Course title
幾何学   [Geometry]
Course category	technology speciality courses,ets.	Requirement		Credit	2
Department		Year	2～4	Semester	Spring
Course type	Spring	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

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. Exercises 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 15. Gauss' divergence theorem

Prerequisites

Linear algenra and calculus

Required Text(s) and Materials

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

Remarks 1

Remarks 2

Related URL

Lecture Language

Japanese

Language Subject

Last update

3/9/2017 2:43:00 PM