Single variable calculus : early transcendentals / James Stewart.

Contents
1. 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
Review
Problems Plus
2. LIMITS AND DERIVATIVES
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using Limit Laws
The Precise Definition of a Limit
Continuity
Limits at Infinity; Horizontal Asymptotes
Tangents, Velocities, and Other Rates of Change
Derivatives
Writing Project: Early Methods for Finding Tangents
The Derivative as a Function
Review
Problems Plus
3. 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
Higher Derivatives
Applied Project: Where Should a Pilot Start Descent?
Derivatives of Logarithmic Functions
Hyperbolic Functions
Related Rates
Linear Approximations and Differentials
Laboratory Project: Taylor Polynomials
Review
Problems Plus
4. 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
Intermediate 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 Economics
Newton''''s Method
Antiderivatives
Review
Problems Plus
5. 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
The Logarithm Defined as an Integral
Review
Problems Plus
6. 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
7. 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
8. FURTHER APPLICATIONS OF INTEGRATION Arc Length
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
9. 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
10. 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
11. 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 a Power Series
Taylor and Maclaurin Series
The Binomial Series
Writing Project: How Newton Discovered the Binomial Series
Applications of Taylor Polynomials
Applied Project: Radiation from the Stars

Includes index : p. A107-A115