.
lesson8 Smooth maps.
lesson9 Differentiations of smooth maps.
lesson10 Regular submanifolds.
lesson11 Tangent bundles.
lesson12 Vector fields and flows.
lesson13 Riemannian metrics.
lesson14 Covariant derivatives.
lesson15 Exam

Mini tests and reports are carried out each lesson.
The final Exam will be held.

Text/Reference
Books,etc. Tayoutai-no-kiso (Matsumoto, Y.)

PC or AV used in
Class,etc. 　

(More Details) The teams system

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review (1--5) Recall topology theory. Try exercises.
(6--14) Recall linear algebras and basic analysis. Try exercises.

Requirements

Grading Method Examination is jointed to Geometry A

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	HB090000	Subject Classification	Specialized Education
Subject Name	幾何学Ｂ演習
Subject Name （Katakana）	キカガクBエンシュウ
Subject Name in English	Exercises in Geometry B
Instructor	OKUDA TAKAYUKI
Instructor (Katakana)	オクダ　タカユキ
Campus	Higashi-Hiroshima	Semester/Term	3rd-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Weds7-8,Fri9-10：SCI E211
Lesson Style	Seminar	Lesson Style (More Details)
Face-to-Face
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	3 : Undergraduate High-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Manifolds
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 （Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). ・To acquire skills to formulate and solve mathematical questions.
Class Objectives /Class Outline	This course provides introductions to differentiable manifolds.
Class Schedule	lesson1 Introduction, local coordinates. lesson2 Topological manifolds. lesson3 Coordinates transformations. lesson4 Smooth manifolds. lesson5 Smooth functions on manifolds. lesson6 Definition of Tangent spaces. lesson7 Coordinate basis of Tangent spaces. lesson8 Smooth maps. lesson9 Differentiations of smooth maps. lesson10 Regular submanifolds. lesson11 Tangent bundles. lesson12 Vector fields and flows. lesson13 Riemannian metrics. lesson14 Covariant derivatives. lesson15 Exam Mini tests and reports are carried out each lesson. The final Exam will be held.
Text/Reference Books,etc.	Tayoutai-no-kiso (Matsumoto, Y.)
PC or AV used in Class,etc.
(More Details)	The teams system
Learning techniques to be incorporated
Suggestions on Preparation and Review	(1--5) Recall topology theory. Try exercises. (6--14) Recall linear algebras and basic analysis. Try exercises.
Requirements
Grading Method	Examination is jointed to Geometry A
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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