Finite Mathematics and Calculus with Applications, 11th edition

• 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. Systems of Linear Equations and Matrices

• 2.1 Solution of Linear Systems by the Echelon Method
• 2.2 Solution of Linear Systems by the Gauss-Jordan Method
• 2.3 Addition and Subtraction of Matrices
• 2.4 Multiplication of Matrices
• 2.5 Matrix Inverses
• 2.6 Input-Output Models
• Chapter 2 Review
• Extended Application: Contagion

3. Linear Programming: The Graphical Method

• 3.1 Graphing Linear Inequalities
• 3.2 Solving Linear Programming Problems Graphically
• 3.3 Applications of Linear Programming
• Chapter 3 Review
• Extended Application: Sensitivity Analysis

4. Linear Programming: The Simplex Method

• 4.1 Slack Variables and the Pivot
• 4.2 Maximization Problems
• 4.3 Minimization Problems; Duality
• 4.4 Nonstandard Problems
• Chapter 4 Review
• Extended Application: Using Integer Programming in the Stock-Cutting
• Problem

5. Mathematics of Finance

• 5.1 Simple and Compound Interest
• 5.2 Future Value of an Annuity
• 5.3 Present Value of an Annuity; Amortization
• Chapter 5 Review
• Extended Application: Time, Money, and Polynomials

6. Logic

• 6.1 Statements
• 6.2 Truth Tables and Equivalent Statements
• 6.3 The Conditional and Circuits
• 6.4 More on the Conditional
• 6.5 Analyzing Arguments and Proofs
• 6.6 Analyzing Arguments with Quantifiers
• Chapter 6 Review
• Extended Application: Logic Puzzles

7. Sets and Probability

• 7.1 Sets
• 7.2 Applications of Venn Diagrams
• 7.3 Introduction to Probability
• 7.4 Basic Concepts of Probability
• 7.5 Conditional Probability; Independent Events
• 7.6 Bayes' Theorem
• Chapter 7 Review
• Extended Application: Medical Diagnosis

8. Counting Principles; Further Probability Topics

• 8.1 The Multiplication Principle; Permutations
• 8.2 Combinations
• 8.3 Probability Applications of Counting Principles
• 8.4 Binomial Probability
• 8.5 Probability Distributions; Expected Value
• Chapter 8 Review
• Extended Application: Optimal Inventory for a Service Truck

9. Statistics

• 9.1 Frequency Distributions; Measures of Central Tendency
• 9.2 Measures of Variation
• 9.3 The Normal Distribution
• 9.4 Normal Approximation to the Binomial Distribution
• Chapter 9 Review
• Extended Application Statistics in the Law: the Castaneda Decision

10. Nonlinear Functions

• 10.1 Properties of Functions
• 10.2 Quadratic Functions; Translation and Reflection
• 10.3 Polynomial and Rational Functions
• 10.4 Exponential Functions
• 10.5 Logarithmic Functions
• 10.6 Applications: Growth and Decay; Mathematics of Finance
• Chapter 10 Review
• Extended Application: Power Functions

11. The Derivative

• 11.1 Limits
• 11.2 Continuity
• 11.3 Rates of Change
• 11.4 Definition of the Derivative
• 11.5 Graphical Differentiation
• Chapter 11 Review
• Extended Application: A Model for Drugs Administered Intravenously

12. Calculating the Derivative

• 12.1 Techniques for Finding Derivatives
• 12.2 Derivatives of Products and Quotients
• 12.3 The Chain Rule
• 12.4 Derivatives of Exponential Functions
• 12.5 Derivatives of Logarithmic Functions
• Chapter 12 Review
• Extended Application: Electric Potential and Electric Field

13. Graphs and the Derivative

• 13.1 Increasing and Decreasing Functions
• 13.2 Relative Extrema
• 13.3 Higher Derivatives, Concavity, and the Second Derivative Test
• 13.4 Curve Sketching
• Chapter 13 Review
• Extended Application: A Drug Concentration Model for Orally Administered Medications

14. Applications of the Derivative

• 14.1 Absolute Extrema
• 14.2 Applications of Extrema
• 14.3 Further Business Applications
• 14.4 Implicit Differentiation
• 14.5 Related Rates
• 14.6 Differentials: Linear Approximation
• Chapter 14 Review
• Extended Application: A Total Model for a Training Program

15. Integration

• 15.1 Antiderivatives
• 15.2 Substitution
• 15.3 Area and the Definite Integral
• 15.4 The Fundamental Theorem of Calculus
• 15.5 The Area Between Two Curves
• 15.6 Numerical Integration
• Chapter 15 Review
• Extended Application Estimating Depletion Dates for Minerals

16. Further Techniques and Applications of Integration

• 16.1 Integration by Parts
• 16.2 Volume and Average Value
• 16.3 Continuous Money Flow
• 16.4 Improper Integrals
• 16.5 Solutions of Elementary and Separable Differential Equations
• Chapter 16 Review
• Extended Application: Estimating Learning Curves in Manufacturing With Integrals

17. Multivariable Calculus

• 17.1 Functions of Several Variables
• 17.2 Partial Derivatives
• 17.3 Maxima and Minima
• 17.4 Lagrange Multipliers
• 17.5 Total Differentials and Approximations
• 17.6 Double Integrals
• Chapter 17 Review
• Extended Application: Using Multivariable Fitting to Create a Response Surface Design

18. Probability and Calculus

• 18.1 Continuous Probability Models
• 18.2 Expected Value and Variance of Continuous Random Variables
• 18.3 Special Probability Density Functions
• Chapter 18 Review
• Extended Application Exponential Waiting Times