| A Word from the Authors (Preface) |
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xi | |
| Index of Applications |
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xxxi | |
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1 | (38) |
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3 | (8) |
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Linear Models and Rates of Change |
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11 | (9) |
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Functions and Their Graphs |
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20 | (11) |
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31 | (8) |
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37 | (2) |
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Limits and Their Properties |
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39 | (50) |
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41 | (6) |
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Finding Limits Graphically and Numerically |
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47 | (9) |
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Evaluating Limits Analytically |
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56 | (11) |
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Continuity and One-Sided Limits |
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67 | (12) |
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79 | (10) |
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87 | (2) |
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89 | (64) |
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The Derivative and the Tangent Line Problem |
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91 | (11) |
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Basic Differentiation Rules and Rates of Change |
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102 | (12) |
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The Product and Quotient Rules and Higher-Order Derivatives |
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114 | (10) |
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124 | (10) |
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134 | (7) |
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141 | (12) |
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150 | (3) |
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Applications of Differentiation |
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153 | (86) |
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155 | (8) |
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Rolle's Theorem and the Mean Value Theorem |
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163 | (6) |
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Increasing and Decreasing Functions and the First Derivative Test |
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169 | (10) |
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Concavity and the Second Derivative Test |
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179 | (8) |
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187 | (9) |
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A Summary of Curve Sketching |
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196 | (9) |
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205 | (10) |
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215 | (6) |
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221 | (7) |
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Business and Economics Applications |
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228 | (11) |
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235 | (4) |
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239 | (70) |
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Antiderivatives and Indefinite Integration |
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241 | (11) |
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252 | (12) |
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Riemann Sums and Definite Integrals |
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264 | (10) |
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The fundamental Theorem of Calculus |
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274 | (13) |
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Integration by Substitution |
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287 | (12) |
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299 | (10) |
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306 | (3) |
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Logarithmic, Exponential, and Other Transcendental Functions |
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309 | (96) |
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The Natural Logarithmic Function and Differentiation |
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311 | (10) |
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The Natural Logarithmic function and Integration |
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321 | (8) |
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329 | (9) |
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Exponential Functions: Differentiation and Integration |
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338 | (10) |
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Bases Other than e and Applications |
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348 | (10) |
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Differential Equations: Growth and Decay |
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358 | (8) |
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Differential Equations: Separation of Variables |
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366 | (11) |
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Inverse Trigonometric Functions and Differentiation |
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377 | (8) |
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Inverse Trigonometric Functions and Integration |
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385 | (7) |
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392 | (13) |
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402 | (3) |
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Applications of Integration |
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405 | (68) |
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Area of a Region Between Two Curves |
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407 | (9) |
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416 | (11) |
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427 | (8) |
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Arc Length and Surfaces of Revolution |
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435 | (10) |
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445 | (9) |
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Moments, Centers of Mass, and Centroids |
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454 | (11) |
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Fluid Pressure and Fluid Force |
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465 | (8) |
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471 | (2) |
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Integration Techniques, L'Hopital's Rule, and Improper Integrals |
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473 | (72) |
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475 | (6) |
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481 | (9) |
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490 | (9) |
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Trigonometric Substitution |
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499 | (9) |
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508 | (9) |
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Integration by Tables and Other Integration Techniques |
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517 | (6) |
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Indeterminate Forms and L'Hopital's Rule |
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523 | (10) |
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533 | (12) |
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542 | (3) |
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545 | (90) |
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547 | (11) |
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558 | (10) |
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The Integral Test and p-Series |
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568 | (6) |
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574 | (7) |
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581 | (7) |
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588 | (8) |
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Taylor Polynomials and Approximations |
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596 | (10) |
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606 | (9) |
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Representation of Functions by Power Series |
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615 | (7) |
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Taylor and Maclaurin Series |
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622 | (13) |
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632 | (3) |
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Conics, Parametric Equations, and Polar Coordinates |
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635 | (64) |
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637 | (15) |
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Plane Curves and Parametric Equations |
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652 | (10) |
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Parametric Equations and Calculus |
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662 | (9) |
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Polar Coordinates and Polar Graphs |
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671 | (10) |
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Area and Arc Length in Polar Coordinates |
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681 | (8) |
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Polar Equations of Conics and Kepler's Laws |
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689 | (10) |
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696 | (3) |
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Vectors and the Geometry of Space |
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699 | (68) |
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701 | (11) |
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Space Coordinates and Vectors in Space |
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712 | (8) |
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The Dot Product of Two Vectors |
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720 | (9) |
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Teh Cross Product of Two Vectors in Space |
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729 | (8) |
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Lines and Planes in Space |
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737 | (11) |
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748 | (10) |
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Cyclindrical and Spherical Coordinates |
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758 | (9) |
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765 | (2) |
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767 | (50) |
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769 | (8) |
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Differentiation and Integration of Vector-Valued Functions |
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777 | (8) |
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Velocity and Acceleration |
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785 | (9) |
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Tangent Vectors and Normal Vectors |
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794 | (9) |
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803 | (14) |
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815 | (2) |
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Functions of Several Variables |
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817 | (96) |
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Introduction to Functions of Several Variables |
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819 | (12) |
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831 | (9) |
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840 | (9) |
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849 | (8) |
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Chain Rules for Functions of Several Variables |
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857 | (8) |
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Directional Derivatives and Gradients |
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865 | (12) |
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Tangent Planes and Normal Lines |
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877 | (9) |
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Extrema of Functions of Two Variables |
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886 | (8) |
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Applications of Extrema of Functions of Two Variables |
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894 | (8) |
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902 | (11) |
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910 | (3) |
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913 | (70) |
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Interated Integrals and Area in the Plane |
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915 | (8) |
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Double Itegrals and Volume |
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923 | (11) |
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Change of Variables: Polar Coordinates |
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934 | (8) |
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Center of Mass and Moments of Inertia |
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942 | (8) |
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950 | (7) |
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Triple Integrals and Applications |
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957 | (10) |
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Triple Integrals in Cylindrical and Spherical Coordinates |
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967 | (7) |
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Change of Variables: Jacobians |
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974 | (9) |
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980 | (3) |
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983 | (84) |
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985 | (11) |
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996 | (13) |
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Conservative Vector Fields and Independence of Path |
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1009 | (10) |
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1019 | (9) |
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1028 | (10) |
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1038 | (12) |
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1050 | (8) |
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1058 | (9) |
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1064 | (3) |
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1067 | |
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Exact First-Order Equations |
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1069 | |
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First-Order Linear Differential Equations |
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1076 | |
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Second-Order Homogeneous Linear Equations |
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1085 | |
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Second-Order Nonhomogeneous Linear Equations |
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1093 | |
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Series Solutions of Differential Equations |
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1101 | |
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1104 | |
| Appendix A Precalculus Review |
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A1 | |
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A.1 Real Numbers and the Real Line |
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A1 | |
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A10 | |
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A.3 Review of Trigonometric Functions |
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A17 | |
| Appendix B Proofs of Selected Theorems |
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A28 | |
| Appendix C Basic Differentiation Rules for Elementary Functions |
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A44 | |
| Appendix D Integration Tables |
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A45 | |
| Appendix E Rotation and the General Second-Degree Equation |
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A51 | |
| Appendix F Complex Numbers |
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A57 | |
| Answers to Odd-Numbered Exercises |
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A69 | |
| Index |
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A197 | |
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