Anton / Kolman Applied Finite Mathematics

1. Auflage 2014
ISBN: 978-1-4832-7137-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 492 Seiten, Web PDF

Applied Finite Mathematics 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. Applications in fields such as business, biology, behavioral sciences, and social sciences are included. Comprised of nine chapters, this book begins with an introduction to set theory, explaining concepts such as sets and union and intersection of sets as well as counting elements in sets. The next chapter deals with coordinate systems and graphs, along with applications of linear equations and graphs of linear inequalities. The discussion then turns to linear programming; matrices and linear systems; probability; and statistics. Examples of applications are given, including those of game theory, Markov chains, and probability. The final chapter is devoted to computers and programming languages such as FORTRAN. This monograph is intended for students and instructors of applied mathematics.

Autoren/Hrsg.

Anton, Howard

Kolman, Bernard

Inhaltsverzeichnis

1;Front Cover;1
2;Applied Finite Mathematics;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;PREFACE;12
7;ACKNOWLEDGMENTS;16
8;CHAPTER 1. SET THEORY;18
8.1;1.1 INTRODUCTION TO SETS;18
8.2;1.2 UNION AND INTERSECTION OF SETS;25
8.3;1.3 COMPLEMENTATION AND CARTESIAN PRODUCT OF SETS;36
8.4;1.4 COUNTING ELEMENTS IN SETS;48
9;CHAPTER 2. COORDINATE SYSTEMS AND GRAPHS;60
9.1;2.1 COORDINATE SYSTEMS;60
9.2;2.2 THE STRAIGHT LINE;68
9.3;2.3 APPLICATIONS OF LINEAR EQUATIONS;82
9.4;2.4 LINEAR INEQUALITIES AND THEIR GRAPHS;92
10;CHAPTER 3. LINEAR PROGRAMMING(A GEOMETRIC APPROACH;100
10.1;3.1 WHAT IS LINEAR PROGRAMMING?;100
10.2;3.2 SOLVING LINEAR PROGRAMMING PROBLEMS GEOMETRICALLY;108
11;CHAPTER 4. MATRICES AND LINEAR SYSTEMS;119
11.1;4.1 LINEAR SYSTEMS;119
11.2;4.2 GAUSS-JORDAN ELIMINATION;127
11.3;4.3 MATRICES; MATRIX ADDITION AND SCALAR MULTIPLICATION;139
11.4;4.4 MATRIX MULTIPLICATION;149
11.5;4.5 INVERSES OF MATRICES;160
12;CHAPTER 5. LINEAR PROGRAMMING (AN ALGEBRAIC APPROACH);172
12.1;5.1 INTRODUCTION; SLACK VARIABLES;172
12.2;5.2 THE KEY IDEAS OF THE SIMPLEX METHOD;181
12.3;5.3 THE SIMPLEX METHOD;192
12.4;5.4 NONSTANDARD LINEAR PROGRAMMING PROBLEMS; DUALITY;210
13;CHAPTER 6. PROBABILITY;218
13.1;6.1 INTRODUCTION; SAMPLE SPACE AND EVENTS;218
13.2;6.2 PROBABILITY MODELS FOR FINITE SAMPLE SPACES;228
13.3;6.3 BASIC THEOREMS OF PROBABILITY;236
13.4;6.4 COUNTING TECHNIQUES;PERMUTATIONS AND COMBINATIONS;246
13.5;6.6 BAYES' FORMULA;276
14;CHAPTER 7. STATISTICS;285
14.1;7.1 INTRODUCTION; RANDOM VARIABLES;285
14.2;7.2 EXPECTED VALUE OF A RANDOM VARIABLE;292
14.3;7.3 VARIANCE OF A RANDOM VARIABLE;302
14.4;7.4 CHEBYSHEV'S INEQUALITY;APPLICATIONS OF MEAN AND VARIANCE;312
14.5;7.5 BINOMIAL RANDOM VARIABLES;320
14.6;7.6 THE NORMAL APPROXIMATIONTO THE BINOMIAL;330
14.7;7.7 HYPOTHESIS TESTING; THE CHI-SQUARE TEST;344
15;CHAPTER 8. APPLICATIONS;355
15.1;8.1 AN APPLICATION OF CONDITIONAL PROBABILITY TO MEDICAL DIAGNOSIS;355
15.2;8.2 AN APPLICATION OF PROBABILITY TO GENETICS; THE HARDY-WEINBERG STABILITY PRINCIPLE;360
15.3;8.3 APPLICATIONS OF PROBABILITY AND EXPECTED VALUE TO LIFE INSURANCEAND MORTALITY;369
15.4;8.4 INTRODUCTION TO GAME THEORY AND APPLICATIONS;376
15.5;8.5 GAMES WITH MIXED STRATEGIES;389
15.6;8.6 MARKOV CHAINS AND APPLICATIONS;403
16;CHAPTER 9. COMPUTERS;422
16.1;9.1 WHAT IS A COMPUTER;422
16.2;9.2 COMMUNICATING WITH THE COMPUTER;423
16.3;9.3 FORTRAN, A PROGRAMMING LANGUAGE OF SCIENCE;431
16.4;9.4 FORTRAN, CONTINUED (LOOPS AND DECISIONS);441
16.5;9.5 FLOW CHARTS;448
16.6;9.6 OTHER PROGRAMMING LANGUAGES;457
17;APPENDIX/TABLES;458
17.1;Areas under the Standard Normal Curve;458
17.2;Table of Binomial Probabilities;459
17.3;Table of 5% Critical Levels for x2-Curves;461
17.4;Table of Square Roots;461
18;ANSWERS TO SELECTED EXERCISES;462
19;INDEX;488