교과목개요

The subject vector analysis is to study the calculus of vector valued functions, that is to say, to tie together the vector differential calculus and the vector integral calculus. There are always three important theorems; Green’s theorem, Gauss’ theorem and Stokes’ theorem. Green’s theorem, discovered in the early part of the 19th century, arose in connection with potential theory, which includes gravitational and electrical potentials. Gauss’ theorem-the Divergence theorem-arose in connection with electrostatics. Stokes’ theorem first appeared in a letter to Stokes from the physicist Lord Kelvin, and was used by Stokes on the examination for the Smith Prize.

This course provides the necessary examples and tools to study the geometry of Euclidean space, thus it is one of most important courses in mathematics and engineering science.

교수목표

Besides computational skills, we intend to exhibit a beauty of mathematical principles-so called duality, which is observed in many branches of mathematics. An interaction of object(function) and space is expressed in terms of integrations of a function with respect to a background space such as divergence theorem and Stokes theorem.

주요 학습내용 및 수업진행방법

This course is based on lectures and assignments.

학습 성과 평가방법

Attendence(20%), Homework(20%), Two Examinations(60%)

교재 및 참고문헌

No main textbook. The lecture note would be available.

Reference: Vector Calculus, Marsden and Tromba

미적분학 2, 김홍종(서울대 출판부)

Calculus: Early transcendental 6e