수학 및 연습2

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자연과학 >수학ㆍ물리ㆍ천문ㆍ지리 >수학
강의학기

2017년 2학기

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강의계획서

This lecture is consisted of vectors (Chap. 11, 12, 15), partial derivatives (Chap. 13), and multiple integrals (Chap. 14). The vector section deals with relationship between vectors and geometry and vector calculus such as intergral and derivatives. In partial derivatives, functions of two or more variables and the basic idea of diffrential calculus to such funtions will be studied. Finally, we extend the idea of a definite integral to double and triple integrals of functions of two or three variables.

수강안내 및 수강신청
※ 수강확인증 발급을 위해서는 수강신청이 필요합니다

Vectors and the Geometry of Space

차시별 강의

1.	Vectors and the Geometry of Space	Three-dimensional coordinate systems, Vectors, and The dot product
	Vectors and the Geometry of Space	Projection, The cross product
2.	Vectors and the Geometry of Space	equations of lines and planes
	Vectors and the Geometry of Space	Cylinders and quadric surfaces
3.	Vector functions	Vector functions and space curves, Derivatives and integrals of vector functions
	Vector functions	Arc length and curvature
	Vector functions	Tangential and Mormal components of acceleration, Kepler's Laws of Planetary Motion, Graphs
4.	Partial derivatives	Limits and continuity, Partial derivatives, Higher Derivatives
	Partial derivatives	Tangent planes and linear approximations, and The chain rule
5.	Partial derivatives	Directional derivatives and the gradient vector
	Partial derivatives	maximum and minimum values, Lagrange multipliers
6.	Multiple integrals	Doulbe integrals over rectangles and iterated integrals
	Multiple integrals	Double integrals over general regions and double integrals in polar coordinates
7.	Multiple integrals	Applications of double integrals
	Multiple integrals	surface area, and triple integrals
8.	Multiple integrals	Triple integrals in cylindrical coordinates and spherical coordinates,
	Multiple integrals	Change of varialbles in multiple integrals
9.	Vector calculus	Vector fields
	Vector calculus	line integral and the fundamental therom for line integrals
10.	Vector calculus	Surface integrals