Top
| Note: Each chapter concludes with Review Exercises and P.S. Problem Solving | |
| Preparation for Calculus | |
| Graphs and Model | |
| Linear Models and Rates of Change | |
| Functions and Their Graphs | |
| Fitting Models to Data | |
| Limits and Their Properties | |
| A Preview of Calculus | |
| Finding Limits Graphically and Numerically | |
| Evaluating Limits Analytically | |
| Continuity and One-Sided Limits | |
| Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions | |
| Differentiation | |
| The Derivative and the Tangent Line Problem | |
| Basic Differentiation Rules and Rates of Change | |
| The Product and Quotient Rules and Higher-Order Derivatives | |
| The Chain Rule | |
| Implicit Differentiation Section Project: Optical Illusions | |
| Related Rates | |
| Applications of Differentiation | |
| Extrema on an Interval | |
| Rolle''s Theorem and the Mean Value Theorem | |
| Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows | |
| Concavity and the Second Derivative Test | |
| Limits at Infinity | |
| A Summary of Curve Sketching | |
| Optimization Problems Section Project: Connecticut River | |
| Newton''s Method | |
| Differentials | |
| Integration | |
| Antiderivatives and Indefinite Integration | |
| Area | |
| Reimann Sums and Definite Integrals | |
| The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem | |
| Integration by Substitution | |
| Numerical Integration | |
| Logarithmic, Exponential, and Other Transcendental Functions | |
| The Natural Logarithmic Function: Differentiation | |
| The Natural Logarithmic Function: Integration | |
| Inverse Functions | |
| Exponential Functions: Differentiation and Integration | |
| Bases Other Than e and Applications Section Project: Using Graphing Utilities to Estimate Slope | |
| Differential Equations: Growth and Decay | |
| Differential Equations: Separation of Variables | |
| Inverse Trigonometric Functions: Differentiation | |
| Inverse Trigonometric Functions: Integration | |
| Hyperbolic Functions Section Project: St. Louis Arch | |
| Applications of Integration | |
| Area of a Region Between Two Curves | |
| Volume: The Disk Method | |
| Volume: The Shell Method Section Project: Saturn | |
| Arc Length and Surfaces of Revolution | |
| Work Section Project: Tidal Energy | |
| Moments, Centers of Mass, and Centroids | |
| Fluid Pressure and Fluid Force | |
| Integration Techniques, L''Hocirc;pital''s Rule, and Improper Integrals | |
| Basic Integration Rules | |
| Integration by Parts | |
| Trigonometric Integrals Section Project: Power Lines | |
| Trigonometric Substitution | |
| Partial Fractions | |
| Integration by Tables and Other Integration Techniques | |
| Indeterminant Forms and L''Hocirc;pital''s Rule | |
| Improper Integrals | |
| Infinite Series | |
| Sequences | |
| Series and Convergence Section Project: Cantor''s Disappearing Table | |
| The Integral Test and p-Series Section Project: The Harmonic Series | |
| Comparisons of Series Section Project: Solera Method | |
| Alternating Series | |
| The Ratio and Root Tests | |
| Taylor Polynomials and Approximations | |
| Power Series | |
| Representation of Functions by Power Series | |
| Taylor and Maclaurin Series | |
| Conics, Parametric Equations, and Polar Coordinates | |
| Conics and Calculus | |
| Plane Curves and Parametric Equations Section Project: Cycloids | |
| Parametric Equations and Calculus | |
| Polar Coordinates and Polar Graphs Section Project: Anamorphic Art | |
| Area and Arc Length in Polar Coordinates | |
| Polar Equations of Conics and Kepler''s Laws | |
| Vectors and the Geometry of Space | |
| Vectors in the Plane | |
| Space Coordinates and Vectors in Space | |
| The Dot Product of Two Vectors | |
| The Cross Product of Two Vectors in Space | |
| Lines and Planes in Space Section Project: Distances in Space | |
| Surfaces in Space | |
| Cylindrical and Spherical Coordinates | |
| Vector-Valued Functions | |
| Vector-Valued Functions Section Project: Witch of Agnesi | |
| Differentiation and Integration of Vector-Valued Functions | |
| Velocity and Acceleration | |
| Tangent Vectors and Normal Vectors | |
| Arc Length and Curvature | |
| Functions of Several Variables | |
| Introduction to Functions of Several Variables | |
| Limits and Continuity | |
| Partial Derivatives Section Project: Moireacute; Fringes | |
| Differentials | |
| Chain Rules for Functions of Several Variables | |
| Directional Derivatives and Gradients | |
| Tangent Planes and Normal Lines Section Project: Wildflowers | |
| Extrema of Functions of Two Variables | |
| Applications of Extrema of Functions of Two Variables Section Project: Building a Pipeline | |
| Lagrange Multipliers | |
| Multiple Integration | |
| Iterated Integrals and Area in the Plane | |
| Double Integrals and Volume | |
| Change of Variables: Polar Coordinates | |
| Center of Mass and Moments of Inertia Section Project: Center of Pressure on a Sail | |
| Surface Area Section Project: Capillary Action | |
| Triple Integrals and Applications | |
| Triple Integrals in Cylindrical and Spherical Coordinates Section Project: Wrinkled and Bumpy Spheres | |
| Change of Variables: Jacobians | |
| Vector Analysis | |
| Vector Fields | |
| Line Integrals | |
| Conservative Vector Fields and Independence of Path | |
| Green''s Theorem Section Project: Hyperbolic and Trigonometric Functions | |
| Parametric Surfaces | |
| Surface Integrals Section Project: Hyperboloid of One Sheet | |
| Divergence Theorem | |
| Stoke''s Theorem Section Project: The Planimeter | |
| Appendices | |
| Additional Topics in Differential Equations | |
| Proofs of Selected Theorems | |
| Integration Tables | |
| Precalculus Review | |
| Rotation and the General Second-Degree Equation | |
| Complex Numbers | |
| Business and Economic Applications | |
| Table of Contents provided by Publisher. All Rights Reserved. |
