M
MacDonald function, 509
Maclaurin
--- formula, 415
--- series expansion, 418
Macsyma (computer algebra system), 953
majorant series, 413
manifold
--- center manifold theorem
--- local, 835
mappings, 835
--- of solutions, 890
--- stable, 806 , 812
--- unstable, 806 , 812
manipulation
--- algebraic expressions, 979
--- non-polynomial expressions, 981
mantissa, 10 , 939
manyness set, 298
Maple (computer algebra system), 953
Maple
--- addendum to syntax, 978
--- algebraic expressions, 971
manipulation, 981
multiplication, 981
--- array, 973
--- attribute, 978
--- basic structure elements, 968
--- context, 978
--- conversion of numbers, different bases, 970
Maple (continued)
--- differential equations, 997
--- differential operators, 977
--- differentiation, 995
--- eigenvalues, eigenvectors, 992
--- elements of linear algebra, 989
--- environment variable, 978
--- equation
--- one unknown, 986
--- transcendental, 987
--- factorization of polynomials, 982
--- floating-point number, conversion, 970
--- formula manipulation, introduction, 953
--- functions, 975
--- graphics, 1005
--- introduction, 955
--- three-dimensional, 1008
--- two-dimensional, 1005
--- help and information, 978
--- input, output, 949 , 969
--- input-output, 953
--- integral
--- definite, 997
--- indefinite, 996
multiple, 997
--- lists, 972
manipulation, general expressions, 983
matrices, 973
--- numerical calculations, introduction, 954
--- numerical mathematics, 949
--- differential equations, 952
--- equations, 950
--- expressions and functions, 949
--- integration, 951
--- object classes, 968
--- objects, 968
--- operations
--- important, 986
--- polynomials, 983
--- operators
--- functional, 976
--- important, 971
--- partial fraction decomposition, 983
--- procedures, 975
--- programming, 977
--- sequences, 972
--- short characteristc, 953
--- special package plots, 1007
--- system description, 968
--- system of equations, 987
--- systems of equations, linear, 990
--- table structures, 973
--- types, 968
--- types of numbers, 970
--- vectors, 973
mapping, 294 , 296
--- between groups, 302
--- bijective, 296 , 600
--- complex number plane, 684
--- conformal, 674
--- circular transformation, 676
--- exponential function, 679
--- fixed-point, 675 , 676
--- inversion, 676
--- linear fractional, 676
--- linear function, 675
--- logarithm, 678
--- quadratic function, 677
--- square root, 677
--- sum of linear and fractional linear functions, 678
--- contracting, 608
--- equivalent, 843
--- function, 48 , 294
--- Henon mapping, 812
--- horseshoe, 827
--- injective, 296 , 600
--- inverse mapping, 296
--- kernel, 302
--- lifted, 843
--- linear, 317 , 319 , 600
modulo, 816
--- one-to-one, 296
--- Poincare, 827
--- Poincare mapping, 808
--- reduced, 835
--- regular, 318
--- rotation mapping, 817
--- shift, 820
--- surjective, 296 , 600
--- tent, 816
--- topological conjugate, 813
--- unit circle, 843
marginal distribution, 754
mass
--- double integral, 474
--- line integral, first type, 464
--- triple integral, 480
matching, 356
maximal, 356
--- perfect, 356
--- saturated, 356
Mathcad (computer algebra system), 953
Mathematica (computer algebra system), 953
Mathematica
--- 3D graphics, 1004
--- algebraic expressions, manipulation, 979
--- algebraic expressions, multiplication, 979
--- apply, 965
--- attribute, 966
--- basic structure element, 956
--- context, 966
--- curves
--- parametric representation, 1003
--- two-dimensional, 1002
--- differential and integral calculus, 992
--- differential equation, 994
--- differential quotient, 992
--- differentiation, 965
--- eigenvalues, eigenvectors, 989
--- elements, 956
--- elements of linear algebra, 988
--- equation, 985
manipulation, 984
--- transcendent, 985
--- expression, 956
--- factorization, polynomials, 980
Mathematica (continued)
--- FixedPoint, 965
--- FixedPointList, 965
--- floating-point number, conversion, 958
--- formula manipulation, introduction, 953
--- function, inverse, 965
--- functional operations, 964
--- functions, 963
--- graphics, 998
--- functions, 1001
--- introduction. 955
--- options, 1000
--- primitives, 998 , 999
--- head, 956
--- input and output, 946
--- input-output, 953 , 957
--- integral
--- definite, 994
--- indefinite, 993
multiple, 994
--- lists, 959
manipulation with matrices. 962
manipulation with vectors. 962
Map, 965
matrices as lists, 961
messages, 967
--- Nest, 965
--- NestList, 965
--- numerical calculations, introduction, 954
--- numerical mathematics, 946
--- curve fitting, 946
--- differential equations, 948
--- integration, 948
--- interpolation, 947
--- polynomial equations, 947
--- objects, three-dimensional, 1004
--- operations, polynomials, 980
--- operators, important, 959
--- partial fraction decomposition, 980
--- pattern, 964
--- programming, 966
--- short characteristc, 953
--- surfaces, 1004
--- surfaces and space curves, 1003
--- syntax, additional information, 966
--- system description, 956
--- system of equations, 986
--- general case, 988
--- special case, 988
--- types of numbers, 957
--- vectors as lists, 961
mathematics, discrete, 286
matrices
--- arithmetical operations, 254
--- associative law, 254
--- commutative law, 254 , 255
--- distributive law, 254
--- division, 254
--- eigenvalue, 278
--- eigenvalue problem, 278
--- eigenvectors, 278
--- equality, 254
multiplication, 254
--- powers, 258
--- rules of calculation, 257
matrix, 251
--- adjacency, 350
--- adjoint, 251 , 260
--- admittance, 355
--- anti-Hermitian, 253
--- antisymmetric, 252
--- block tridiagonal, 912
--- complex, 251
--- conjugate, 251
--- deflation, 284
--- degree, 355
--- diagonal, 252
--- distance, 351
--- extended coefficient, 892
--- full rank, 277
--- fundamental, 802
--- Hermitian, 253
--- Hessian, 869
--- identity, 253
--- incidence, 350
--- inverse, 256 , 260
--- inverse calculation, 272
--- Jacobian, 897
--- Jordan, 282
--- lower triangular, 892
main diagonal element, 252
monodromy, 803 , 812
--- normal, 252
--- of coefficients, 272
--- augmented, 273
--- orthogonal, 257
--- rank, 255
--- real, 251
--- rectangular, 251
--- regular, 256
--- rotation, 257
--- scalar, 252
--- self-adjoint, 253
--- singular, 256
--- size, 251
--- skew-symmetric, 252
--- spanning tree theorem, 355
--- sparse, 912
--- spur, 252
--- square, 251 , 252
--- stochastic, 766
--- symmetric, 252
--- trace, 252
--- transposed, 251
--- triangle decomposition, 890
--- triangular, 253
--- unitary, 257
--- upper triangular, 892
--- zero, 251
matrix exponential function, 802
matrix product, disappearing, 257
max-min composition, 371
maximum
--- absolute, 60 , 123 , 390
--- global, 390
--- point, 847
maximum (continued)
--- relative, 390
maximum-criterion method, 373
Maxwell, diagonal method, 684
mean
--- arithmetic, 19 , 753 , 790
--- estimate, 771
--- geometric, 20
--- golden, 845
--- harmonic, 20
--- quadratic, 20
--- sample function, 771
--- statistics, 773
--- value, 19
--- weighted, 753 , 790 , 793
mean squares problem
--- different versions, 403
--- non-linear, 922
mean squares value problem
--- linear, 277
--- rank deficiency case, 278
mean value formula, 899
mean value function, integral calculus, 444
mean value method, 107
mean value theorem
--- differential calculus, 389
--- generalized, 390
--- integral calculus, 444
--- generalized, 445
measure
--- concentrated on a set, 816
--- counting, 635
--- degrees, 130
--- dimension, 824
--- Dirac, 636 , 816
--- ergodic, 817
--- function, convergence theorems. 638
--- Hausdorff, 822
--- invariant, 816
--- Lebesgue, 636 , 816
--- natural, 816
--- physical, 817
--- probability, 638
--- invariant, 816
--- SBR (Sinai-Bowen-Ruelle), 817
--- a-algebra, 635
--- (T-finite, 638
--- support, 816
measured value, 787
measurement
--- error, 787
--- error density, 788
--- error, characterization, 788
--- protocol, 788
measuring error, distribution, 788
median, 142
--- sample function, 772
--- statistics, 774
--- triangle, 132
Mellin transformation, 707
Melnikov method, 841
membership
--- degree, 360
--- function, 360 , 361
--- bell-shaped, 362
--- trapezoidal, 361
--- relation, 290
meridian, 160 , 244
--- convergence, 169
--- tangential, 176
method
--- Bairstow, 889
--- barrier, 876
--- Bernoulli, 889
--- bisection, 283
--- broken line, Euler, 904
--- center of area, 374
--- center of gravity, 373
--- generalized, 374
--- parametrized, 374
--- Cholesky, 278 , 893
--- collocation
--- boundary value problem, 909
--- integral equation, 576
--- partial integral equation, 913
--- cryptoanalysis, 337
--- cryptography, 335
--- cutting plane, 877
--- descent, 868
--- difference
--- ordinary differential equations, 908
--- partial differential equations, 911
--- extrapolation, 905
--- Fibonacci, 868
--- finite difference, 534
--- finite element, 534 , 561. 913
--- Galerkin, 909
--- Gauss elimination, 890
--- Gauss-Newton, 897
--- derivative free, 898
--- Gauss-Seidel, 895
--- gradient. 561
--- Graeffe, 889
--- Green, 531 , 532
--- Hildreth-d'Esopo, 867
--- Householder, 278 , 921
--- Hungarian, 860
--- inner digits of squares, 783
--- integrating factor, 490
--- iteration, 283 , 884 , 890 , 895
--- ordinary, 884 , 896
--- Jacobi, 283 , 895
--- Kelley's, optimization, 877
--- Lagrange multiplier, 862
--- Lanczos, 283
--- largest area. 374
--- least squares, 107 , 890 , 909 , 913 , 919 , 921
Mamdani, 374
maximum-criterion, 373
mean-of-maximum, 373
Monte Carlo, 783
multi-step, 905
multiple-target, 910
--- Newton, 885 , 897
modified, 885
--- non-linear operators, 632
method (continued)
--- operator, 709
--- orthogonalization, 278 , 893 , 894
--- parametrized center of area, 374
--- pivoting, 271
--- polygonal, Euler, 904
--- predictor-corrector, 906
--- public key, 338
--- regula falsi, 886
--- relaxation, 896
--- Riemann, 530
--- Ritz, 560 , 909
--- Romberg, 901
--- RSA encryption, 339
--- Runge-Kutta, 904
--- separation of variables, 489
--- shooting, 910
--- single-target, 910
--- SOR (successive overrelaxation), 896
--- statistical experiment, 787
--- steepest descent, 869
--- Steffensen, 886
--- successive approximation
--- Banach space, 621
--- Picard, 496
--- Sugeno, 375
--- transformation, 283
--- undetermined coefficients, 16 , 497
--- variation of constants, 501
--- Vigenere cypher, 336
--- Wolfe, 865
metric, 604
--- Euclidean, 604
--- surface, 247
Meusnier, theorem, 247
midpoint line segment
--- plane, 192
--- space, 213
midpoint rule, 906
minimal surface, 249
minimum
--- absolute, 60. 123 , 390
--- global, 390
--- point, 862
--- global, 862
--- local, 862
--- problem, 847
--- relative, 390
Minkowski
--- inequality, 32
--- integrals, 32
--- series, 32
mixed product, 187
modal value, statistics, 774
mode, statistics, 774
model
--- Hopf-Landau, turbulence, 841
--- urn model, 755
module of an element, 603
modulo
--- congruence, 297 , 327
mapping, 816
modulus, analytic function, 672
--- de Moivre formula
--- complex number, 37
--- hyperbolic functions, 90
--- trigonometric functions, 79
Mollweide equations, 142
moment of inertia, 263 , 452
--- double integral, 474
--- line integral, first type, 464
--- triple integral, 480
moment, order n, 753
monodromy matrix, 803 , 804 , 812
monotonicity, 635
monotony, 388
--- function, 49
--- sequence, numbers, 404
Monte Carlo method, 783
--- application in numerical mathematics, 785
--- usual, 785
Monte Carlo simulation, 783
--- example, 784
Morse-Smale system, 815
multi-index, 613
multi-scale analysis, 743
multi-step method, 905
multiple integral, 471
--- transformation, 709
multiple-target method, 910
multiplication
--- complex numbers, 36
--- computer calculation, 940
--- polynomials, 11
--- rational numbers, 1
multiplicity, of divisors, 320
multiplier, 490 , 803 , 804 , 812
--- Lagrange method, 403
mutation, 870
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