9780495011613

Single Variable Calculus

by
  • ISBN13:

    9780495011613

  • ISBN10:

    0495011614

  • Edition: 6th
  • Format: Hardcover
  • Copyright: 3/29/2007
  • Publisher: Cengage Learning
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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, 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
Review
Principles of Problem Solving
Limits
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Laws
The Precise Definition of a Limit
Continuity
Review
Problems Plus
Derivatives
Derivatives and Rates of Change
Writing Project: Early Methods for Finding Tangents
The Derivative as a Function
Differentiation Formulas
Applied Project: Building a Better Roller Coaster
Derivatives of Trigonometric Functions
The Chain Rule
Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation
Rates of Change in the Natural and Social Sciences
Related Rates
Linear Approximations and Differentials
Laboratory Project: Taylor Polynomials
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
Limits at Infinity
Horizontal Asymptotes
Summary of Curve Sketching
Graphing with Calculus and Calculators
Optimization Problems
Applied Project: The Shape of a Can
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 Net 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
Review
Problems Plus
Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
Inverse Functions. (Instructors may cover either Sections 7.2-7.4 or Sections 7.2*-7.4*. See the Preface.)
Exponential Functions and Their Derivatives
Logarithmic Functions
Derivatives of Logarithmic Functions
The Natural Logarithmic Function
The Natural Exponential Function
General Logarithmic and Exponential Functions
Exponential Growth and Decay
Inverse Trigonometric Functions
Applied Project: Where to Sit at the Movies
Hyperbolic Functions
Indeterminate Forms and L'Hospital's Rule
Writing Project: The Origins of L'Hospital's Rule
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
Discovery Project: Complementary Coffee Cups
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? Models for Population Growth
Applied Project: Calculus and Baseball
Linear Equations
Predator-Prey Systems
Review
Problems Plus
Parametric Equations and Polar Coordinates
Curves Defined by Parametric Equations
Laboratory Project: Families of Hypocycloids
Calculus with Parametric Curves
Laboratory Project: Bezier Curves
Polar Coordinates
Areas and Lengths in Polar Coordinates
Conic Sections
Conic Sections in Polar Coordinates
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
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