Calculus: Late Transcendentals, Multivariable (Chapters 11-18)

Cover Page......Page 1
Title in Calculus, Fourth Edition......Page 2
Copyright in Calculus: Early Transcendentals, Fourth Edition......Page 3
About The Authors......Page 5
Contents......Page 7
PREFACE......Page 10
ACKNOWLEDGMENTS......Page 20
Introduction to Calculus......Page 29
Chapter 11 Infinite Series......Page 33
11.1 Sequences in Chapter 11 Infinite Series......Page 35
11.2 Summing an Infinite Series in Chapter 11 Infinite Series......Page 64
11.3 Convergence of Series with Positive Terms in Chapter 11 Infinite Series......Page 92
11.4 Absolute and Conditional Convergence in Chapter 11 Infinite Series......Page 115
11.5 The Ratio and Root Tests and Strategies for Choosing Tests in Chapter 11 Infinite Series......Page 129
11.6 Power Series in Chapter 11 Infinite Series......Page 142
11.7 Taylor Polynomials in Chapter 11 Infinite Series......Page 167
11.8 Taylor Series in Chapter 11 Infinite Series......Page 194
Chapter Review Exercises in Chapter 11 Infinite Series......Page 223
Chapter 12 Parametric Equations, Polar Coordinates, and Conic Sections......Page 235
12.1 Parametric Equations in Chapter 12 Parametric Equations, Polar Coordinates, and Conic Sections......Page 236
12.2 Arc Length and Speed in Chapter 12 Parametric Equations, Polar Coordinates, and Conic Sections......Page 269
12.3 Polar Coordinates in Chapter 12 Parametric Equations, Polar Coordinates, and Conic Sections......Page 285
12.4 Area and Arc Length in Polar Coordinates in Chapter 12 Parametric Equations, Polar Coordinates, and Conic Sections......Page 310
12.5 Conic Sections in Chapter 12 Parametric Equations, Polar Coordinates, and Conic Sections......Page 326
Chapter Review Exercises in Chapter 12 Parametric Equations, Polar Coordinates, and Conic Sections......Page 359
Chapter 13 Vector Geometry......Page 364
13.1 Vectors in the Plane in Chapter 13 Vector Geometry......Page 366
13.2 Three-Dimensional Space: Surfaces, Vectors, and Curves in Chapter 13 Vector Geometry......Page 394
13.3 Dot Product and the Angle Between two Vectors in Chapter 13 Vector Geometry......Page 420
13.4 The Cross Product in Chapter 13 Vector Geometry......Page 450
13.5 Planes in 3-Space in Chapter 13 Vector Geometry......Page 479
13.6 A Survey of Quadric Surfaces in Chapter 13 Vector Geometry......Page 497
13.7 Cylindrical and Spherical Coordinates in Chapter 13 Vector Geometry......Page 517
Chapter Review Exercises in Chapter 13 Vector Geometry......Page 540
14 Calculus of Vector-Valued Functions......Page 546
14.1 Vector-Valued Functions......Page 547
14.2 Calculus of Vector-Valued Functions in Chapter 14 Calculus of Vector-Valued Functions......Page 564
14.3 Arc Length and Speed in Chapter 14 Calculus of Vector-Valued Functions......Page 587
14.4 Curvature in Chapter 14 Calculus of Vector-Valued Functions......Page 599
14.5 Motion in 3-Space in Chapter 14 Calculus of Vector-Valued Functions......Page 629
14.6 Planetary Motion According to Kepler and Newton in Chapter 14 Calculus of Vector-Valued Functions......Page 651
Chapter Review Exercises in Chapter 14 Calculus of Vector-Valued Functions......Page 667
Chapter 15 Differentiation in Several Variables......Page 671
15.1 Functions of Two or More Variables in Chapter 15 Differentiation in Several Variables......Page 672
15.2 Limits and Continuity in Several Variables in Chapter 15 Differentiation in Several Variables......Page 699
15.3 Partial Derivatives in Chapter 15 Differentiation in Several Variables......Page 716
15.4 Differentiability, Tangent Planes, and Linear Approximation in Chapter 15 Differentiation in Several Variables......Page 740
15.5 The Gradient and Directional Derivatives in Chapter 15 Differentiation in Several Variables......Page 760
15.6 The Gradient and Directional Derivatives in Chapter 15 Differentiation in Several Variables......Page 790
15.7 Optimization in Several Variables in Chapter 15 Differentiation in Several Variables......Page 812
15.8 Lagrange Multipliers: Optimizing with a Constraint in Chapter 15 Differentiation in Several Variables......Page 847
Chapter Review Exercises in Chapter 15 Differentiation in Several Variables......Page 870
Chapter 16 Multiple Integration......Page 878
16.1 Integration in Two Variables in Chapter 16 Multiple Integration......Page 879
16.2 Double Integrals over More General Regions in Chapter 16 Multiple Integration......Page 906
16.3 Triple Integrals in Chapter 16 Multiple Integration......Page 942
16.4 Integration in Polar, Cylindrical, and Spherical Coordinates in Chapter 16 Multiple Integration......Page 967
16.5 Applications of Multiple Integrals in Chapter 16 Multiple Integration......Page 995
16.6 Change of Variables in Chapter 16 Multiple Integration......Page 1024
Chapter 16 Multiple Integration......Page 1052
Chapter 17 Line and Surface......Page 1060
17.1 Vector Fields in Chapter 17 Line and Surface......Page 1061
17.2 Line Integrals in Chapter 17 Line and Surface......Page 1085
17.3 Conservative Vector Fields in Chapter 17 Line and Surface......Page 1120
17.4 Parametrized Surfaces and Surface Integrals in Chapter 17 Line and Surface......Page 1147
17.5 Surface Integrals of Vector Fields in Chapter 17 Line and Surface......Page 1178
Chapter Review Exercises in Chapter 17 Line and Surface......Page 1202
Chapter 18 Fundamental Theorems of Vector Analysis......Page 1208
18.1 Green’s Theorem in Chapter 18 Fundamental Theorems of Vector Analysis......Page 1210
18.2 Stokes’ Theorem in Chapter 18 Fundamental Theorems of Vector Analysis......Page 1242
18.3 Divergence Theorem in Chapter 18 Fundamental Theorems of Vector Analysis......Page 1267
Chapter Review Exercises in Chapter 18 Fundamental Theorems of Vector Analysis......Page 1296
A The Language of Mathematics in Calculus......Page 1304
B Properties of Real Numbers in Calculus......Page 1316
C Induction and The Binomial Theorem in Calculus......Page 1324
D Additional Proofs in Calculus......Page 1332
Answers to Odd-Numbered Exercises......Page 1346
Chapter 1 Precalculus Review......Page 1347
Index......Page 1349
Algebra......Page 1386
Back Cover......Page 1413