A Word from the Authors (Preface) [xi]
Index of Applications [xxxi]
Chapter P Preparation for Calculus [1]
P.1 Graphs and Models [3]
P.2 Linear Models and Rates of Change [11]
P.3 Functions and Their Graphs [20]
P.4 Fitting Models to Data [31]
Review Exercises [37]
Chapter 1 Limits and Their Properties [39]
1.1 A Preview of Calculus [41]
1.2 Finding Limits Graphically and Numerically [47]
1.3 Evaluating Limits Analytically [56]
1.4 Continuity and OneSided Limits [67]
1.5 Infinite Limits [79]
Review Exercises [87]
Chapter 2 Differentiation [89]
2.1 The Derivative and the Tangent Line Problem [91]
2.2 Basic Differentiation Rules and Rates of Change [102]
2.3 The Product and Quotient Rules and HigherOrder Derivatives [114]
2.4 The Chain Rule [124]
2.5 Implicit Differentiation [134]
2.6 Related Rates [141]
Review Exercises [150]
Chapter 3 Applications of Differentiation [153]
3.1 Extrema on an Interval [155]
3.2 Rolle's Theorem and the Mean Value Theorem [163]
3.3 Increasing and Decreasing Functions and the First Derivative Test [169]
3.4 Concavity and the Second Derivative Test [179]
3.5 Limits at Infinity [187]
3.6 A Summary of Curve Sketching [196]
3.7 Optimization Problems [205]
3.8 Newton's Method [215]
3.9 Differentials [221]
3.10 Business and Economics Applications [228]
Review Exercises [235]
Chapter 4 Integration [239]
4.1 Antiderivatives and Indefinite Integration [241]
4.2 Area [252]
4.3 Riemann Sums and Definite Integrals [264]
4.4 The Fundamental Theorem of Calculus [274]
4.5 Integration by Substitution [287]
4.6 Numerical Integration [299]
Review Exercises [306]
Chapter 5 Logarithmic, Exponential, and Other Transcendental Functions [309]
5.1 The Natural Logarithmic Function and Differentiation [311]
5.2 The Natural Logarithmic Function and Integration [321]
5.3 Inverse Functions [329]
5.4 Exponential Functions: Differentiation and Integration [338]
5.5 Bases Other than e and Applications [348]
5.6 Differential Equations: Growth and Decay [358]
5.7 Differential Equations: Separation of Variables [366]
5.8 Inverse Trigonometric Functions and Differentiation [377]
5.9 Inverse Trigonometric Functions and Integration [385]
5.10 Hyperbolic Functions [392]
Review Exercises [402]
Chapter 6 Applications of Integration [405]
6.1 Area of a Region Between Two Curves [407]
6.2 Volume: The Disc Method [416]
6.3 Volume: The Shell Method [427]
6.4 Arc Length and Surfaces of Revolution [435]
6.5 Work [445]
6.6 Moments, Centers of Mass, and Centroids [454]
6.7 Fluid Pressure and Fluid Force [465]
Review Exercises [471]
Chapter 7 Integration Techniques, L'Hôpital's Rule, and Improper Integrals [473]
7.1 Basic Integration Rules [475]
7.2 Integration by Parts [481]
7.3 Trigonometric Integrals [490]
7.4 Trigonometric Substitution [499]
7.5 Partial Fractions [508]
7.6 Integration by Tables and Other Integration Techniques [517]
7.7 Indeterminate Forms and L'Hôpital's Rule [523]
7.8 Improper Integrals [533]
Review Exercises [542]
Chapter 8 Infinite Series
8.1 Sequences [547]
8.2 Series and Convergence [558]
8.3 The Integral Test and pSeries [568]
8.4 Comparisons of Series [574]
8.5 Alternating Series [581]
8.6 The Ratio and Root Tests [588]
8.7 Taylor Polynomials and Approximations [596]
8.8 Power Series [606]
8.9 Representation of Functions by Power Series [615]
8.10 Taylor and Maclaurin Series [622]
Review Exercises [632]
Chapter 9 Conics, Parametric Equations, and Polar Coordinates [635]
9.1 Conics and Calculus [637]
9.2 Plane Curves and Parametric Equations [652]
9.3 Parametric Equations and Calculus [662]
9.4 Polar Coordinates and Polar Graphs [671]
9.5 Area and Arc Length in Polar Coordinates [681]
9.6 Polar Equations of Conics and Kepler's Laws [689]
Review Exercises [696]
Chapter 10 Vectors and the Geometry of Space [699]
10.1 Vectors in the Plane [701]
10.2 Space Coordinates and Vectors in Space [712]
10.3 The Dot Product of Two Vectors [720]
10.4 The Cross Product of Two Vectors in Space [729]
10.5 Lines and Planes in Space [737]
10.6 Surfaces in Space [748]
10.7 Cylindrical and Spherical Coordinates [758]
Review Exercises [765]
Chapter 11 VectorValued Functions [767]
11.1 VectorValued Functions [769]
11.2 Differentiation and Integration of VectorValued Functions [777]
11.3 Velocity and Acceleration [785]
11.4 Tangent Vectors and Normal Vectors [794]
11.5 Arc Length and Curvature [803]
Review Exercises [815]
Chapter 12 Functions of Several Variables [817]
12.1 Introduction to Functions of Several Variables [819]
12.2 Limits and Continuity [831]
12.3 Partial Derivatives [840]
12.4 Differentials [849]
12.5 Chain Rules for Functions of Several Variables [857]
12.6 Directional Derivatives and Gradients [865]
12.7 Tangent Planes and Normal Lines [877]
12.8 Extrema of Functions of Two Variables [886]
12.9 Applications of Extrema of Functions of Two Variables [894]
12.10 Lagrange Multipliers [902]
Review Exercises [910]
Chapter 13 Multiple Integration [913]
13.1 Iterated Integrals and Area in the Plane [915]
13.2 Double Integrals and Volume [923]
13.3 Change of Variables: Polar Coordinates [934]
13.4 Center of Mass and Moments of Inertia [942]
13.5 Surface Area [950]
13.6 Triple Integrals and Applications [957]
13.7 Triple Integrals in Cylindrical and Spherical
Coordinates [967]
13.8 Change of Variables: Jacobians [974]
Review Exercises [980]
Chapter 14 Vector Analysis [983]
14.1 Vector Fields [985]
14.2 Line Integrals [996]
14.3 Conservative Vector Fields and Independence
of Path [1009]
14.4 Green's Theorem [1019]
14.5 Parametric Surfaces [1028]
14.6 Surface Integrals [1038]
14.7 Divergence Theorem [1050]
14.8 Stokes's Theorem [1058]
Review Exercises [1064]
Chapter 15 Differential Equations [1067]
15.1 Exact FirstOrder Equations [1069]
15.2 FirstOrder Linear Differential Equations [1076]
15.3 SecondOrder Homogeneous Linear Equations [1085]
15.4 SecondOrder Nonhomogeneous Linear Equations [1093]
15.5 Series Solutions of Differential Equations [1101]
Review Exercises [1104]
Appendix A Precalculus Review [A1]
A.1 Real Numbers and the Real Line [A1]
A.2 The Cartesian Plane [A10]
A.3 Review of Trigonometric Functions [A17]
Appendix B Proofs of Selected Theorems [A28]
Appendix C Basic Differentiation Rules for Elementary Functions [A44]
Appendix D Integration Tables [A45]
Appendix E Rotation and the General SecondDegree Equation [A51]
Appendix F Complex Numbers [A57]
Answers to OddNumbered Exercises [A69]
Index [A197]
