| Course title | |||||
| 幾何学 [Geometry] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | 1st | |
| Course type | 1st | Course code | 022804 | ||
| Instructor(s) | |||||
| 原 伸生 [HARA Nobuo] | |||||
| Facility affiliation | Faculty of Engineering | Office | 12-214 | Email address | |
| Course description |
| This is an introductory lecture to vector analysis, which is an important tool to describe and analyze various phisical phenomena appearing in engineering. |
| Expected Learning |
|
1) capable to compute derivatives and integrals of vector-valued functions 2) to understand basic notions on curves, surfaces and vector fields, and capable to apply them to concrete computations 3) to understand line and surface integrals and capable to apply theorems on integrals Corresponding criteria in the Diploma Policy: See the Curriculum maps |
| Course schedule |
|
1. Review of linear algenra 2. Vector-valued functions and thier differentials 3. Description of dinamical phenomena via vector-valued functions 4. Basic theory of space curves 5. Frenet-Serret's formula 6. Basic theory of surfaces 7. Application to computing the area of surfaces 8. Summary: Exercises and/or midterm exam 9. Scalar fields and directional derivatives 10. Gradient and nabla operators 11. Divergence and rotation operators 12. Formulae involving gradient, divergence and rotation 13. Line integrals 14. Surface integrals and Gauss' divergence theorem 15. Summary: Exercises and/or term exam |
| Prerequisites |
|
Linear algebra and calculus. Remark: In addition to 30 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending appropriate amount of time and using the lecture handouts as well as the references specified in the lecture. |
| Required Text(s) and Materials |
|
None. Remark: This lecture will be given in Japanese. Students who want to use a textbook written in English should consult the lecturer. |
| References |
| Assessment/Grading |
| Midterm exam 50%, Term exam 50% |
| Message from instructor(s) |
| Course keywords |
| Frenet-Serre's formula, line element, unit normal vector, Gauss' divergence theorem, Stokes' theorem |
| Office hours |
| Arranged taking into account of students' requests |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 4/2/2019 10:33:11 AM |