MATHEMATICAL APPLICATIONS FOR THE MANAGEMENT , LIFE AND SOCIAL SCIENCES

Preliminary Contents 0. Algebraic Concepts 0.1 Sets 0.2 The Real Numbers 0.3 Integral Expressions 0.4 Radicals and Rational Expressions 0.5 Operations with Algebraic Exponents 0.6 Factoring 0.7 Algebraic Fractions Extended Applications/Group Projects: Campaign Management; Pricing for Maximum Profit 1. Linear Equations and Functions 1.1 Solution of Linear Equations 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: Extended Applications/Group Projects: Hospital Administration; Fund Raising 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 (Optional) Extended Applications/Group Projects: Maximizing Profit; International E-mail Usage 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 Extended Applications/Group Projects: Taxation; Company Profits After Bonuses And Taxes 4. Inequalities and Linear Programming 4.1 Linear Inequalities in One Variable 4.2 Linear Inequalities in Two Variables 4.3 Linear Programming: Graphical Methods 4.4 The Simplex Method: Maximization 4.5 The Simplex Method: Duality and Minimization 4.6 The Simplex Method with Mixed Constraints Extended Applications/Group Projects: Transportation; Sensitivity Analysis; Minimizing Cost for Electrical Transmission 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 Extended Applications/Group Projects: Agricultural Business Management; National Debt 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 Extended Applications/Group Projects: Mail Solicitation Home Equity Loans--Are These Good Deals?; Profit Reinvesting; Purchasing a Home 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 Extended Applications/Group Projects: Phone Numbers; Competition in the Telecommunications Industry 8. Further Topics in Probability; Data Description 8.1 Binomial Probability Experiments 8.2 Data Description 8.3 Discrete Probability Distributions; Decision Making 8.4 The Binomial Distribution 8.5 Normal Probability Distribution Extended Applications/Group Projects: Lotteries; Statistics in Medical Research; Hypothesis Testing 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 Product and Quotient Rules 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 Extended Applications/Group Projects: Marginal Return to Sales; Marginal Cost, Marginal Revenue, and Maximum Profit; Tangent Lines and Optimization 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 Extended Applications/Group Projects: Production Management; Room Pricing in the Off Season 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 Extended Applications/Group Projects: Inflation; Knowledge Workers 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 Indefinite Integrals in Business and Economics 12.5 Differential Equations Extended Applications/Group Projects: Employee Production Rate; Supply and Demand 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 Extended Applications/Group Projects: Retirement Planning; Purchasing Electrical Power 14. Functions of Two of 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 Extended Applications/Group Projects: Advertising; Competitive Pricing Appendix Table I. Amount of an Ordinary Annuity of $1 Table II. Present Value of an Ordinary Annuity of $1 Table III. Areas Under the Standard Normal CurveHARSHBARGER / REYNOLDS is the author of 'MATHEMATICAL APPLICATIONS FOR THE MANAGEMENT , LIFE AND SOCIAL SCIENCES' with ISBN 9780618293582 and ISBN 0618293582.