Multivariable Calculus, Metric Version, 9th Edition PDF by James Stewart, Daniel Clegg and Saleem Watson

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Multivariable Calculus, Metric Version, Ninth Edition

By James Stewart, Daniel Clegg and Saleem Watson

Multivariable Calculus, Metric Version, 9th Edition PDF 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

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