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Mathematical Applications for the Management, Life, and Social Sciences, 13th Edition
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Overview
"Mathematical Applications for the Management, Life, and Social Sciences," 13th Edition, engages students with a concept-based approach, presentation methods and relevant applications in a flexible volume designed to be used for the applied math sequence. A new introduction to college algebra, with material preparing for calculus, ensures the text is at the right level for all students. Harshbarger and Reynolds focus on examples and exercises drawn from real-life in the management, social and life sciences. Updates to over 300 application examples and exercises include real data on topics ranging from AI to the Body Roundness Index. WebAssign, Cengage’s online learning platform for STEM courses, delivers the right content to students at the right time. In addition to text-specific activities and assignments, corequisite support offers flexible resources for any implementation model.
- Text-specific assignments and activities are available in Cengage’s WebAssign platform, including resources to support any corequisite model.
- More than 300 examples and exercises have been updated, including many with real data. New applications include big data revenue, alternative fuel vehicles and plastic waste.
- Chapter 6 on mathematics of finance has been thoroughly revised to help students better understand strategies to approach problems and to introduce the CAGR matric.
- A new introduction to college algebra, as well as new material preparing students for calculus, offers tools to help students succeed in the course.
- Designed to be used for all or part of the applied math sequence, topics in the text are organized flexibly to support a variety of course organizations.
- Case studies at the end of each chapter offer illustrations of the ways that mathematics can support business and personal decision-making.
- Warm-Ups at the beginning of each chapter support student preparation, testing skills that are important to understanding the chapter.
- Technology, Calculator and Excel Notes throughout the text guide students in using technology to solve mathematical problems.
Part I: COLLEGE ALGEBRA AND FINITE MATHEMATICS.
0. ALGEBRAIC CONCEPTS.
Sets. The Real Numbers. Integral Exponents. Radicals and Rational Exponents. Operations with Algebraic Expressions. Factoring. Algebraic Fractions. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
1. LINEAR EQUATIONS AND FUNCTIONS.
Solutions of Linear Equations and Inequalities in One Variable. Functions. Linear Functions. Graphs and Graphing Utilities. Solutions of Systems of Linear Equations. Applications of Functions in Business and Economics. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
2. QUADRATIC AND OTHER SPECIAL FUNCTIONS.
Quadratic Equations. Quadratic Functions: Parabolas. Business Applications Using Quadratics. Special Functions and Their Graphs. Modeling; Fitting Curves to Data with Graphing Utilities (optional). Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
3. MATRICES.
Matrices. Multiplication of Matrices. Gauss-Jordan Elimination: Solving Systems of Equations. Inverse of a Square Matrix; Matrix Equations. Applications of Matrices: Leontief Input-Output Models. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
4. INEQUALITIES AND LINEAR PROGRAMMING.
Linear Inequalities in Two Variables. Linear Programming: Graphical Methods. The Simplex Method: Maximization. The Simplex Method: Duality and Minimization. The Simplex Method with Mixed Constraints. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Logarithmic Functions and Their Properties. Equations and Applications with Exponential and Logarithmic Functions. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
6. MATHEMATICS OF FINANCE.
Simple Interest; Sequences. Compound Interest; Geometric Sequences. Future Values of Annuities. Present Values of Annuities. Loans and Amortization.
7. INTRODUCTION TO PROBABILITY.
Probability; Odds. Unions and Intersections of Events: One-Trial Experiments. Conditional Probability: The Product Rule. Probability Trees and Bayes' Formula. Counting: Permutations and Combinations. Permutations Combinations and Probability. Markov Chains. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
8. FURTHER TOPICS IN PROBABILITY; DATA DESCRIPTION.
Binomial Probability Experiments. Descriptive Statistics. Discrete Probability Distributions. The Binomial Distribution. Normal Probability Distribution. The Normal Curve Approximation to the Binomial Distribution. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
Part II: PREPARATION FOR CALCULUS.
9. DERIVATIVES.
Limits. Continuous Functions; Limits at Infinity. Rates of Change and Derivatives. Derivative Formulas. The Product Rule and the Quotient Rule. The Chain Rule and the Power Rule. Using Derivative Formulas. Higher-Order Derivatives. Applications: Marginals and Derivatives. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
10. APPLICATIONS AND DERIVATIVES.
Relative Maxima and Minima: Curve Sketching. Concavity: Points of Inflection. Optimization in Business and Economics. Applications of Maxima and Minima. Rational Functions: More Curve Sketching. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
11. DERIVATIVES CONTINUED.
Derivatives of Logarithmic Functions. Derivatives of Exponential Functions. Implicit Differentiation. Related Rates. Applications in Business and Economics. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
12. INDEFINITE INTEGRALS.
Indefinite Integrals. The Power Rule. Integrals Involving Exponential and Logarithmic Functions. Applications of the Indefinite Integral in Business and Economics. Differential Equations. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
13. DEFINITE INTEGRALS: TECHNIQUES OF INTEGRATION.
Area Under a Curve. The Definite Integral: The Fundamental Theorem of Calculus. Area Between Two Curves. Applications of Definite Integrals in Business and Economics. Using Tables of Integrals. Integration by Parts. Improper Integrals and Their Applications. Numerical Integration Methods: The Trapezoidal Rule and Simpson's Rule. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
14. FUNCTIONS OF TWO OR MORE VARIABLES.
Functions of Two or More Variables. Partial Differentiation. Applications of Functions of Two Variables in Business and Economics. Maxima and Minima. Maxima and Minima of Functions Subject to Constraints: Lagrange Multipliers. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test . Extended Applications and Group Projects.
APPENDICES.
A. Graphing Calculator Guide.
B. Excel Guide.
C. Areas Under the Standard Normal Curve.
0. ALGEBRAIC CONCEPTS.
Sets. The Real Numbers. Integral Exponents. Radicals and Rational Exponents. Operations with Algebraic Expressions. Factoring. Algebraic Fractions. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
1. LINEAR EQUATIONS AND FUNCTIONS.
Solutions of Linear Equations and Inequalities in One Variable. Functions. Linear Functions. Graphs and Graphing Utilities. Solutions of Systems of Linear Equations. Applications of Functions in Business and Economics. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
2. QUADRATIC AND OTHER SPECIAL FUNCTIONS.
Quadratic Equations. Quadratic Functions: Parabolas. Business Applications Using Quadratics. Special Functions and Their Graphs. Modeling; Fitting Curves to Data with Graphing Utilities (optional). Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
3. MATRICES.
Matrices. Multiplication of Matrices. Gauss-Jordan Elimination: Solving Systems of Equations. Inverse of a Square Matrix; Matrix Equations. Applications of Matrices: Leontief Input-Output Models. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
4. INEQUALITIES AND LINEAR PROGRAMMING.
Linear Inequalities in Two Variables. Linear Programming: Graphical Methods. The Simplex Method: Maximization. The Simplex Method: Duality and Minimization. The Simplex Method with Mixed Constraints. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Logarithmic Functions and Their Properties. Equations and Applications with Exponential and Logarithmic Functions. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
6. MATHEMATICS OF FINANCE.
Simple Interest; Sequences. Compound Interest; Geometric Sequences. Future Values of Annuities. Present Values of Annuities. Loans and Amortization.
7. INTRODUCTION TO PROBABILITY.
Probability; Odds. Unions and Intersections of Events: One-Trial Experiments. Conditional Probability: The Product Rule. Probability Trees and Bayes' Formula. Counting: Permutations and Combinations. Permutations Combinations and Probability. Markov Chains. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
8. FURTHER TOPICS IN PROBABILITY; DATA DESCRIPTION.
Binomial Probability Experiments. Descriptive Statistics. Discrete Probability Distributions. The Binomial Distribution. Normal Probability Distribution. The Normal Curve Approximation to the Binomial Distribution. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
Part II: PREPARATION FOR CALCULUS.
9. DERIVATIVES.
Limits. Continuous Functions; Limits at Infinity. Rates of Change and Derivatives. Derivative Formulas. The Product Rule and the Quotient Rule. The Chain Rule and the Power Rule. Using Derivative Formulas. Higher-Order Derivatives. Applications: Marginals and Derivatives. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
10. APPLICATIONS AND DERIVATIVES.
Relative Maxima and Minima: Curve Sketching. Concavity: Points of Inflection. Optimization in Business and Economics. Applications of Maxima and Minima. Rational Functions: More Curve Sketching. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
11. DERIVATIVES CONTINUED.
Derivatives of Logarithmic Functions. Derivatives of Exponential Functions. Implicit Differentiation. Related Rates. Applications in Business and Economics. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
12. INDEFINITE INTEGRALS.
Indefinite Integrals. The Power Rule. Integrals Involving Exponential and Logarithmic Functions. Applications of the Indefinite Integral in Business and Economics. Differential Equations. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
13. DEFINITE INTEGRALS: TECHNIQUES OF INTEGRATION.
Area Under a Curve. The Definite Integral: The Fundamental Theorem of Calculus. Area Between Two Curves. Applications of Definite Integrals in Business and Economics. Using Tables of Integrals. Integration by Parts. Improper Integrals and Their Applications. Numerical Integration Methods: The Trapezoidal Rule and Simpson's Rule. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test. Extended Applications and Group Projects.
14. FUNCTIONS OF TWO OR MORE VARIABLES.
Functions of Two or More Variables. Partial Differentiation. Applications of Functions of Two Variables in Business and Economics. Maxima and Minima. Maxima and Minima of Functions Subject to Constraints: Lagrange Multipliers. Key Terms and Formulas. Chapter Summary & Review. Review Exercises. Chapter Test . Extended Applications and Group Projects.
APPENDICES.
A. Graphing Calculator Guide.
B. Excel Guide.
C. Areas Under the Standard Normal Curve.
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