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Mathematical Applications for the Management, Life, and Social Sciences, 12th Edition
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Overview
MATHEMATICAL APPLICATIONS FOR THE MANAGEMENT, LIFE, AND SOCIAL SCIENCES, 12th Edition, engages students with its concept-based approach, multiple presentation methods and relevant applications throughout. Intended for two-semester applied calculus or combined finite mathematics and applied calculus courses, the book places concepts in real-life contexts to help students strengthen their understanding. A focus on modeling--with modeling problems clearly labeled in the examples and problems, so they can be treated as optional--and flexible content organization accommodate different teaching approaches, enabling instructors to decide the order in which topics may be presented and the degree to which they may be emphasized. Resources for the instructor include an Instructor Companion site, a Complete Solutions Manual, Cengage Testing Powered by Cognero®, and WebAssign.
- NOTE: This title is also available in WebAssign with Corequisite Support that provides the flexibility to match any corequisite implementation model and empowers you to deliver high quality content at the right time for your students at an affordable price.
- More step-by-step details for using graphing calculators have been integrated into the Calculator Notes in the text. The Calculator Guide for TI-84 Calculators in Appendix A provides additional details to supplement the Calculator Notes.
- Many of the Spreadsheet Notes have been expanded to include specific Excel steps, along with references to Appendix B, which provides additional details to supplement the Spreadsheet Notes.
- More than 250 real-data application examples, exercises and Group Projects have been updated or replaced to keep the material fresh and timely (projects are available online).
- Applications: Numerous real-life application examples and exercises motivate the material and demonstrate the relevance of each topic.
- Comprehensive Exercise Sets: While the overall variety and grading of drill and application exercises offer problems for different skill levels, there are enough challenging problems to stimulate students in thoughtful investigations. Many sets contain critical thinking and thought-provoking, multi-step problems that extend students' knowledge and skills.
- Technology: An icon throughout the text denotes Technology Notes, Calculator Notes and Spreadsheet Notes. Step-by-step instructions for using the various features of a graphing calculator or Microsoft® Excel® are included in two appendices. These skills--and the modeling skills also discussed--can be omitted without loss of continuity.
- Objective Lists: Every section begins with a brief list of objectives that outline the goals of that section and aid instructors in lesson planning and preparation.
- Flexibility: To accommodate alternate teaching approaches, the text offers a great deal of flexibility in the order in which topics may be presented and the degree to which they may be emphasized. Consequently, the book can be adapted to variations in coverage and sequencing of topics at different colleges and universities, depending upon the purpose of the course and the nature of the student audience.
- Checkpoints: Checkpoints ask questions and pose problems within each section's discussion, allowing students to check their understanding of the skills and concepts under discussion before they proceed.
- Intuitive Viewpoint: The text is written with an emphasis on concepts and problem solving rather than mathematical theory. Each topic is carefully developed and explained, and examples illustrate the techniques involved.
- Application Previews: Each section begins with an application that motivates the material and references a completely worked Application Preview example that appears later in the section.
0. ALGEBRAIC CONCEPTS.
Sets. The Real Numbers. Integral Exponents. Radicals and Rational Exponents. Operations with Algebraic Expressions. Factoring. Algebraic Fractions.
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.
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).
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.
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.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Logarithmic Functions and Their Properties. Equations and Applications with Exponential and Logarithmic Functions.
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.
8. FURTHER TOPICS IN PROBABILITY; DATA DESCRIPTION.
Binomial Probability Experiments. Data Description. Discrete Probability Distributions; The Binomial Distribution. Normal Probability Distribution. The Normal Curve Approximation to the Binomial Distribution.
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.
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.
11. DERIVATIVES CONTINUED.
Derivatives of Logarithmic Functions. Derivatives of Exponential Functions. Implicit Differentiation. Related Rates. Applications in Business and Economics.
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.
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.
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.
APPENDICES.
A. Graphing Calculator Guide.
B. Excel Guide.
C. Areas Under the Standard Normal Curve.
Sets. The Real Numbers. Integral Exponents. Radicals and Rational Exponents. Operations with Algebraic Expressions. Factoring. Algebraic Fractions.
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.
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).
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.
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.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Logarithmic Functions and Their Properties. Equations and Applications with Exponential and Logarithmic Functions.
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.
8. FURTHER TOPICS IN PROBABILITY; DATA DESCRIPTION.
Binomial Probability Experiments. Data Description. Discrete Probability Distributions; The Binomial Distribution. Normal Probability Distribution. The Normal Curve Approximation to the Binomial Distribution.
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.
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.
11. DERIVATIVES CONTINUED.
Derivatives of Logarithmic Functions. Derivatives of Exponential Functions. Implicit Differentiation. Related Rates. Applications in Business and Economics.
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.
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.
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.
APPENDICES.
A. Graphing Calculator Guide.
B. Excel Guide.
C. Areas Under the Standard Normal Curve.
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- ISBN-10: 0357539214
- ISBN-13: 9780357539217
- RETAIL $84.95
- ISBN-10: 1337625345
- ISBN-13: 9781337625340
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