chapter twelve THREE-DIMENSIONAL SPACE; VECTORS 786
12.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 786
12.2 Vectors 792
12.3 Dot Product; Projections 804
12.4 Cross Product 813
12.5 Parametric Equations of Lines 824
12.6 Planes in 3-Space 831
12.7 Quadric Surfaces 839
12.8 Cylindrical and Spherical Coordinates 850

chapter thirteen VECTOR-VALUED FUNCTIONS 859
13.1 Introduction to Vector-Valued Functions 859
13.2 Calculus of Vector-Valued Functions 865
13.3 Change of Parameter; Arc Length 876
13.4 Unit Tangent, Normal, and Binormal Vectors 886
13.5 Curvature 892
13.6 Motion Along a Curve 901
13.7 Kepler’s Laws of Planetary Motion 914

chapter fourteen PARTIAL DERIVATIVES 924
14.1 Functions of Two or More Variables 924
14.2 Limits and Continuity 936
14.3 Partial Derivatives 945
14.4 Differentiability, Differentials, and Local Linearity 959
14.5 The Chain Rule 968
14.6 Directional Derivatives and Gradients 978
14.7 Tangent Planes and Normal Vectors 989
14.8 Maxima and Minima of Functions of Two Variables 996
14.9 Lagrange Multipliers 1008

chapter fifteen MULTIPLE INTEGRALS 1018
15.1 Double Integrals 1018
15.2 Double Integrals over Nonrectangular Regions 1026
15.3 Double Integrals in Polar Coordinates 1035
15.4 Parametric Surfaces; Surface Area 1043
15.5 Triple Integrals 1056
15.6 Centroid, Center of Gravity, Theorem of Pappus 1065
15.7 Triple Integrals in Cylindrical and Spherical Coordinates 1076
15.8 Change of Variables in Multiple Integrals; Jacobians 1087

chapter sixteen  TOPICS IN VECTOR CALCULUS 1102 
16.1 Vector Fields 1102
16.2 Line Integrals 1112
16.3 Independence of Path; Conservative Vector Fields 1129
16.4 Green’s Theorem 1139
16.5 Surface Integrals 1147
16.6 Applications of Surface Integrals; Flux 1155
16.7 The Divergence Theorem 1164
16.8 Stokes’Theorem 1173
Horizon Module: Hurricane Modeling 1183

ANSWERS  A33 

PHOTOCREDITS C1 

INDEX  I-1 

web appendix  a  TRIGONOMETRY REVIEW W1 
web appendix  b  SOLVING POLYNOMIAL EQUATIONS W15 
web appendix  c  SELECTED PROOFS W22 
web appendix  d  REAL NUMBERS,INTERVALS, AND INEQUALITIES W31
web appendix  e  ABSOLUTE VALUE W41 
web appendix  f  COORDINATE PLANES, LINES, AND LINEAR FUNCTIONS W47 
web appendix  g  DISTANCE, CIRCLES, AND QUADRATIC FUNCTIONS W62 
web appendix  h  THE DISCRIMINANT W72 

additional material  PARAMETRIC EQUATIONS
additional material  MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
additional material  ANALYTIC GEOMETRY IN CALCULUS