微积分：第2版。下册

chapter 8 infinite series
8.1 sequences of real numbers
8.2 infinite series
8.3 the integral test and comparison tests
8.4 alternating series
8.5 absolute convergence and the ratio test
8.6 power series
8.7 taylor series
8.8 applications of taylor series
8.9 fourier series
chapter 9 parametric equations and polar coordinates
9.1 plane curves and parametric equations
9.2 calculus and parametric equations
9.3 arc length and surface area in parametric equations
9.4 polar coordinates
9.5 calculus and polar coordinates
9.6 conic sections
9.7 conic sections in polar coordinates
chapter 10 vectors and the geometry of space
10.1 vectors in the plane
10.2 vectors in space
10.3 the dot product
10.4 the cross product
10.5 lines and planes in space
10.6 surfaces in space
chapter 11 vector-valued functions
11.1 vector-valued functions
11.2 the calculus of vector-valued functions
11.3 motion in space
11.4 curvature
11.5 tangent and normal vectors
chapter 12 functions of several variables and partial differentiation
12.1 functions of several variables
12.2 limits and continuity
12.3 partial derivatives
12.4 tangent planes and linear approximations
12.5 the chain rule
12.6 the gradient and directional derivatives
12.7 extrema of functions of several variables
12.8 constrained optimization and lagrange multipliers
chapter 13 multiple integrals
13.1 double integrals
13.2 area, volume and center of mass
13.3 double integrals in polar coordinates
13.4 surface area
13.5 triple integrals
13.6 cylindrical coordinates
13.7 spherical coordinates
13.8 change of variables in multiple integrals
chapter 14 vector calculus
14.1 vector fields
14.2 line integrals
14.3 independence of path and conservative vector fields
14.4 green's theorem
14.5 curl and divergence
14.6 surface integrals
14.7 the divergence theorem
14.8 stokes' theorem
appendix a proofs of select theorems
appendix b answers to odd-numbered exercises
bibliography
credits
index