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| MacNeil D.B. — Modern Mathematics for the Practical Man |
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| Предметный указатель |
Acceptance sampling 124
Average 119
Binomial distribution 102
Cartesian products 9
Combinatorial mathematics, game theory 208 ff.
Combinatorial mathematics, integer programming 202
Combinatorial mathematics, linear programming 208
Combinatorial mathematics, network flow problems 213
Combinatorial mathematics, network flow problems, trees and loops 222
complex numbers 18
Complex numbers, absolute value of 22
Complex numbers, addition of 18
Complex numbers, division of 20
Complex numbers, multiplication of 20
Complex numbers, representation of 23
Complex numbers, subtraction of 18
Coordinate systems, axes, rotation of 248
Coordinate systems, axes, translation of 242
Coordinate systems, bipolar 240
Coordinate systems, bipolar and hyperbolic functions 237
Coordinate systems, Cartesian 226
Coordinate systems, cylindrical 232
Coordinate systems, cylindrical and polar coordinate system 236
Coordinate systems, spherical polar 229
Coordinate systems, spherical polar and polar coordinate system 236
Crystal structure 30
de Morgans Laws 7
Degeneracy 188
Determinants 47 (see also “Matrices”)
Determinants, fourth order 32
Determinants, in solution of simultaneous linear equations 59
Determinants, minors 56
Determinants, of  and  matrices 49
Determinants, permutations 47
Difference tables 273
Equations, algebraic, numerical solution of 279
Equations, consistency of 64
Euler — Maclaurin formula 291
games of chance 92
Games, theory of,  games 143
Games, theory of, games 149
Games, theory of, and linear programming 208
Games, theory of, mixed strategies 137
Games, theory of, saddle points 134
Games, theory of, two-person, zero-sum 131
Games, theory of, two-person, zero-sum, grand strategy 132
Games, theory of, two-person, zero-sum, pure strategy 132
Geometric mean 167
Gregory’s formula 293
Groups, definition of 26 (see also “Sets” “Numbers” and Theory
Harmonic mean 167
Heaviside operational calculus 267
Hypergeometric distribution 103
Inequalities and linear programming 172
Inequalities and linear programming, and integer programming 202
Inequalities and linear programming, Simplex method 190
Inequalities and linear programming, Simplex method, dual 196
Inequalities and linear programming, transportation problem 176
Inequalities and linear programming, transportation problem, modification of 186
Inequalities of averages 167
Inequalities of averages, geometric mean 167
Inequalities of averages, harmonic mean 167
Inequalities, fundamentals of, axioms 162
Inequalities, fundamentals of, axioms, operations 163
Inequalities, fundamentals of, axioms, operations, addition 164
Inequalities, fundamentals of, axioms, operations, division 166
Inequalities, fundamentals of, axioms, operations, exponents 166
Inequalities, fundamentals of, axioms, operations, multiplication 165
Inequalities, fundamentals of, axioms, operations, subtraction 164
Inequalities, fundamentals of, axioms, operations, transitivity 164
Inequalities, fundamentals of, axioms, symbols 162
Inequalities, Schwarz 168
Inequalities, systems of 169
Inequalities, transportation problems 176—186
Inequalities, transportation problems, degeneracy 188
Integral numbers 16
intersections 4
Laplace transform, and Heaviside operational calculus 267
Laplace transform, applications of 262
Laplace transform, evaluation of 255
Laplace transform, general considerations 254
Laplace transform, inverse 260
Laplace transform, properties of 257
Least squares method 297
Linear programming 172
Linear programming, and game theory 208
Linear programming, and integer programming 202
Linear programming, fundamentals 172
Linear programming, simplex method 190
Linear programming, Simplex method, dual 196
Linear programming, transportation problem 176
Linear programming, transportation problem, modification of 186
Markov processes 96
Matrices see also “Determinants”
Matrices, addition 39
Matrices, and consistency of equations 64
Matrices, and vectors 69
Matrices, application of 46 69
Matrices, characteristic equations of 68
Matrices, characteristic equations of, root of 69
Matrices, diagonal 76
Matrices, inversion of 77
Matrices, multiplication of, by matrices 42
Matrices, non-singular 76
Matrices, properties of 50
Matrices, rank of 64
Matrices, scalar multiplication 41
Matrices, singular 76
Matrices, transpose of 78
Matrices, unit 76
Median 119
MODE 119
Molecular structure 30
Natural numbers, operations with 15
Network flow 213
Normal distribution 109
Number sets 13
Numbers see “Sets” “Numbers” and Theory
Numerical analysis, difference tables 273
Numerical analysis, difference tables, used for interpolation 274
Numerical analysis, least squares method 297
Numerical analysis, nature of 271
Numerical analysis, numerical differentiation 294
Numerical analysis, numerical integration 287
Numerical analysis, numerical integration, Euler — Maclaurin formula 291
Numerical analysis, numerical integration, Gregory’s formula 293
| Numerical analysis, numerical integration, Simpson’s parabolic rule 288
Numerical analysis, numerical integration, trapezoidal rule 287
Numerical analysis, numerical integration, Weddle’s rule 289
Numerical differentiation 294
Ordered sets 10
Peano axioms 15
poisson 104
Poisson distribution 104
probability see also “Statistics”
Probability, distributions 102
Probability, distributions, binomial 102
Probability, distributions, hypergeometric 103
Probability, distributions, normal 109
Probability, fundamental concepts 83
Probability, fundamental concepts, Venn diagrams 89
Probability, games of chance 92
Probability, introduction 83
Probability, Markov processes 96
Probability, random variables 97
Probability, random walk processes 43
Probability, statistical definitions 100
Probability, statistical definitions, notations 100
Probability, stochastic processes 96
Programming, integer 202
Programming, linear 172
Programming, linear, dual 196
Programming, linear, simplex method 190
Quality control 120
Random numbers 115
Random variables 97
Random walk processes 43
Rational numbers 16
Real numbers 17
Saddle points 134
Schwarz inequality 168
Sets of sets 4
Sets, Numbers, and Groups, Theory of, absolute complement 8
Sets, Numbers, and Groups, Theory of, Cartesian products 9
Sets, Numbers, and Groups, Theory of, complement 7
Sets, Numbers, and Groups, Theory of, complement, absolute 8
Sets, Numbers, and Groups, Theory of, complex numbers 18
Sets, Numbers, and Groups, Theory of, complex numbers, absolute value of 22
Sets, Numbers, and Groups, Theory of, complex numbers, addition of 18
Sets, Numbers, and Groups, Theory of, complex numbers, division of 20
Sets, Numbers, and Groups, Theory of, complex numbers, multiplication of 20
Sets, Numbers, and Groups, Theory of, complex numbers, representation of 23
Sets, Numbers, and Groups, Theory of, complex numbers, subtraction of 18
Sets, Numbers, and Groups, Theory of, de Morgan’s Laws 7
Sets, Numbers, and Groups, Theory of, domain 10
Sets, Numbers, and Groups, Theory of, equality 2
Sets, Numbers, and Groups, Theory of, function 10 11
Sets, Numbers, and Groups, Theory of, groups, definition of 26
Sets, Numbers, and Groups, Theory of, integral numbers 16
Sets, Numbers, and Groups, Theory of, natural numbers, operations with 15
Sets, Numbers, and Groups, Theory of, negatives 4
Sets, Numbers, and Groups, Theory of, number sets 13
Sets, Numbers, and Groups, Theory of, number sets, Peano axioms 15
Sets, Numbers, and Groups, Theory of, ordered parts 9
Sets, Numbers, and Groups, Theory of, ordered sets 10
Sets, Numbers, and Groups, Theory of, permutation groups, crystal and molecular structure 30
Sets, Numbers, and Groups, Theory of, permutation groups, symmetry point groups, table of 35
Sets, Numbers, and Groups, Theory of, powers 9
Sets, Numbers, and Groups, Theory of, range 10
Sets, Numbers, and Groups, Theory of, rational numbers 16
Sets, Numbers, and Groups, Theory of, real numbers 17
Sets, Numbers, and Groups, Theory of, set membership 1
Sets, Numbers, and Groups, Theory of, sets of sets 4
Sets, Numbers, and Groups, Theory of, sets, subsets, and inclusion 3
Sets, Numbers, and Groups, Theory of, transcendental numbers 24
Sets, Numbers, and Groups, Theory of, transfinite numbers 25
Sets, Numbers, and Groups, Theory of, trigonometric and logarithmic numbers 20
Sets, Numbers, and Groups, Theory of, unions and intersections 4 6
Sets, Numbers, and Groups, Theory of, unions and intersections, Venn diagrams 4
Sets, subsets, and inclusions 3
Simplex method 190
Simplex method, dual 196
Simpson’s parabolic rule 288
Simultaneous linear equations 59
skewness 120
Standard deviation 120
Statistics see also “Probability”
Statistics, definitions 100
Statistics, fundamental concepts 114
Statistics, fundamental concepts, average 119
Statistics, fundamental concepts, median 119
Statistics, fundamental concepts, mode 119
Statistics, fundamental concepts, skewness 120
Statistics, fundamental concepts, standard deviation 120
Statistics, notations 100
Statistics, quality control 120
Statistics, quality control, acceptance sampling 124
Statistics, random numbers 115
Stochastic processes 96
Strategy, grand 132
Strategy, mixed 137
Strategy, pure 132
Transcendental numbers 24
Transfinite numbers 25
Transformations and Transforms, axes, coordinate, rotation of 248
Transformations and Transforms, axes, coordinate, translation of 242
Transformations and Transforms, bipolar coordinates 240
Transformations and Transforms, bipolar coordinates and hyperbolic functions 237
Transformations and Transforms, Cartesian coordinates 226
Transformations and Transforms, coordinate systems 226
Transformations and Transforms, cylindrical coordinates 232
Transformations and Transforms, cylindrical coordinates and polar coordinate system 236
Transformations and Transforms, Laplace and Heaviside operational calculus 267
Transformations and Transforms, Laplace, applications of 262
Transformations and Transforms, Laplace, evaluation of 255
Transformations and Transforms, Laplace, general considerations 254
Transformations and Transforms, Laplace, inverse 260
Transformations and Transforms, Laplace, properties of 257
Transformations and Transforms, spherical polar coordinates 229
Transformations and Transforms, spherical polar coordinates and polar coordinate system 236
transforms see also “Transformations”
Transforms, Laplace and Heaviside operational calculus 267
Transforms, Laplace, applications of 262
Transforms, Laplace, evaluation of 255
Transforms, Laplace, general considerations 254
Transforms, Laplace, inverse 260
Transforms, Laplace, properties of 257
Transportation problem 176 (see also “Inequalities”)
Trapezoidal rule 287
Unions and intersections 4
Venn diagrams 4 89
Weddle’s rule 289
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