Single Variable Calculus Concepts and Contexts

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  • Edition: 4th
  • Format: Hardcover
  • Copyright: 2009-01-07
  • Publisher: Cengage Learning
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Stewart's CALCULUS: CONCEPTS AND CONTEXTS, FOURTH EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

Table of Contents

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
Principles of Problem Solving
Limits and derivatives
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Laws
Limits Involving Infinity
Derivatives and Rates of Change
Writing Project: Early Methods for Finding Tangents
The Derivative as a Function
What Does
Say about
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
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
Focus on Problem Solving
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
Focus on Problem Solving
Applications of Integration
More about Areas
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
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
Focus on Problem Solving
Infinte Sequences and Series
Laboratory Project: Logistic Sequences
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
Focus on Problem Solving
Intervals, Inequalities, and Absolute Values
Coordinate Geometry
Precise Definitions of Limits
A Few Proofs
Sigma Notation
Integration of Rational Functions by Partial Fractions
Polar Coordinates
Complex Numbers
Answers to Odd-Numbered Exercises
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