Single Variable Calculus Early Transcendentals

by Stewart, James

• ISBN13: 9780495011699
• ISBN10: 049501169X
• Additional ISBN(s): 9780534393304, 9780538498678
• Edition: 6th
• Format: Hardcover
• Copyright: 2007-01-25
• Publisher: Brooks Cole
• More Book Details

Summary

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

Table of Contents

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

Review

Principles of Problem Solving

Limits and Derivatives

The Tangent and Velocity Problems

The Limit of a Function

Calculating Limits Using the Limit Laws

The Precise Definition of a Limit

Continuity

Limits at Infinity

Horizontal Asymptotes

Derivatives and Rates of Change

Writing Project: Early Methods for Finding Tangents

The Derivative as a Function

Review

Problems Plus

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

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

Derivatives of Logarithmic Functions

Rates of Change in the Natural and Social Sciences

Exponential Growth and Decay

Related Rates

Linear Approximations and Differentials

Laboratory Project: Taylor Polynomials

Hyperbolic Functions

Review

Problems Plus

Applications of Differentiation

Maximum and Minimum Values

Applied Project: The Calculus of Rainbows

The Mean Value Theorem

How Derivatives Affect the Shape of a Graph

Indeterminate Forms and L?Hospital?s Rule

Writing Project: The Origins of L?Hospital?s Rule

Summary of Curve Sketching

Graphing with Calculus and Calculators

Optimization Problems

Applied Project: The Shape of a Can

Applications to Business and Economics

Newton?s Method

Antiderivatives

Review

Problems Plus

Integrals

Areas and Distances

The Definite Integral

Discovery Project: Area Functions

The Fundamental Theorem of Calculus

Indefinite Integrals and the Total Change Theorem

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

The Substitution Rule

Review

Problems Plus

Applications of Integration

Areas between Curves

Volume

Volumes by Cylindrical Shells

Work

Average Value of a Function

Applied Project: Where to Sit at the Movies

Review

Problems Plus

Techniques of Integration

Integration by Parts

Trigonometric Integrals

Trigonometric Substitution

Integration of Rational Functions by Partial Fractions

Strategy for Integration

Integration Using Tables and Computer Algebra Systems

Discovery Project: Patterns in Integrals

Approximate Integration

Improper Integrals

Review

Problems Plus

Further Applications of Integration

Arc Length

Discovery Project: Arc Length Contest

Area of a Surface of Revolution

Discovery Project: Rotating on a Slant

Applications to Physics and Engineering

Applications to Economics and Biology

Probability

Review

Problems Plus

Differential Equations

Modeling with Differential Equations

Direction Fields and Euler?s Method

Separable Equations

Applied Project: Which is Faster, Going Up or Coming Down? Exponential Growth and Decay

Applied Project: Calculus and Baseball

The Logistic Equation

Linear Equations

Predator-Prey Systems

Review

Problems Plus

Parametric Equations and Polar Coordinates

Curves Defined by Parametric Equations

Laboratory Project: Families of Hypocycloids

Tangents and Areas

Laboratory Project: Bezier Curves

Arc Length and Surface Area

Polar Coordinates

Areas and Lengths in Polar Coordinates

Conic Sections

Conic Sections in Polar Coordinates

Applied Project: Transfer Orbits

Review

Problems Plus

Infinite Sequences and Series

Sequences

Laboratory Project: Logistic Sequences

Series

The Integral Test and Estimates of Sums

The Comparison Tests

Alternating Series

Absolute Convergence and the Ratio and Root Tests

Strategy for Testing Series

Power Series

Representation of Functions as Power Series

Taylor and Maclaurin Series The Binomial Series

Writing Project: How Newton Discovered the Binomial Series

Applications of Taylor Polynomials

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