Preface
Prerequisite Skills Diagnostic Test
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 1 Review
Extended Application: Predicting 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 2 Review
Extended Application: Power Functions
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 4 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 5 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
6.4 Implicit Differentiation
6.5 Related Rates
6.6 Differentials: Linear Approximation
Chapter 6 Review
Extended Application: A Total 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 7 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 8 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 9 Review
Extended Application: Using Multivariable Fitting to Create a Response Surface Design
Appendix
- Solutions to Prerequisite Skills Diagnostic Test
- Tables
Answers to Selected Exercises
Credits
Index of Applications
Index
Sources
