Anton / Kolman Applied Finite Mathematics

2. Auflage 2014
ISBN: 978-1-4832-7096-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 576 Seiten, Web PDF

Applied Finite Mathematics, 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. Some applications of probability, game theory, and Markov chains are given. Comprised of 10 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 and algebraic point of view; matrices, the solution of linear systems, and applications; the simplex method for solving linear programming problems; and probability and probability models for finite sample spaces as well as permutations, combinations, and counting methods. Basic concepts in statistics are also considered, along with the mathematics of finance. The final chapter is devoted to computers and programming languages such as BASIC. 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;20
8.1;1.1 INTRODUCTION TO SETS;20
8.2;1.2 UNION AND INTERSECTION OF SETS;27
8.3;1.3 COMPLEMENTATION AND CARTESIAN PRODUCT OF SETS;38
8.4;1.4 COUNTING ELEMENTS IN SETS;50
9;CHAPTER 2. COORDINATE SYSTEMS AND GRAPHS;62
9.1;2.1 COORDINATE SYSTEMS;62
9.2;2.2 THE STRAIGHT LINE;70
9.3;2.3 APPLICATIONS OF LINEAR EQUATIONS;84
9.4;2.4 LINEAR INEQUALITIES AND THEIR GRAPHS;94
10;CHAPTER 3. LINEAR PROGRAMMING (A GEOMETRIC APPROACH);102
10.1;3.1 WHAT IS LINEAR PROGRAMMING?;102
10.2;3.2 SOLVING LINEAR PROGRAMMING PROBLEMS GEOMETRICALLY;110
11;CHAPTER 4. MATRICES AND LINEAR SYSTEMS;121
11.1;4.1 LINEAR SYSTEMS;121
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;151
11.5;4.5 INVERSES OF MATRICES;162
12;CHAPTER 5. LINEAR PROGRAMMING (AN ALGEBRAIC APPROACH);174
12.1;5.1 INTRODUCTION; SLACK VARIABLES;174
12.2;5.2 THE KEY IDEAS OF THE SIMPLEX METHOD;183
12.3;5.3 THE SIMPLEX METHOD;194
12.4;5.4 NONSTANDARD LINEAR PROGRAMMING PROBLEMS; DUALITY;212
13;CHAPTER 6. PROBABILITY;220
13.1;6.1 INTRODUCTION; SAMPLE SPACE AND EVENTS;220
13.2;6.2 PROBABILITY MODELS FOR FINITE SAMPLE SPACES;230
13.3;6.3 BASIC THEOREMS OF PROBABILITY;238
13.4;6.4 COUNTING TECHNIQUES; PERMUTATIONS AND COMBINATIONS;248
13.5;6.5 CONDITIONAL PROBABILITY; INDEPENDENCE;265
13.6;6.6 BAYES' FORMULA;281
14;CHAPTER 7. STATISTICS;293
14.1;7.1 INTRODUCTION; RANDOM VARIABLES;293
14.2;7.2 EXPECTED VALUE OF A RANDOM VARIABLE;300
14.3;7.3 VARIANCE OF A RANDOM VARIABLE;310
14.4;7.4 CHEBYSHEV'S INEQUALITY; APPLICATIONS OF MEAN AND VARIANCE;320
14.5;7.5 BINOMIAL RANDOM VARIABLES;328
14.6;7.6 THE NORMAL APPROXIMATION TO THE BINOMIAL;338
14.7;7.7 HYPOTHESIS TESTING; THE CHI-SQUARE TEST;352
15;CHAPTER 8. APPLICATIONS;363
15.1;8.1 AN APPLICATION OF CONDITIONAL PROBABILITY TO MEDICAL DIAGNOSIS;363
15.2;8.2 AN APPLICATION OF PROBABILITY TO GENETICS; THE HARDY-WEINBERG STABILITY PRINCIPLE;368
15.3;8.3 APPLICATIONS OF PROBABILITY AND EXPECTED VALUE TO LIFE INSURANCE AND MORTALITY;377
15.4;8.4 INTRODUCTION TO GAME THEORY AND APPLICATIONS;384
15.5;8.5 GAMES WITH MIXED STRATEGIES;397
15.6;8.6 MARKOV CHAINS AND APPLICATIONS;411
16;CHAPTER 9.
MATHEMATICS OF FINANCE;430
16.1;9.1 EXPONENTS AND LOGARITHMS—A REVIEW;430
16.2;9.2 MATHEMATICS OF FINANCE;439
17;CHAPTER 10.
COMPUTERS;461
17.1;10.1 WHAT IS A COMPUTER?;461
17.2;10.2 COMMUNICATING WITH THE COMPUTER;462
17.3;10.3 BASIC, A PROGRAMMING LANGUAGE;470
17.4;10.4 BASIC CONTINUED (PRINT AND DATA INSTRUCTIONS);481
17.5;10.5 BASIC CONTINUED (LOOPS AND DECISIONS);488
17.6;10.6 FLOW CHARTS;497
17.7;10.7 OTHER PROGRAMMING LANGUAGES;506
18;APPENDIX/TABLES;507
19;ANSWERS TO ODD-NUMBERED EXERCISES;543
20;INDEX;572