| Academic Year |
2024Year |
School/Graduate School |
School of Science |
| Lecture Code |
HB080000 |
Subject Classification |
Specialized Education |
| Subject Name |
幾何学Ｂ |
Subject Name
（Katakana） |
キカガクB |
Subject Name in
English |
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) Weds5-6,Fri7-8：SCI E211 |
| Lesson Style |
Lecture |
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
（Knowledge and Understanding）
・Understanding on primary theory of modern mathematics established on classical theory.
（Abilities and Skills）
・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). |
|---|
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) |
Details undecided. |
| 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 |
Exam 50%, Report 50% |
| 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. |