Multivariable Calculus: Metric Version, Ninth Edition
By James Stewart, Daniel Clegg and Saleem Watson
Contents:
Preface Vii
Technology In The Ninth Edition Xvi
To The Student Xvii
10 Parametric Equations And Polar Coordinates 661
10.1 Curves Defined By Parametric Equations 662
Discovery Project • Running Circles Around Circles 672
10.2 Calculus With Parametric Curves 673
Discovery Project • Bézier Curves 684
10.3 Polar Coordinates 684
Discovery Project • Families Of Polar Curves 694
10.4 Calculus In Polar Coordinates 694
10.5 Conic Sections 702
10.6 Conic Sections In Polar Coordinates 711
Review 719
Problems Plus 722
11 Sequences, Series, And Power Series 723
11.1 Sequences 724
Discovery Project • Logistic Sequences 738
11.2 Series 738
11.3 The Integral Test And Estimates Of Sums 751
11.4 The Comparison Tests 760
11.5 Alternating Series And Absolute Convergence 765
11.6 The Ratio And Root Tests 774
11.7 Strategy For Testing Series 779
11.8 Power Series 781
11.9 Representations Of Functions As Power Series 787
11.10 Taylor And Maclaurin Series 795
Discovery Project • An Elusive Limit 810
Writing Project • How Newton Discovered The Binomial Series 811
11.11 Applications Of Taylor Polynomials 811
Applied Project • Radiation From The Stars 820
Review 821
Problems Plus 825
12 Vectors And The Geometry Of Space 829
12.1 Three-Dimensional Coordinate Systems 830
12.2 Vectors 836
Discovery Project • The Shape Of A Hanging Chain 846
12.3 The Dot Product 847
12.4 The Cross Product 855
Discovery Project • The Geometry Of A Tetrahedron 864
12.5 Equations Of Lines And Planes 864
Discovery Project • Putting 3d In Perspective 874
12.6 Cylinders And Quadric Surfaces 875
Review 883
Problems Plus 887
13 Vector Functions 889
13.1 Vector Functions And Space Curves 890
13.2 Derivatives And Integrals Of Vector Functions 898
13.3 Arc Length And Curvature 904
13.4 Motion In Space: Velocity And Acceleration 916
Applied Project • Kepler’s Laws 925
Review 927
Problems Plus 930
14 Partial Derivatives 933
14.1 Functions Of Several Variables 934
14.2 Limits And Continuity 951
14.3 Partial Derivatives 961
Discovery Project • Deriving The Cobb-Douglas Production Function 973
14.4 Tangent Planes And Linear Approximations 974
Applied Project • The Speedo Lzr Racer 984
14.5 The Chain Rule 985
14.6 Directional Derivatives And The Gradient Vector 994
14.7 Maximum And Minimum Values 1008
Discovery Project • Quadratic Approximations And Critical Points 1019
14.8 Lagrange Multipliers 1020
Applied Project • Rocket Science 1028
Applied Project • Hydro-Turbine Optimization 1030
Review 1031
Problems Plus 1035
15 Multiple Integrals 1037
15.1 Double Integrals Over Rectangles 1038
15.2 Double Integrals Over General Regions 1051
15.3 Double Integrals In Polar Coordinates 1062
15.4 Applications Of Double Integrals 1069
15.5 Surface Area 1079
15.6 Triple Integrals 1082
Discovery Project • Volumes Of Hyperspheres 1095
15.7 Triple Integrals In Cylindrical Coordinates 1095
Discovery Project • The Intersection Of Three Cylinders 1101
15.8 Triple Integrals In Spherical Coordinates 1102
Applied Project • Roller Derby 1108
15.9 Change Of Variables In Multiple Integrals 1109
Review 1117
Problems Plus 1121
16 Vector Calculus 1123
16.1 Vector Fields 1124
16.2 Line Integrals 1131
16.3 The Fundamental Theorem For Line Integrals 1144
16.4 Green’s Theorem 1154
16.5 Curl And Divergence 1161
16.6 Parametric Surfaces And Their Areas 1170
16.7 Surface Integrals 1182
16.8 Stokes’ Theorem 1195
16.9 The Divergence Theorem 1201
16.10 Summary 1208
Review 1209
Problems Plus 1213
Appendixes A1
F Proofs Of Theorems A1
G Answers To Odd-Numbered Exercises A5
Index A39