11 Infinite Sequences and Series 689
11.1 Sequences 690
Laboratory Project Logistic Sequences 703
11.2 Series 703
11.3 The Integral Test and Estimates of Sums 714
11.4 The Comparison Tests 722
11.5 Alternating Series 727
11.6 Absolute Convergence and the Ratio and Root Tests 732
11.7 Strategy for Testing Series 739
11.8 Power Series 741
11.9 Representations of Functions as Power Series 746
11.10 Taylor and Maclaurin Series 753
Laboratory Project An Elusive Limit 767
Writing Project How Newton Discovered the Binomial Series 767
11.11 Applications of Taylor Polynomials 768
Applied Project Radiation from the Stars 777
Review 778
Problems Plus 781
12 Vectors and the Geometry of Space 785
12.1 Three-Dimensional Coordinate Systems 786
12.2 Vectors 791
12.3 The Dot Product 800
12.4 The Cross Product 808
Discovery Project The Geometry of a Tetrahedron 816
12.5 Equations of Lines and Planes 816
Laboratory Project Putting 3D in Perspective 826
12.6 Cylinders and Quadric Surfaces 827
Review 834
Problems Plus 837
13 Vector Functions 839
13.1 Vector Functions and Space Curves 840
13.2 Derivatives and Integrals of Vector Functions 847
13.3 Arc Length and Curvature 853
13.4 Motion in Space:Velocity and Acceleration 862
Applied Project Kepler's Laws 872
Review 873
Problems Plus 876
14 Partial Derivatives 877
14.1 Functions of Several Variables 878
14.2 Limits and Continuity 892
14.3 Partial Derivatives 900
14.4 Tangent Planes and Linear Approximations 915
14.5 The Chain Rule 924
14.6 Directional Derivatives and the Gradient Vector 933
14.7 Maximum and Minimum Values 946
Applied Project Designing a Dumpster 956
Discovery Project Quadratic Approximations and Critical Points 956
14.8 Lagrange Multipliers 957
Applied Project Rocket Science 964
Applied Project Hydro-Turbine Optimization 966
Review 967
Problems Plus 971
15 Multiple Integrals 973
15.1 Double Integrals over Rectangles 974
15.2 Iterated Integrals 982
15.3 Double Integrals over General Regions 988
15.4 Double Integrals in Polar Coordinates 997
15.5 Applications of Double Integrals 1003
15.6 Surface Area 1013
15.7 Triple Integrals 1017
Discovery Project Volumes of Hyperspheres 1027
15.8 Triple Integrals in Cylindrical Coordinates 1027
Laboratory Project The Intersection of Three Cylinders 1032
15.9 Triple Integrals in Spherical Coordinates 1033
Applied Project Roller Derby 1039
15.10 Change of Variables in Multiple Integrals 1040
Review 1049
Problems Plus 1053
16 Vector Calculus 1055
16.1 Vector Fields 1056
16.2 Line Integrals 1063
16.3 The Fundamental Theorem for Line Integrals 1075
16.4 Green's Theorem 1084
16.5 Curl and Divergence 1091
16.6 Parametric Surfaces and Their Areas 1099
16.7 Surface Integrals 1110
16.8 Stokes'Theorem 1122
Writing Project Three Men and Two Theorems 1128
16.9 The Divergence Theorem 1128
16.10 Summary 1135
Review 1136
Problems Plus 1139
17 Second-Order Differential Equations 1141
17.1 Second-Order Linear Equations 1142
17.2 Nonhomogeneous Linear Equations 1148
17.3 Applications of Second-Order Differential Equations 1156
17.4 Series Solutions 1164
Review 1169