(Dover Books on Mathematics)
David B. MacNeil
Dover Publications | 2013 | páginas | rar - epub | 17,67 Mb
link (password: matav)
Students and others wishing to know a little more about the practical side of mathematics will find this volume a highly informative resource. An excellent supplement to college and high school courses as well as a guide to independent study, the book covers examples of pure mathematics as well as concepts of applied mathematics useful for solving problems that arise in business, industry, science, and technology.
Contents include examinations of the theory of sets, numbers and groups; matrices and determinants; probability, statistics, and quality control; and game theory. Additional subjects include inequalities, linear programming, and the transportation problem; combinatorial mathematics; transformations and transforms; and numerical analysis. Accessible explanations of important concepts feature a total of more than 150 diagrams and graphs, in addition to worked-out examples with step-by-step explanations of methods. Answers to exercises and problems appear at the end.
CONTENTS
CHAPTER 1 THEORY OF SETS, NUMBERS AND GROUPS
1.SET MEMBERSHIP
2.EQUALITY
3.SETS, SUBSETS AND INCLUSION
4.SET OF SETS
5.NEGATIVES
6.UNIONS AND INTERSECTIONS
7.RELATIONS INVOLVING UNIONS AND INTERSECTIONS
8.THE COMPLEMENT
9.THE ABSOLUTE COMPLEMENT
10.POWERS
11.ORDERED PARTS AND CARTESIAN PRODUCTS
12.RELATIONS: FUNCTION, DOMAIN AND RANGE
13.FUNCTIONS
14.NUMBERED SETS
15.OPERATIONS WITH NATURAL NUMBERS
16.INTEGRAL NUMBERS OR INTEGERS
17.RATIONAL NUMBERS
18.REAL NUMBERS
19.COMPLEX NUMBERS
20.TRIGONOMETRIC AND LOGARITHMIC NUMBERS
21.TRANSCENDENTAL NUMBERS
22.TRANSFINITE NUMBERS
23.GROUPS, DEFINITION OF
24.PERMUTATION GROUPS
CHAPTER 2 MATRICES AND DETERMINANTS
25.ADDITION OF MATRICES
26.SCALAR MULTIPLICATION OF MATRICES
27.MULTIPLICATION OF MATRICES BY MATRICES
28.APPLICATION OF MATRICES
29.DETERMINANTS
30.FINDING THE DETERMINANTS OF 2 × 2 AND 3 × 3 MATRICES
31.PROPERTIES OF MATRICES AND DETERMINANTS
32.MINORS AND THE EVALUATION OF 4TH ORDER DETERMINANTS
33.THE SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS BY DETERMINANTS
34.RANK OF A MATRIX AND CONSISTENCY OF EQUATIONS
35.CHARACTERISTIC EQUATION OF A MATRIX
36.VECTORS
37.THE APPLICATION OF MATRICES IN DESCRIBING GEOMETRICAL DISTORTIONS AND TRANSFORMATIONS
38.MATRICES. OTHER OPERATIONS AND DEFINITIONS
CHAPTER 3 PROBABILITY, STATISTICS, AND QUALITY CONTROL
39.INTRODUCTION
40.FUNDAMENTAL CONCEPTS
41.PROBABILITY
42.GAMES OF CHANCE
43.RANDOM WALK PROCESSES
44.MARKOV PROCESSES
45.RANDOM VARIABLES
46.STATISTICAL DEFINITIONS AND THEIR NOTATION
47.IMPORTANT DISTRIBUTIONS. THE BINOMIAL DISTRIBUTION
48.ELEMENTS OF STATISTICS
49.OTHER FUNDAMENTAL CONCEPTS
50.STATISTICAL QUALITY CONTROL
CHAPTER 4THE THEORY OF GAMES
51.INTRODUCTION
52.TWO-PERSON ZERO-SUM GAMES
53.SADDLE POINTS
54.MIXED STRATEGIES
55.2 × N GAMES
56.3 × 3 GAMES
57.CONCLUSION
CHAPTER 5 INEQUALITIES, LINEAR PROGRAMMING, AND THE TRANSPORTATION PROBLEM
58.INTRODUCTION
59.FUNDAMENTAL SYMBOLS AND AXIOMS
60.FUNDAMENTAL OPERATIONS
61.INEQUALITIES OF AVERAGES
62.PROPER-NAME INEQUALITIES
63.SYSTEMS OF INEQUALITIES
64.LINEAR PROGRAMMING
65.THE TRANSPORTATION PROBLEM
66.THE TRANSPORTATION PROBLEM REVISED
67.DEGENERACY AND FORMAL CHARACTERISTICS
68.THE SIMPLEX METHOD
69.THE DUAL SIMPLEX METHOD
CHAPTER 6 COMBINATORIAL MATHEMATICS
70.INTEGER PROGRAMMING
71.LINEAR PROGRAMMING AND GAME THEORY
72.NETWORK FLOW PROBLEMS
73.TREES AND LOOPS
CHAPTER 7 TRANSFORMATIONS AND TRANSFORMS
74.COORDINATE SYSTEMS
75.CARTESIAN COORDINATES
76.SPHERICAL POLAR COORDINATES
77.CYLINDRICAL COORDINATES
78.THE POLAR COORDINATE SYSTEM
79.HYPERBOLIC FUNCTIONS
80.BIPOLAR COORDINATES
81.TRANSLATION OF COORDINATE AXES
82.ROTATION OF COORDINATE AXES
83.LAPLACE TRANSFORMATIONS. GENERAL CONSIDERATIONS
84.EVALUATING LAPLACE TRANSFORMS
85.PROPERTIES OF THE LAPLACE TRANSFORM
86.THE INVERSE LAPLACE TRANSFORM
87.APPLICATIONS OF THE LAPLACE TRANSFORM
88.HEAVISIDE OPERATIONAL CALCULUS
89.OTHER TRANSFORMS
CHAPTER 8 NUMERICAL ANALYSIS
90.NATURE OF NUMERICAL ANALYSIS
91.DIFFERENCE TABLES
92.DIFFERENCE TABLES USED FOR INTERPOLATION
93.NUMERICAL SOLUTION OF ALGEBRAIC EQUATIONS
94.NUMERICAL INTEGRATIONS
95.NUMERICAL DIFFERENTIATION
96.THE METHOD OF LEAST SQUARES
ANSWERS TO EXERCISES AND PROBLEMS
INDEX
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