16-3 polar equations of circles, conics, and spirals
16-4 arc length and tangent lines
16-5 areas in polar coordinates
chapter 17: parametric equations
17-1 parametric equations of curves
17-2 the cycloid and other similar curves
17-3 vector algebra
17-4 derivatives of vector function
17-5 curvature and the unit normal vector
17-6 tangential and normal components of acceleration
17-7 kepler's laws and newton's laws of gravitation
chapter 18: vectors in three-dimensional space
18-1 coordinates and vectors in three-dimensional space
18-2 the dot product of two vectors
18-3 the cross product of two vectors
18-4 lines and planes
18-5 cylinders and surfaces of revolution
18-6 quadric surfaces
18-7 cylindrical and spherical coordinates
chapter 19: partial derivatives
19-1 functions of several variables
19-2 partial derivatives
19-3 the tangent plane to a surface
19-4 increments and differentials
19-5 directional derivatives and the gradient
19-6 the chain rule for partial derivatives
19-7 maximum and minimum problems
19-8 constrained maxima and minima
19-9 laplace's equation, the heat equation, and the wave equation
19-10 (optional) implicit functions
chapter 20: multiple integrals
20-1 volumes as iterated integrals
20-2 double integrals and iterated integrals
20-3 physical applications of double integrals
20-4 double integrals in polar coordinates
20-5 triple integrals
20-6 cylindrical coordinates
20-7 spherical coordinates
20-8 areas of curved surfaces
chapter 21: line and surface integrals
21-1 green's theorem, gauss's theorem, and stokes' theorem
21-2 line integrals in the plane
21-3 independence of path
21-4 green's theorem
21-5 surface integrals and gauss's theorem
21-6 maxwell's equations : a final thought
appendices
a: the theory of calculus
a-1 the real number system
a-2 theorems about limits
a-3 some deeper properties of continuous functions
a-4 the mean value theorem
a-5 the integrability of continuous functions
a-6 another proof of the fundamental theorem of calculus
a-7 continuous curves with no length
a-8 the existence of e = lim h->0 (1 + h) <^>1/h
a-9 functions that cannot be integrated
a-10 the validity of integration by inverse substitution
a-11 proof of the partial fractions theorem
a-12 the extended ratio tests of raabe and gauss
a-13 absolute vs conditional convergence
a-14 dirichlet's test
a-15 uniform convergence for power series
a-16 division of power series
a-17 the equality of mixed partial derivatives
a-18 differentiation under the integral sign
a-19 a proof of the fundamental lemma
a-20 a proof of the implicit function theorem
a-21 change of variables in multiple integrals
b: a few review topics
b-1 the binomial theorem
b-2 mathematical induction 

微积分与解析几何-(影印版.原书第2版) 作者简介

乔治·西蒙斯(George F.Simmons) 博士毕业于耶鲁大学。他通常能用简练精妙的语言表达深刻的数学思想，他在科罗拉多学院任教的日子，以其鲜明的个性以及引入入胜的教学方式，赢得学生的喜爱。

 4/4   首页 上一页 2 3 4

教材 研究生/本科/专科教材

在线阅读