Description: Contents Note: Each chapter concludes with Review Exercises and P.S. Problem Solving. P. Preparation for Calculus P.1 Graphs and Models P.2 Linear Models and Rates of Change P.3 Functions and Their Graphs P.4 Fitting Models to Data 1. Limits and Their Properties 1.1 A Preview of Calculus 1.2 Finding Limits Graphically and Numerically 1.3 Evaluating Limits Analytically 1.4 Continuity and One-Sided Limits 1.5 Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions 2. Differentiation 2.1 The Derivative and the Tangent Line Problem 2.2 Basic Differentiation Rules and Rates of Change 2.3 The Product and Quotient Rules and Higher-Order Derivatives 2.4 The Chain Rule 2.5 Implicit Differentiation Section Project: Optical Illusions 2.6 Related Rates 3. Applications of Differentiation 3.1 Extrema on an Interval 3.2 Rolle's Theorem and the Mean Value Theorem 3.3 Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows 3.4 Concavity and the Second Derivative Test 3.5 Limits at Infinity 3.6 A Summary of Curve Sketching 3.7 Optimization Problems Section Project: Connecticut River 3.8 Newton's Method 3.9 Differentials 4. Integration 4.1 Antiderivatives and Indefinite Integration 4.2 Area 4.3 Reimann Sums and Definite Integrals 4.4 The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem 4.5 Integration by Substitution 4.6 Numerical Integration 5. Logarithmic, Exponential, and Other Transcendental Functions 5.1 The Natural Logarithmic Function: Differentiation 5.2 The Natural Logarithmic Function: Integration 5.3 Inverse Functions 5.4 Exponential Functions: Differentiation and Integration 5.5 Bases Other Than e and Applications Section Project: Using Graphing Utilities to Estimate Slope 5.6 Differential Equations: Growth and Decay 5.7 Differential Equations: Separation of Variables 5.8 Inverse Trigonometric Functions: Differentiation 5.9 Inverse Trigonometric Functions: Integration 5.10 Hyperbolic Functions Section Project: St. Louis Arch 6. Applications of Integration 6.1 Area of a Region Between Two Curves 6.2 Volume: The Disk Method 6.3 Volume: The Shell Method Section Project: Saturn 6.4 Arc Length and Surfaces of Revolution 6.5 Work Section Project: Tidal Energy 6.6 Moments, Centers of Mass, and Centroids 6.7 Fluid Pressure and Fluid Force 7. Integration Techniques, L'Hpital's Rule, and Improper Integrals 7.1 Basic Integration Rules 7.2 Integration by Parts 7.3 Trigonometric Integrals Section Project: Power Lines 7.4 Trigonometric Substitution 7.5 Partial Fractions 7.6 Integration by Tables and Other Integration Techniques 7.7 Indeterminant Forms and L'Hpital's Rule 7.8 Improper Integrals 8. Infinite Series 8.1 Sequences 8.2 Series and Convergence Section Project: Cantor's Disappearing Table 8.3 The Integral Test and p-Series Section Project: The Harmonic Series 8.4 Comparisons of Series Section Project: Solera Method 8.5 Alternating Series 8.6 The Ratio and Root Tests 8.7 Taylor Polynomials and Approximations 8.8 Power Series 8.9 Representation of Functions by Power Series 8.10 Taylor and Maclaurin Series 9. Conics, Parametric Equations, and Polar Coordinates 9.1 Conics and Calculus 9.2 Plane Curves and Parametric Equations Section Project: Cycloids 9.3 Parametric Equations and Calculus 9.4 Polar Coordinates and Polar Graphs Section Project: Anamorphic Art 9.5 Area and Arc Length in Polar Coordinates 9.6 Polar Equations of Conics and Kepler's Laws Appendices A. Additional Topics in Differential Equations B. Proofs of Selected Theorems C. Integration Tables D. Precalculus Review E. Rotation and the General Second-Degree Equation F. Complex Numbers G. Business and Economic Applications

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