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Mathematics with applications in management and economics

Author: Bowen, Earl K. ; Prichett, Gordon D. ; Saber, John C. Series: Irwin series in quantitative analysis for business Publisher: Irwin, 1987.Edition: 6th ed.Language: EnglishDescription: 993 p. : Graphs ; 24 cm.ISBN: 0256031401Type of document: BookBibliography/Index: Includes index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA37.2 .B69 1987
(Browse shelf)
001078199
Available 001078199
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Includes index

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Mathematics With Applications in Management and Economics Contents 1 Linear Equations and Functions, 1 1.1 Introduction, 1 1.2 Vertical and Horizontal Distances, 5 1.3 Problem Set 1-1, 7 1.4 The Distance Formula, 8 1.5 Problem Set 1-2, 11 1.6 Slope, 12 1.7 Problem Set 1-3, 16 1.8 Equation of a Line: Slope-Intercept Form, 18 1.9 Straight-Line Equation Given a Point and Slope, 22 1.10 Straight-Line Equation from Two Points, 24 1.11 Horizontal and Vertical Lines, 25 1.12 Parallel and Perpendicular Lines, 27 1.13 Lines through the Origin, 29 1.14 Problem Set 1-4, 29 1.15 Interpretive Exercise: Cost-Output, 33 1.16 Problem Set 1-5, 35 1.17 Comment on Models, 36 1.18 Break-Even Interpretation: 1, 39 1.19 Break-Even Interpretation: 2, 41 1.20 Linear Demand Functions, 45 1.21 Problem Set 1-6, 48 1.22 Review Problems, 51 2 Systems of Linear Equations and Inequalities, 55 2.1 Introduction, 55 2.2 Number of Solutions Possible, 56 2.3 Intersections of Straight Lines, 56 2.4 Operations on Linear Systems, 58 2.5 Elimination Procedure, 60 2.6 Applications-1, 61 2.7 Problem Set 2-1, 62 2.8 Applications-2: Supply and Demand Analysis, 63 2.9 Problem Set 2-2, 65 2.10 Elimination Procedure: Nonunique Solutions, 66 2.11 Problem Set 2-3, 67 2.12 Definition, m by n System, 68 2.13 3 by 3 System, 68 2.14 Problem Set 2-4, 73 2.15 Applications 3: Introduction to Optimization, 73 2.16 Applications 4: Two-Product Supply and Demand Analysis, 77 2.17 Problem Set 2-5, 78 2.18 Systems of Two Linear Inequalities, 79 2.19 Nonnegativity Constraints, 82 2.20 Applications, 85 2.21 Problem Set 2-6, 88 2.22 Review Problems, 89 3 Introduction to Linear Programming, 92 3.1 Introduction, 92 3.2 Maximization Examples: Product Mix, 93 3.3 Minimization Examples: Ingredient Mix, 100 3.4 Isolines: Three-Step Graphical Procedure, 104 3.5 Problem Set 3-1, 107 3.6 Mix of Constraints, 109 3.7 Problem Set 3-2, 115 3.8 More than Two Variables, 116 3.9 Problem Set 3-3, 121 3.10 More on Formulation, 122 3.11 Problem Set 3-4,.126 3.12 Review Problems, 130 4 Compact Notation: Vectors, Matrices, and Summation, 133 4.1 Introduction, 133 4.2 Matrices and Vectors, 133 4.3 Product of a Number and a Matrix, 135 4.4 Addition and Subtraction of Matrices, 136 4.5 Multiplication of Matrices, 138 4.6 Identity Matrix, 141 4.7 Problem Set 4-1, 142 4.8 Matrix Symbols, 143 4.9 Linear Equations in Matrix Form, 144 4.10 Problem Set 4-2, 146 4.11 Applications-1: Markov Chains, 147 4.12 Problem Set 4-3, 150 4. 13 Row Operations, 151 4.14 The Inverse of a Matrix, 152 4.15 Problem Set 4-4, 160 4.16 Applications-2: Matrix Solution of n by n Linear Systems, 161 4.17 Problem Set 4-5, 169 4.18 Applications-3: Matrix Solution of m by n Linear Systems, 171 4.19 Problem Set 4-6, 176 4.20 Summation Symbol, 177 4. 21 Problem Set 4-7, 178 4.22 Summation on Indices: Linear Equations, 179 4.23 Problem Set 4-8, 180 4.24 Summation Form for Systems, 180 4.25 Linear Programming Problems in Summation Notation, 182 4.26 Problem Set 4-9, 183 4.27 Properties of the Summation Operation, 184 4.28 Problem Set 4-10, 186 4.29 Review Problems, 186 5 Linear Programming: The Simplex Method, 192 5.1 Introduction, 192 5.2 Fundamental Procedures and Terminology, 193 5.3 Tableaus: Changing Basic Variables, 200 5.4 Problem Set 5-1, 205 5.5 The Simplex Procedure, 206 5.6 Problem Set 5-2, 215 5.7 A Minimizing Problem with "-." Constraints, 217 5.8 Problem Set 5-3, 221 5.9 Tie for the Entering or Leaving Variable, 222 5.10 Alternative Optimal Solutions, 230 5.11 Problem Set 5-4, 232 5.12 Unbounded Solutions, 233 5.13 Negative Decision Variables, 235 5.14 Two Penalty/Premium Examples with "" Constraints, 239 5.15 Problem Set 5-5, 244 5.16 Minimization by Maximizing the Dual, 245 5.17 Problem Set 5-6, 253 5.18 Sensitivity Analysis: Shadow Prices and Right-Hand-Side Ranges, 255 5.19 Problem Set 5-7, 267 5.20 Review Problems, 269 6 The Simplex Method (continued): Computer Solutions, 274 6.1 Introduction, 274 6.2 Computer Solutions, 274 6.3 Problem Set 6-1, 279 6.4 Preliminaries to Phase I-Phase II: The Big-M Method, 281 6.5 The Phase I-Phase II Method, 286 6.6 Problem Set 6-2, 296 6.7 No Feasible Solutions, 298 6.8 An Example with "=" Constraints; Phase I-Phase II Method, 302 6.9 Grand Summary of the Simplex Method, 312 6.10 Problem Set 6-3, 315 6.11 Sensitivity Analysis on "" and "= " Constraints, 316 6.12 Sensitivity Analysis on the Objective Function and New Product Analysis, 322 6.13 Problem Set 6-4, 326 6.14 Review Problems, 336 7 Exponential and Logarithmic Functions, 348 7.1 Introduction, 348 7.2 Exponential Functions, 348 7.3 Problem Set 7-1, 353 7.4 The Need for Logarithms, 353 7.5 Natural (Base e) Logarithms, 357 7.6 Problem Set 7-2, 359 7.7 Definition of Logarithms, 359 7.8 Rules of Logarithms, 360 7.9 Application of Inverse Natural Logarithms, 363 7.10 Graph of y = In x, 367 7.11 Computing e and Natural Logarithms (Optional), 369 7.12 Problem Set 7-3, 373 7.13 Review Problems, 375 8 Mathematics of Finance, 377 8.1 Introduction, 377 8.2 Simple Interest and the Future Value, 378 8.3 Simple Discount: Present Value, 383 8.4 Bank Discount, 385 8.5 Effective Rate: Simple Interest, 386 8.6 Problem Set 8-1, 389 8.7 Compound Interest and the Future Value, 390 8.8 The Conversion Period, 393 8.9 Finding the Time, 395 8.10 Finding the Interest Rate, 397 8.11 Problem Set 8-2, 398 8.12 Compound Discount: Present Value, 399 8.13 Problem Set 8-3, 402 8.14 Effective Rate: Compound Interest, 402 8.15 Problem Set 8-4, 404 8.16 Continuous (Instantaneous) Compounding, 405 8.17 Effective Rate: Continuous Compounding, 409 8.18 Problem Set 8-5, 411 8.19 Ordinary Annuities: Future Value, 412 8.20 Ordinary Annuities: Sinking Fund, 415 8.21 Problem Set 8-6, 417 8.22 Ordinary Annuities: Present Value, 419 8.23 Ordinary Annuities: Amortization, 421 8.24 Problem Set 8-7, 426 8.25 Summary of Financial Rules, 427 8.26 Multistep Problems, 430 8. 27 Problem Set 8-8, 434 8.28 Finding the Interest Rate and Time: Ordinary Annuities, 435 8.29 Ordinary Annuities: Continuous Compounding, 437 8.30 Problem Set 8-9, 438 8.31 Review Problems, 439 9 Elementary Probability and Statistics, 443 9.1 Introduction, 443 9.2 Probability and Odds, 443 9.3 Statistical Inference, 444 9.4 Sources of Probabilities, 445 9.5 Probability Symbols and Definitions, 447 9.6 Problem Set 9-1, 455 9.7 Probability Rules, 456 9.8 Practice with Probability Rules, 461 9.9 Problem Set 9-2, 467 9.10 Bayes' Rule, 469 9.11 Problem Set 9-3, 473 9.12 Experiment, Event, Sample Space, 475 9.13 Problem Set 9-4, 477 9.14 Discrete Random Variables, 478 9.15 Problem Set 9-5, 484 9.16 The Binomial Probability Distribution, 485 9.17 Cumulative Binomial Probabilities, 490 9.18 Problem Set 9-6, 493 9.19 Expected Monetary Value (EMV), 495 9.20 Problem Set 9-7, 499 9.21 Review Problems, 500 10 Introduction to Differential Calculus, 506 10.1 Introduction, 506 10.2 Why Study Calculus? 506 10.3 Functional Notation, 510 10.4 Delta Notation, 513 10.5 Problem Set 10-1, 515 10.6 Limits, 516 10.7 Problem Set 10-2, 526 10.8 Continuity, 527 10.9 Problem Set 10-3, 530 10.10 The Difference Quotient, 531 10.11 Definition of the Derivative, 534 10.12 Problem Set 10-4, 540 10.13 The Simple Power Rule, 541 10.14 dldx Notation and Rules of Operations, 545 10.15 Problem Set 10-5, 548 10.16 The Derivative of [f(x)]n, 549 10.17 Problem Set 10-6, 553 10.18 Product and Quotient Rules, 553 10.19 Problem Set 10-7, 558 10.20 Review Problems, 559 11 Applications of Differential Calculus, 562 11.1 Introduction, 562 11.2 Maxima and Minima of Functions, 562 11.3 Problem Set 11-1, 572 11.4 The Second Derivative Test, 573 11.5 Problem Set 11-2, 580 11.6 Maxima and Minima: Applications, 581 11.7 Problem Set 11-3, 590 11.8 More Applications, 594 11.9 Problem Set 11-4, 601 11.10 An Inventory Model, 602 11.11 Problem Set 11-5, 606 11.12 Sketching Graphs of Polynomials, 606 11.13 Problem Set 11-6, 611 11.14 Sketching Rational Functions, 612 11.15 Problem Set 11-7, 618 11.16 Review Problems, 618 12 Further Topics in Differential Calculus, 622 12.1 Introduction, 622 12.2 Derivatives of Exponential Functions, 623 12.3 Response Functions, 632 12.4 Problem Set 12-1, 634 12.5 Derivatives of Logarithmic Functions, 635 12.6 Problem Set 12-2, 637 12.7 Relative Rate of Change, 638 12.8 Problem Set 12-3, 643 12.9 The Chain Rule and Implicit Differentiation, 645 12.10 Marginal Propensity to Consume and the Multiplier, 651 12.11 Problem Set 12-4, 655 12.12 Calculus of Two Independent Variables, 656 12.13 Problem Set 12-5, 659 12.14 Maxima and Minima: Two Independent Variables, 661 12.15 Problem Set 12-6, 671 12.16 Least-Squares Curve Fitting, 672 12.17 Problem Set 12-7, 680 12.18 Review Problems, 681 13 Integral Calculus, 685 13.1 Introduction, 685 13.2 Antiderivatives: The Indefinite Integral, 686 13.3 Problem Set 13-1, 694 13.4 Area and the Definite Integral, 694 13.5 Problem Set 13-2, 706 13.6 The Area between Two Curves, 709 13.7 Problem Set 13-3, 714 13.8 Interpretive Applications of Area, 715 13.9 Interpreting the Area Bounded by Two Functions, 720 13.10 Consumers' and Producers' Surplus, 722 13.11 Problem Set 13-4, 727 13.12 The Integral of (mx + b)-1, 729 13.13 Problem Set 13-5, 731 13.14 Integrals of Exponential Functions, 732 13.15 Problem Set 13-6, 736 13.16 Tables of Integrals, 737 13.17 Problem Set 13-7, 740 13.18 Asymptotic Areas: Improper Integrals, 740 13.19 Problem Set 13-8, 744 13.20 Numerical Integration, 745 13.21 Problem Set 13-9, 753 13.22 Integration by Parts, 754 13.23 Problem Set 13-10, 757 13.24 Differential Equations, 757 13.25 Separable Differential Equations, 760 13.26 Forms of the Constant, 760 13.27 Problem Set 13-11, 764 13.28 Applications of Differential Equations, 764 13.29 Problem Set 13-12, 770 13.30 Review Problems, 771 14 Probability in the Continuous Case, 777 14.1 Introduction, 777 14.2 The Uniform Probability Density Function, 777 14.3 Converting f(x) to a Density Function over an Interval, 779 14.4 Problem Set 14-1, 781 14.5 Expected Value, 781 14.6 Variance and Standard Deviation, 784 14.7 Problem Set 14-2, 786 14.8 The Exponential Distribution, 787 14.9 Problem Set 14-3, 793 14.10 The Normal Density Function, 794 14.11 Normal Probability Table, 795 14.12 Using the Normal Probability Table, 798 14.13 Problem Set 14-4, 801 14.14 Estimating the Mean and the Standard Deviation, 801 14.15 Problem Set 14-5, 804 14.16 N(u,cr) in Actual Use, 804 14.17 Problem Set 14-6, 809 14.18 Review Problems, 810 Appendix One Sets, 813 A1.1 Introduction, 813 A1.2 Set Terminology, 813 A1.3 Set Specification, 815 A1.4 Solution Sets for Equations, 816 A1.5 Relations and Functions, 816 A1.6 Problem Set A1-1, 819 A1.7 Subsets, Unions, and Intersections, 820 A1.8 Problem Set A1-2, 822 A1.9 Review Problems, 823 Appendix Two Elements of Algebra, 825 A2.1 Introduction, 825 A2.2 The Real Numbers, 825 A2.3 Rules of Sign, 826 A2.4 Addition and Subtraction of Signed Numbers, 826 A2.5 Multiplication and Division of Signed Numbers, 829 A2.6 Problem Set A2-1, 830 A2.7 Representing Numbers by Letters, 831 A2.8 Importance of Fundamental Properties, 832 A2.9 Problem Set A2-2, 834 A2.10 Removing Grouping Symbols, 835 A2.11 Definitions: Expression, Term, Factor, 836 A2.12 Elementary Factoring, 837 A2. 13 Problem Set A2-3, 840 A2.14 Properties of the Numbers Zero and One, 842 A2.15 Product of Fractions, 845 A2.16 Addition and Subtraction of Fractions, 849 A2.17 Division of Fractions, 851 A2.18 Problem Set A2-4, 852 A2.19 Exponents, 854 A2.20 Zero Exponent, 855 A2.21 Negative Exponents, 856 A2.22 Power to a Power, 857 A2.23 Fractional Exponents, 858 A2.24 Summary of Exponent Rules, 860 A2.25 Practice Problem Set, 862 A2.26 Problem Set A2-5, 863 A2.27 Review Problems, 865 Appendix Three Formulas, Equations, Inequalities, and Graphs, 867 A3.1 Introduction, 867 A3.2 Some Axioms, 868 A3.3 Solutions by Addition and Multiplication, with Inverses, 869 A3.4 Problem Set A3-1, 874 A3.5 Transposition, 875 A3.6 Formulas, 875 A3.7 Exact Evaluations, 877 A3.8 Problem Set A3-2, 878 A3.9 Coordinate Axes, 880 A3.10 Plotting Observational Data, 881 A3.11 Plotting Equations in Two Variables: Straight Lines, 883 A3.12 Vertical Parabolas, 884 A3.13 Quadratic Equations, 888 A3.14 Problem Set A3-3, 890 A3.15 Definitions and Fundamental Properties of Inequalities, 891 A3.16 Fundamental Operations on Inequalities, 892 A3.17 Solving Single Inequalities, 893 A3.18 Problem Set A3-4, 898 A3.19 Review Problems, 899 Answers to Problem Sets, 903 Tables, 965 Index, 989

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