Complete Solutions Manual for Single Variable Calculus Early Transcendentals 7th Edition by James Stewart ISBN 0538498676 9780538498678

1. 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

2. 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

3. 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

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
• 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
• 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 Net Change Theorem
• Writing Project: Newton, Leibniz, and the Invention of Calculus
• The Substitution Rule
• 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
• 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

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?
• Models for Population Growth
• Applied Project: Calculus and Baseball
• Linear Equations
• Predator-Prey Systems
• Review
• Problems Plus

10. 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

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
• 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
• Review
• Problems Plus