| Course title | |||||
| 物理数学Ⅰおよび演習 [Vector Analysis] | |||||
| Course category | technology speciality courses,ets. | Requirement | Credit | 2 | |
| Department | Year | 2～4 | Semester | Spring | |
| Course type | Spring | Course code | 022515 | ||
| Instructor(s) | |||||
| 石田 寛 [ISHIDA Hiroshi] | |||||
| Facility affiliation | Graduate School of Bio-Applications and Systems Engineering | Office | Email address | ||
| Course description |
|
In physics, motion of an object is described using three-dimensional vectors. Fluid flow, electric field, and magnetic field are all represented as a spatial distribution of vectors in a three-dimensional space. Vector analysis is a field of mathematics concerned with various operations to the vectors, which includes differentiation and integration of vectors. In this course, students will learn the basic points in vector analysis that are required to learn fluid dynamics and electromagnetism. Students will be trained to solve various problems in vector analysis by doing exercises. The topics covered in the course include: - Inner and outer products - Frenet?Serret formulas - Gradient, divergence, and rotation of vector fields - Line and surface integrals |
| Expected Learning |
|
Learners who successfully complete this course will be able to: - Calculate the curvature and torsion of a trajectory by differentiation of a vector function - Calculate the area of a curved surface by integration of a vector function - Calculate the gradient, divergence, and rotation of vector fields |
| Course schedule |
|
Week 1: Introduction Week 2: Unit vector, base vectors, linear independence of vectors Week 3: Dot product, direction cosines Week 4: Vector equations, outer product Week 5: Triple product, differentiation of a vector function of one variable Week 6: Integration of a vector function of one variable, arc length, unit tangent vector, normal vector Week 7: Curvature, binormal vector, torsion, Frenet?Serret formulas, Kepler’s laws Week 8: Midterm exam Week 9: Vector function of two variables, first fundamental quantities, surface element Week 10: Scalar and vector fields, gradient, Hamilton operator Week 11: Directional derivative, divergence Week 12: Rotation, line integrals of a scalar field Week 13: Line integrals of a vector field, surface integrals of a scalar field, surface integrals of a vector field Week 14: Divergence theorem, Stokes’ theorem, Cylindrical and polar coordinate systems Week 15: Exam |
| Prerequisites |
| Basic calculus and algebra courses. |
| Required Text(s) and Materials |
| A textbook written in Japanese will be used. |
| References |
| There are various textbooks on vector analysis. |
| Assessment/Grading |
| Midterm exam (35%), end-of-term exam (35%), and exercises (30%). |
| Message from instructor(s) |
| The course will be given in Japanese. |
| Course keywords |
| Vector, outer product, scalar field, vector field |
| Office hours |
| From 14:30 to 16:30 on Thursday. |
| Remarks 1 |
| Remarks 2 |
| Related URL |
| Lecture Language |
| Japanese |
| Language Subject |
| Last update |
| 4/5/2018 5:50:44 PM |