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 24  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
12/31/2017 4:03:01 PM