Intended for a two-term applied calculus or finite mathematics and applied calculus course, Mathematical Applications, 8/e, presents concepts and skills in an approachable way for students of varying abilities and interests. The Eighth Edition retains the features that have made this text a popular choice, including applications covering diverse topics that are important to students in the management, life, and social sciences. This edition broadens the represented applications by adding a number of environmental science applications. The use of modeling has also been expanded, with modeling problems now clearly labeled in the examples.

• New! Technology Notes have been separated into Calculator Notes and Spreadsheet Notes to provide more precise instruction for using calculators and Excel.
• Chapter Warm Ups appear at the beginning of each chapter to allow instructors and students an easy way to assess whether the student is prepared to begin the new material.
• Check Points ask questions and prose problems that help students check their understanding of skills and concepts before they proceed further into the chapter. Solutions appear before the section exercises.
• New! Application Previews begin each section and establish the context and direction for the concepts that will be covered. In this edition, these previews are revisited in completely worked-out examples later in the lesson.
• Applications contexts are clearly labeled so instructors can select the applications of interest to the students majoring in various disciplines. More than 2000 of the 5500 exercises in the book are applied problems, allowing students to learn practical applications of mathematical concepts.

0. Algebraic Concepts

0.1 Sets
0.2 The Real Numbers
0.3 Integral Exponents
0.4 Radicals and Rational Exponents
0.5 Operations with Algebraic Expressions
0.6 Factoring
0.7 Algebraic Fractions

1. Linear Equations and Functions

1.1 Solution of Linear Equations and Inequalities in one Variable
1.2 Functions
1.3 Linear Functions
1.4 Graphs and Graphing Utilities
1.5 Solutions of Systems of Linear Equations
1.6 Applications of Functions in Business and Economics

2. Special Functions

2.1 Quadratic Equations
2.2 Quadratic Functions: Parabolas
2.3 Business Applications of Quadratic Functions
2.4 Special Functions and Their Graphs
2.5 Modeling; Fitting Curves to Data with Graphing Utilities

3. Matrices

3.1 Matrices
3.2 Multiplication of Matrices
3.3 Gauss-Jordan Elimination: Solving Systems of Equations
3.4 Inverse of a Square Matrix; Matrix Equations
3.5 Applications of Matrices: Leontief Input-Output Models

4. Inequalities and Linear Programming

4.1 Linear Inequalities in Two Variables
4.2 Linear Programming: Graphical Methods
4.3 The Simplex Method: Maximization
4.4 The Simplex Method: Duality and Minimization
4.5 The Simplex Method with Mixed Constraints

5. Exponential and Logarithmic Functions

5.1 Exponential Functions
5.2 Logarithmic Functions and Their Properties
5.3 Solution of Exponential Equations: Applications of Exponential and Logarithmic Functions

6. Mathematics of Finance

6.1 Simple Interest; Sequences
6.2 Compound Interest; Geometric Sequences
6.3 Future Value of Annuities
6.4 Present Value of Annuities
6.5 Loans and Amortization

7. Introduction to Probability

7.1 Probability: Odds
7.2 Unions and Intersections of Events: One-Trial Experiments
7.3 Conditional Probability: The Product Rule
7.4 Probability Trees and Bayes' Formula
7.5 Counting: Permutations and Combinations
7.6 Permutations, Combinations, and Probability
7.7 Markov Chains

8. Further Topics in Probability: Data Description

8.1 Binomial Probability Experiments
8.2 Data Description
8.3 Discrete Probability Distributions
8.4 Normal Probability Distribution

9. Derivatives

9.1 Limits
9.2 Continuous Functions; Limits at Infinity
9.3 Average and Instantaneous Rates of Change: The Derivative
9.4 Derivative Formulas
9.5 The Product Rule and the Quotient Rule
9.6 The Chain Rule and the Power Rule
9.7 Using Derivative Formulas
9.8 Higher-Order Derivatives
9.9 Applications of Derivatives in Business and Economics

10. Applications of Derivatives

10.1 Relative Maxima and Minima: Curve Sketching
10.2 Concavity: Points of Inflection
10.3 Optimization in Business and Economics
10.4 Applications of Maxima and Minima
10.5 Asymptotes: More Curve Sketching

11. Derivatives Continued

11.1 Derivatives of Logarithmic Functions
11.2 Derivatives of Exponential Functions
11.3 Implicit Differentiation
11.4 Related Rates
11.5 Applications in Business and Economics

12. Indefinite Integrals

12.1 The Indefinite Integral
12.2 The Power Rule
12.3 Integrals Involving Exponential and Logarithmic Functions
12.4 Applications of the Indefinite Integral in Business and Economics
12.5 Differential Equations

13. Definite Integrals: Techniques of Integration

13.1 Area Under a Curve
13.2 The Definite Integral: The Fundamental Theorem of Calculus
13.3 Area Between Two Curves
13.4 Applications of Definite Integrals in Business and Economics
13.5 Using Tables of Integrals
13.6 Integration by Parts
13.7 Improper Integrals and Their Applications
13.8 Numerical Integration Methods: Trapezoidal Rule and Simpson's Rule

14. Functions of Two or More Variables

14.1 Functions of Two or more Variables
14.2 Partial Differentiation
14.3 Applications of Functions of Two Variables in Business and Economics
14.4 Maxima and Minima
14.5 Maxima and Minima of Functions Subject to Constraints: Lagrange Multipliers