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  • Edition: 7th
  • Format: Hardcover
  • Copyright: 7/11/2001
  • Publisher: Brooks Cole
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Table of Contents

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
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
Antiderivatives and Indefinite Integration
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
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
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
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
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