Anton / Kolman Mathematics with Applications for the Management, Life, and Social Sciences

2. Auflage 2014
ISBN: 978-1-4832-6437-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 864 Seiten, Web PDF

Mathematics with Applications for the Management, Life, and Social Sciences, Second Edition presents the fundamentals of finite mathematics in a style tailored for beginners, but at the same time covers the subject matter in sufficient depth so that the student can see a rich variety of realistic and relevant applications in management, life sciences, and social sciences. Some applications of probability, game theory, and Markov chains are given. Comprised of 16 chapters, this book begins with an introduction to set theory, followed by a discussion on Cartesian coordinate systems and graphs. Subsequent chapters focus on linear programming from a geometric point of view; matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and permutations, combinations, and counting methods. Probability for finite sample spaces and basic concepts in statistics are also considered, along with the mathematics of finance and applications of calculus. This monograph is intended for students and instructors of applied mathematics.

Autoren/Hrsg.

Anton, Howard

Kolman, Bernard

Inhaltsverzeichnis

1;Front Cover;1
2;Mathematics with Applications for the Management, Life, and Social Sciences;2
3;Copyright Page;3
4;Table of Contents;4
5;PREFACE;8
6;NEW FEATURES IN THE SECOND EDITION;12
7;ACKNOWLEDGMENTS;13
8;CHAPTER ONE. SET THEORY;14
8.1;1.1 INTRODUCTION TO SETS;14
8.2;1.2 UNION AND INTERSECTION OF SETS;20
8.3;1.3 COMPLEMENTATION AND CARTESIAN PRODUCT OF SETS;31
8.4;KEY IDEAS FOR REVIEW;45
9;CHAPTER TWO. COORDINATE SYSTEMS AND GRAPHS;46
9.1;2.1 COORDINATE SYSTEMS;46
9.2;2.2 THE STRAIGHT LINE;55
9.3;2.3 LINEAR SYSTEMS OF TWO EQUATIONS IN TWO UNKNOWNS;68
9.4;2.4 APPLICATIONS OF LINEAR EQUATIONS;76
9.5;2.5 LINEAR INEQUALITIES AND THEIR GRAPHS;88
9.6;KEY IDEAS FOR REVIEW;97
10;CHAPTER THREE. LINEAR PROGRAMMING (A GEOMETRIC APPROACH);99
10.1;3.1 WHAT IS LINEAR PROGRAMMING?;99
10.2;3.2 SOLVING LINEAR PROGRAMMING PROBLEMS GEOMETRICALLY;109
10.3;KEY IDEAS FOR REVIEW;119
11;CHAPTER FOUR. MATRICES AND LINEAR SYSTEMS;120
11.1;4.1 LINEAR SYSTEMS;120
11.2;4.2 GAUSS-JORDAN ELIMINATION;129
11.3;4.3 MATRICES; MATRIX ADDITION AND SCALAR MULTIPLICATION;141
11.4;4.4 MATRIX MULTIPLICATION;152
11.5;4.5 INVERSE OF MATRICES;164
11.6;KEY IDEAS FOR REVIEW;175
12;CHAPTER FIVE. LINEAR PROGRAMMING (AN ALGEBRAIC APPROACH);177
12.1;5.1 INTRODUCTION; SLACK VARIABLES;177
12.2;5.2 THE KEY IDEAS OF THE SIMPLEX METHOD;185
12.3;5.3 THE SIMPLEX METHOD;196
12.4;5.4 NONSTANDARD LINEAR PROGRAMMING PROBLEMS; DUALITY (OPTIONAL);213
12.5;KEY IDEAS FOR REVIEW;220
13;CHAPTER SIX. COUNTING TECHNIQUES; PERMUTATIONS AND COMBINATIONS;221
13.1;6.1 COUNTING ELEMENTS IN SETS;221
13.2;6.2 PERMUTATIONS AND COMBINATIONS;233
13.3;KEY IDEAS FOR REVIEW;247
14;CHAPTER SEVEN. PROBABILITY;249
14.1;7.1 INTRODUCTION; SAMPLE SPACE AND EVENTS;249
14.2;7.2 PROBABILITY MODELS FOR FINITE SAMPLE SPACES;260
14.3;7.3 BASIC THEOREMS OF PROBABILITY;273
14.4;7.4 SOLVING PROBABILITY PROBLEMS;283
14.5;7.5 CONDITIONAL PROBABILITY; INDEPENDENCE;289
14.6;7.6 BAYES' FORMULA (OPTIONAL);305
14.7;KEY IDEAS FOR REVIEW;315
15;CHAPTER EIGHT. STATISTICS;317
15.1;8.1 INTRODUCTION; RANDOM VARIABLES;318
15.2;8.2 EXPECTED VALUE OF A RANDOM VARIABLE;324
15.3;8.3 VARIANCE OF A RANDOM VARIABLE;334
15.4;8.4 CHEBYSHEV'S INEQUALITY; APPLICATIONS OF MEAN AND VARIANCE (OPTIONAL);344
15.5;8.5 BINOMIAL RANDOM VARIABLES;352
15.6;8.6 THE NORMAL APPROXIMATION TO THE BINOMIAL;362
15.7;8.7 HYPOTHESIS TESTING; THE CHI-SQUARE TEST;375
15.8;KEY IDEAS FOR REVIEW;385
16;CHAPTER NINE. APPLICATIONS;387
16.1;9.1 APPLICATIONS OF PROBABILITY AND EXPECTED VALUE TO LIFE INSURANCE AND MORTALITY;387
16.2;9.2 INTRODUCTION TO GAME THEORY AND APPLICATIONS;394
16.3;9.3 GAMES WITH MIXED STRATEGIES;407
16.4;9.4 AN APPLICATION OF PROBABILITY TO GENETICS; THE HARDY-WEINBERG STABILITY PRINCIPLE;420
16.5;9.5 AN APPLICATION OF CONDITIONAL PROBABILITY TO MEDICAL DIAGNOSIS;429
16.6;9.6 MARKOV CHAINS AND APPLICATIONS;434
16.7;KEY IDEAS FOR REVIEW;455
17;CHAPTER 10. MATHEMATICS OF FINANCE;457
17.1;10.1 SIMPLE AND COMPOUND INTEREST;457
17.2;10.2 EFFECTIVE RATE OF INTEREST; SIMPLE DISCOUNT;465
17.3;10.3 ANNUITIES AND SINKING FUNDS;470
17.4;10.4 PRESENT VALUE;476
17.5;10.5 MORTGAGES AND AMORTIZATION SCHEDULES ;481
17.6;KEY IDEAS FOR REVIEW;485
18;CHAPTER 11. FUNCTIONS, LIMITS, AND RATES OF CHANGE;486
18.1;11.1 INTRODUCTION;486
18.2;11.2 FUNCTIONS;487
18.3;11.3 LIMITS;497
18.4;11.4 CONTINUITY;515
18.5;11.6 AVERAGE AND INSTANTANEOUS RATE OF CHANGE;521
18.6;KEY IDEAS FOR REVIEW;533
19;CHAPTER 12. THE DERIVATIVE;535
19.1;12.1 THE DERIVATIVE;535
19.2;12.2 THE CHAIN RULE;547
19.3;12.3 APPLICATIONS OF THE DERIVATIVE;554
19.4;12.4 DERIVATIVES OF THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS;563
19.5;KEY IDEAS FOR REVIEW;569
20;CHAPTER 13. APPLICATIONS OF DIFFERENTIATION;571
20.1;13.1 APPLICATIONS OF DIFFERENTIATION TO OPTIMIZATION;571
20.2;13.2 FIRST AND SECOND DERIVATIVE TESTS;586
20.3;13.3 MORE APPLICATIONS TO OPTIMIZATION;596
20.4;13.4 SKETCHING GRAPHS OF POLYNOMIAL FUNCTIONS;605
20.5;13.5 APPLICATIONS TO EXPONENTIAL GROWTH AND DECAY MODELS;609
20.6;KEY IDEAS FOR REVIEW;622
21;CHAPTER 14. INTEGRATION;624
21.1;1 4.1 ANTIDERIVATIVES AND INDEFINITE INTEGRALS;624
21.2;14.2 THE DEFINITE INTEGRAL;631
21.3;14.3 PROPERTIES OF THE DEFINITE INTEGRAL;644
21.4;1 4.4 TECHNIQUES OF INTEGRATION;656
21.5;14.5 IMPROPER INTEGRALS;665
21.6;KEY IDEAS FOR REVIEW;669
22;CHAPTER 15. APPLICATIONS OF INTEGRATION;671
22.1;15.1 INTEGRATING RATES OF CHANGE;671
22.2;15.2 DIFFERENTIAL EQUATIONS;678
22.3;15.3 APPLICATIONS OF INTEGRATION IN PROBABILITY;697
22.4;KEY IDEAS FOR REVIEW;704
23;CHAPTER 16. FUNCTIONS OF SEVERAL VARIABLES;706
23.1;16.1 FUNCTIONS OF TWO VARIABLES; COORDINATE SYSTEMS IN THREE DIMENSIONS;706
23.2;16.2 PARTIAL DERIVATIVES;712
23.3;KEY IDEAS FOR REVIEW;726
24;ALGEBRA REVIEW;728
24.1;A.1 REAL NUMBERS;728
24.2;A.2 ALGEBRAIC NOTATION AND THE BASIC RULES OF ALGEBRA;734
24.3;A.3 SOLVING EQUATIONS; LINEAR EQUATIONS;737
24.4;A.4 EXPONENTS AND RADICALS;742
24.5;A.5 POLYNOMIALS AND FACTORING;749
24.6;A.6 RATIONAL EXPRESSIONS;754
24.7;A.7 QUADRATIC EQUATIONS;759
24.8;A.8 LOGARITHMS;763
25;APPENDIX / TABLES;769
26;ANSWERS TO ODD-NUMBERED EXERCISES;806
27;INDEX;860