Calculus: With Analytic Geometry

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''HÔpital''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''HÔpital''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 10. Vectors and the Geometry of Space 10.1 Vectors in the Plane 10.2 Space Coordinates and Vectors in Space 10.3 The Dot Product of Two Vectors 10.4 The Cross Product of Two Vectors in Space 10.5 Lines and Planes in Space Section Project: Distances in Space 10.6 Surfaces in Space 10.7 Cylindrical and Spherical Coordinates 11. Vector-Valued Functions 11.1 Vector-Valued Functions Section Project: Witch of Agnesi 11.2 Differentiation and Integration of Vector-Valued Functions 11.3 Velocity and Acceleration 11.4 Tangent Vectors and Normal Vectors 11.5 Arc Length and Curvature 12. Functions of Several Variables 12.1 Introduction to Functions of Several Variables 12.2 Limits and Continuity 12.3 Partial Derivatives Section Project: MoirÉ Fringes 12.4 Differentials 12.5 Chain Rules for Functions of Several Variables 12.6 Directional Derivatives and Gradients 12.7 Tangent Planes and Normal Lines Section Project: Wildflowers 12.8 Extrema of Functions of Two Variables 12.9 Applications of Extrema of Functions of Two Variables Section Project: Building a Pipeline 12.10 Lagrange Multipliers 13. Multiple Integration 13.1 Iterated Integrals and Area in the Plane 13.2 Double Integrals and Volume 13.3 Change of Variables: Polar Coordinates 13.4 Center of Mass and Moments of Inertia Section Project: Center of Pressure on a Sail 13.5 Surface Area Section Project: Capillary Action 13.6 Triple Integrals and Applications 13.7 Triple Integrals in Cylindrical and Spherical Coordinates Section Project: Wrinkled and Bumpy Spheres 13.8 Change of Variables: Jacobians 14. Vector Analysis 14.1 Vector Fields 14.2 Line Integrals 14.3 Conservative Vector Fields and Independence of Path 14.4 Green''s Theorem Section Project: Hyperbolic and Trigonometric Functions 14.5 Parametric Surfaces 14.6 Surface Integrals Section Project: Hyperboloid of One Sheet 14.7 Divergence Theorem 14.8 Stoke''s Theorem Section Project: The Planimeter 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 ApplicationsLarson, Ron is the author of 'Calculus: With Analytic Geometry' with ISBN 9780618141807 and ISBN 0618141804.