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• Title Page
• Copyright Page
• Contents
• Preface
• Prerequisite Skills Diagnostic Test
• Chapter R: Algebra Reference
• R.1. Polynomials
• R.2. Factoring
• R.3. Rational Expressions
• R.4. Equations
• R.5. Inequalities
• R.6. Exponents
• R.7. Radicals
• Chapter 1: Linear Functions
• 1.1. Slopes and Equations of Lines
• 1.2. Linear Functions and Applications
• 1.3. The Least Squares Line
• Chapter 1: Review
• Extended Application: Using Extrapolation to Predict Life Expectancy
• Chapter 2: Nonlinear Functions
• 2.1. Properties of Functions
• 2.2. Quadratic Functions; Translation and Reflection
• 2.3. Polynomial and Rational Functions
• 2.4. Exponential Functions
• 2.5. Logarithmic Functions
• 2.6. Applications: Growth and Decay; Mathematics of Finance
• Chapter 2: Review
• Extended Application: Power Functions
• Chapter 3: The Derivative
• 3.1. Limits
• 3.2. Continuity
• 3.3. Rates of Change
• 3.4. Definition of the Derivative
• 3.5. Graphical Differentiation
• Chapter 3: Review
• Extended Application: A Model for Drugs Administered Intravenously
• Chapter 4: Calculating the Derivative
• 4.1. Techniques for Finding Derivatives
• 4.2. Derivatives of Products and Quotients
• 4.3. The Chain Rule
• 4.4. Derivatives of Exponential Functions
• 4.5. Derivatives of Logarithmic Functions
• Chapter 4: Review
• Extended Application: Electric Potential and Electric Field
• Chapter 5: Graphs and the Derivative
• 5.1. Increasing and Decreasing Functions
• 5.2. Relative Extrema
• 5.3. Higher Derivatives, Concavity, and the Second Derivative Test
• 5.4. Curve Sketching
• Chapter 5: Review
• Extended Application: A Drug Concentration Model for Orally Administered Medications
• Chapter 6: Applications of the Derivative
• 6.1. Absolute Extrema
• 6.2. Applications of Extrema
• 6.3. Further Business Applications: Economic Lot Size; Economic Order Quantity; Elasticity of Demand
• 6.4. Implicit Differentiation
• 6.5. Related Rates
• 6.6. Differentials: Linear Approximation
• Chapter 6: Review
• Extended Application: A Total Cost Model for a Training Program
• Chapter 7: Integration
• 7.1. Antiderivatives
• 7.2. Substitution
• 7.3. Area and the Definite Integral
• 7.4. The Fundamental Theorem of Calculus
• 7.5. The Area Between Two Curves
• 7.6. Numerical Integration
• Chapter 7: Review
• Extended Application: Estimating Depletion Dates for Minerals
• Chapter 8: Further Techniques and Applications of Integration
• 8.1. Integration by Parts
• 8.2. Volume and Average Value
• 8.3. Continuous Money Flow
• 8.4. Improper Integrals
• Chapter 8: Review
• Extended Application: Estimating Learning Curves in Manufacturing with Integrals
• Chapter 9: Multivariable Calculus
• 9.1. Functions of Several Variables
• 9.2. Partial Derivatives
• 9.3. Maxima and Minima
• 9.4. Lagrange Multipliers
• 9.5. Total Differentials and Approximations
• 9.6. Double Integrals
• Chapter 9: Review
• Extended Application: Using Multivariable Fitting to Create a Response Surface Design
• Chapter 10: Differential Equations
• 10.1. Solutions of Elementary and Separable Differential Equations
• 10.2. Linear First-Order Differential Equations
• 10.3. Euler’s Method
• 10.4. Applications of Differential Equations
• Chapter 10: Review
• Extended Application: Pollution of the Great Lakes
• Chapter 11: Probability and Calculus
• 11.1. Continuous Probability Models
• 11.2. Expected Value and Variance of Continuous Random Variables
• 11.3. Special Probability Density Functions
• Chapter 11: Review
• Extended Application: Exponential Waiting Times
• Chapter 12: Sequences and Series
• 12.1. Geometric Sequences
• 12.2. Annuities: An Application of Sequences
• 12.3. Taylor Polynomials at 0
• 12.4. Infinite Series
• 12.5. Taylor Series
• 12.6. Newton’s Method
• 12.7. L’Hospital’s Rule
• Chapter 12: Review
• Extended Application: Living Assistance and Subsidized Housing
• Chapter 13: The Trigonometric Functions
• 13.1. Definitions of the Trigonometric Functions
• 13.2. Derivatives of Trigonometric Functions
• 13.3. Integrals of Trigonometric Functions
• Chapter 13: Review
• Extended Application: The Shortest Time and the Cheapest Path
• Appendix A: Solutions to Prerequisite Skills Diagnostic Test
• Appendix B: Tables
• Answers to Selected Exercises
• Credits
• Index of Applications
• Index
• Sources
• Key Definitions, Theorems, and Formulas
• Back Cover