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 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 Review
Extended Application: Characteristics of the Monkeyface Prickleback
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 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 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 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 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 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 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 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 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 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
12-4 Infinite Series
12-5 Taylor Series
12-6 Newton's Method
12-7 L'Hospital's Rule
Chapter Review
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 Review
Extended Application: The Shortest Time and the Cheapest Path
Tables
Table 1 Formulas of Geometry
Table 2 Area Under a Normal Curve
Table 3 Integrals
Table 4 Integrals Involving Trigonometric Functions
Answers to Selected Exercises
Photo Acknowledgements
Index
