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List price: $299.95 Edition: 4th Copyright year: 2010 Publisher: Brooks/Cole Publication date: 3/9/2009 Binding: Hardcover Pages: 1152 Size: 9.00" wide x 10.00" long x 1.50" tall Weight: 5.082 Language: English

AuthorTable of Contents

Preface

To the Student

Diagnostic Tests

A Preview of Calculus

Functions and Models

Four Ways to Represent a Function

Mathematical Models: A Catalog of Essential Functions

New Functions from Old Functions

Graphing Calculators and Computers

Exponential Functions

Inverse Functions and Logarithms

Parametric Curves

Laboratory Project: Running Circles around Circles

Review

Principles of Problem Solving

Limits and Derivatives

The Tangent and Velocity Problems

The Limit of a Function

Calculating Limits Using the Limit Laws

Continuity

Limits Involving Infinity

Derivatives and Rates of Change

Writing Project: Early Methods for Finding Tangents

The Derivative as a Function

What Does f?? Say about f? Review

Focus on Problem Solving

Differentiation Rules

Derivatives of Polynomials and Exponential Functions

Applied Project: Building a Better Roller Coaster

The Product and Quotient Rules

Derivatives of Trigonometric Functions

The Chain Rule

Laboratory Project: BTzier Curves

Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation

Inverse Trigonometric Functions and their Derivatives

Derivatives of Logarithmic Functions

Discovery Project: Hyperbolic Functions

Rates of Change in the Natural and Social Sciences

Linear Approximations and Differentials

Laboratory Project: Taylor Polynomials

Review

Focus on Problem Solving

Applications of Differentiation

Related Rates

Maximum and Minimum Values

Applied Project: The Calculus of Rainbows

Derivatives and the Shapes of Curves

Graphing with Calculus and Calculators

Indeterminate Forms and l'Hospital's Rule

Writing Project: The Origins of l'Hospital's Rule

Optimization Problems

Applied Project: The Shape of a Can

Newton's Method

Antiderivatives

Review

Focus on Problem Solving

Integrals

Areas and Distances

The Definite Integral

Evaluating Definite Integrals

Discovery Project: Area Functions

The Fundamental Theorem of Calculus

Writing Project: Newton, Leibniz, and the Invention of Calculus

The Substitution Rule

Integration by Parts

Additional Techniques of Integration

Integration Using Tables and Computer Algebra Systems

Discovery Project: Patterns in Integrals

Approximate Integration

Improper Integrals

Review

Focus on Problem Solving

Applications of Integration

More about Areas

Volumes

Discovery Project: Rotating on a Slant

Volumes by Cylindrical Shells

Arc Length

Discovery Project: Arc Length Contest

Average Value of a Function

Applied Project: Where To Sit at the Movies

Applications to Physics and Engineering

Discovery Project: Complementary Coffee Cups

Applications to Economics and Biology

Probability

Review

Focus on Problem Solving

Differential Equations

Modeling with Differential Equations

Direction Fields and Euler's Method

Separable Equations

Applied Project: How Fast Does a Tank Drain? Applied Project: Which Is Faster, Going Up or Coming Down? Exponential Growth and Decay

Applied Project: Calculus and Baseball

The Logistic Equation

Predator-Prey Systems

Review

Focus on Problem Solving

Infinte Sequences and Series

Sequences

Laboratory Project: Logistic Sequences

Series

The Integral and Comparison Tests

Estimating Sums

Other Convergence Tests

Power Series

Representations of Functions as Power Series

Taylor and Maclaurin Series

Laboratory Project: An Elusive Limit

Writing Project: How Newton Discovered the Binomial Series

Applications of Taylor Polynomials

Applied Project: Radiation from the Stars

Review

Focus on Problem Solving

Vectors and the Geometry of Space

Three-Dimensional Coordinate Systems

Vectors

The Dot Product

The Cross Product

Discovery Project: The Geometry of a Tetrahedron

Equations of Lines and Planes

Laboratory Project: Putting 3D in Perspective

Functions and Surfaces

Cylindrical and Spherical Coordinates

Laboratory Project: Families of Surfaces

Review

Focus on Problem Solving

Vector Functions

Vector Func

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