College Mathematics for Business, Economics, Life Sciences and Social Sciences / Edition 10

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Overview

Designed to be accessible, this book develops a thorough, functional understanding of mathematical concepts in preparation for their application in other areas. Coverage concentrates on developing concepts and ideas followed immediately by developing computational skills and problem solving. This book features a collection of important topics from mathematics of finance, linear algebra, linear programming, probability, and statistics, with an emphasis on cross-discipline principles and practices. For the professional who wants to acquire essential mathematical tools for application in business, economics, and the life and social sciences.

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Product Details

  • ISBN-13: 9780131432093
  • Publisher: Pearson
  • Publication date: 6/24/2004
  • Edition description: Older Edition
  • Edition number: 10
  • Pages: 1100
  • Product dimensions: 8.20 (w) x 10.10 (h) x 1.70 (d)

Table of Contents

(Each chapter concludes with Important Terms, Symbols, and Concepts; Review Exercise; and Group Activities.)

PART ONE. A LIBRARY OF ELEMENTARY FUNCTIONS.

CHAPTER 1. A Beginning Library of Elementary Functions.

1-1 Functions.

1-2 Elementary Functions: Graphs and Transformations.

1-3 Linear Functions and Straight Lines.

1-4 Quadratic Functions.

Group Activity 1: Introduction to Regression Analysis.

Group Activity 2: Mathematical Modeling in Business.

CHAPTER 2. Additional Elementary Functions.

2-1 Polynomial and Rational Functions.

2-2 Exponential Functions.

2-3 Logarithmic Functions.

Group Activity 1: Comparing the Growth of Exponential and Polynomial Functions, and Logarithmic and Root Functions.

Group Activity 2: Comparing Regression Models.

PART TWO. FINITE MATHEMATICS.

CHAPTER 3. Mathematics of Finance.

3-1 Simple Interest.

3-2 Compound Interest.

3-3 Future Value of an Annuity; Sinking Funds.

3-4 Present Value of an Annuity; Amortization.

Group Activity 1: Reducing Interest Payments on a Home Mortgage.

Group Activity 2: Yield to Maturity and Internal Rate of Return.

CHAPTER 4. Systems of Linear Equations; Matrices.

4-1 Review: Systems of Linear Equations in Two Variables.

4-2 Systems of Linear Equations and Augmented Matrices.

4-3 Gauss-Jordan Elimination.

4-4 Matrices: Basic Operations.

4-5 Inverse of a Square Matrix.

4-6 Matrix Equations and Systems of Linear Equations.

4-7 Leontief Input-Output Analysis.

Group Activity 1: Using Matrices to Find Cost, Revenue, and Profit.

Group Activity 2: Direct and Indirect Operating Costs.

CHAPTER 5. Linear Inequalities and Linear Programming.

5-1 Systems of Linear Inequalities in Two Variables.

5-2 Linear Programming in Two Dimensions—A Geometric Approach.

5-3 A Geometric Introduction to the Simplex Method.

5-4 The Simplex Method: Maximization with Problem Constraints of the Form =.

5-5 The Dual; Minimization with Problem Constraints of the Form =.

5-6 Maximization and Minimization with Mixed Problem Constraints.

Group Activity 1: The Two-Phase Method (An Alternative to the Big M Method).

Group Activity 2: Production Scheduling.

CHAPTER 6. Logic, Sets, and Counting.

6-1 Logic.

6-2 Sets.

6-3 Basic Counting Principles.

6-4 Permutations and Combinations.

Group Activity 1: Combinations with Repetition Allowed.

Group Activity 2: Subset Lattices of Finite Sets.

CHAPTER 7. Probability.

7-1 Sample Spaces, Events, and Probability.

7-2 Union, Intersection, and Complement of Events; Odds.

7-3 Conditional Probability, Intersection, and Independence.

7-4 Bayes' Formula.

7-5 Random Variable, Probability Distribution, and Expected Value.

Group Activity 1: Car and Crying Towels.

Group Activity 2: Simulation—A Draft Lottery for Professional Sports.

CHAPTER 8. Markov Chains.

8-1 Properties of Markov Chains.

8-2 Regular Markov Chains.

8-3 Absorbing Markov Chains.

Group Activity 1: Social Mobility.

Group Activity 2: Gambler's Ruin.

PART THREE. CALCULUS.

CHAPTER 9. The Derivative.

9-1 Introduction to Limits.

9-2 Limits and Continuity.

9-3 The Derivative.

9-4 Derivative of Constants, Power Forms, and Sums.

9-5 Derivatives of Products and Quotients.

9-6 Chain Rule: Power Form.

9-7 Marginal Analysis in Business and Economics.

Group Activity 1: Minimal Average Cost.

Group Activity 2: Numerical Differentiation on a Graphing Utility.

CHAPTER 10. Graphing and Optimization.

10-1 First Derivative and Graphs.

10-2 Second Derivative and Graphs.

10-3 Curve Sketching Techniques; Unified and Extended.

10-4 Optimization; Absolute Maxima and Minima.

Group Activity 1: Maximizing Profit.

Group Activity 2: Minimizing Construction Costs.

CHAPTER 11. Additional Derivative Topics.

11-1 The Constant e and Continuous Compound Interest.

11-2 Derivatives of Logarithmic and Exponential Functions.

11-3 Chain Rule: General Form.

11-4 Implicit Differentiation.

11-5 Related Rates.

Group Activity 1: Elasticity of Demand.

Group Activity 2: Point of Diminishing Returns.

CHAPTER 12. Integration.

12-1 Antiderivatives and Indefinite Integrals.

12-2 Integration by Substitution.

12-3 Differential Equations; Growth and Decay.

12-4 The Definite Integral.

12-5 The Fundamental Theorem of Calculus.

Group Activity 1: Simpson's Rule.

Group Activity 2: Bell-Shaped Curves.

CHAPTER 13. Additional Integration Topics.

13-1 Area Between Curves.

13-2 Applications in Business and Economics.

13-3 Integration by Parts.

13-4 Integration Using Tables.

Group Activity 1: Analysis of Income Concentration from Raw Data.

Group Activity 2: Grain Exchange.

CHAPTER 14. Multivariable Calculus.

14-1 Functions of Several Variables.

14-2 Partial Derivatives.

14-3 Maxima and Minima.

14-4 Maxima and Minima Using Lagrange Multipliers.

14-5 Method of Least Squares.

14-6 Double Integrals Over Rectangular Regions.

Group Activity 1: City Planning.

Group Activity 2: Numerical Integration of Multivariable Functions.

APPENDIX A. Basic Algebra Review.
APPENDIX B. Special Topics.

B-1 Sequences, Series, and Summation Notation.

APPENDIX C. Tables.
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