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 some important theorems to do this, 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.
The only technical prerequisite for this theme is a standard course in the calculus of functions of one variable and two variables. In particular, the necessary matrix arithmetic and algebra (not linear algebra) are needed.
교수목표
1. To develope in students a conceptual grasp of calculus for vector functions to help them understand more advanced mathematics
2. To develope the ability to resolve various problems using Green's theorem
3. To develope the ability to resolve various problems using Gauss' theorem
4. To develope the ability to resolve various problems using Stokes theorem
주요 학습내용 및 수업진행방법
Lecture
학습 성과 평가방법
Attendence(5%), Homework(5%), 3 Examinations(90%)
교재 및 참고문헌
Textbook : Div, grad, curl, and all that : an informal text on vector calculus, H.M. Schey(4th edition)
Rreference books :
1. Vector calculus, Marsden and Tromba
2. Vector calculus, Susan J. Colley