Single Variable Calculus Concepts and Contexts

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  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 11/4/2004
  • Publisher: Brooks Cole
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Stewart's clear, direct writing style in SINGLE VARIABLE CALCULUS guides you through key ideas, theorems, and problem-solving steps. Every concept is supported by thoughtfully worked examples and carefully chosen exercises. Many of the detailed examples display solutions that are presented graphically, analytically, or numerically to provide further insight into mathematical concepts. Margin notes expand on and clarify the steps of the solution.

Table of Contents

Functions and Models
Four Ways to Represent a Function
Mathematical Models
New Functions from Old Functions
Graphing Calculators and Computers
Exponential Functions
Inverse Functions and Logarithms
Parametric Curves
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
Tangents, Velocities, and Other Rates of Change
The Derivative as a Function
Linear Approximations
What does f' say about f? Review
Focus on Problem Solving
Differentiation Rules
Derivatives of Polynomials and Exponential Functions
The Product and Quotient Rules
Rates of Change in the Natural and Social Sciences
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Derivatives of Logarithmic Functions
Linear Approximations and Differentials
Focus on Problem Solving
Applications of Differentiation
Related Rates
Maximum and Minimum Values
Derivatives and the Shapes of Curves
Graphing with Calculus and Calculators
Indeterminate Forms and l'Hospital's Rule
Optimization Problems
Applications to Economics
Newton's Method
Focus on Problem Solving
Areas and Distances
The Definite Integral
Evaluating Definite Integrals
The Fundamental Theorem of Calculus
The Substitution Rule
Integration by Parts
Additional Techniques of Integration
Integration Using Tables and Computer Algebra Systems
Approximate Integration
Improper Integrals
Focus on Problem Solving
Applications of Integration
More about Areas
Arc Length
Average Value of a Function
Applications to Physics and Engineering
Applications to Economics and Biology
Focus on Problem Solving
Differential Equations
Modeling with Differential Equations
Direction Fields and Euler's Method
Separable Equations
Exponential Growth and Decay
The Logistic Equation
Predator-Prey Systems
Focus on Problem Solving
Infinite Sequences And Series
The Integral and Comparison Tests; Estimating Sums
Other Convergence Tests
Power Series
Representation of Functions as Power Series
Taylor and Maclaurin Series
The Binomial Series
Applications of Taylor Polynomials
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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