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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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

 

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