INDEX
recurrence relations, 611–612
second kindYν(x), 607
graph of, 607
series, 604
ν= 0, 606
ν=± 1 /2, 605
sphericalj(x), 615, 741
zeros of, 729, 739
Bessel inequality, 246, 559
best unbiased estimator, 1232
beta function, 638
bias of estimator, 1231
bilinear transformation, general, 110
binary chopping, 990
binomial coefficientnCk, 27–30, 1135–1137
elementary properties, 26
identities, 27
in Leibnitz’ theorem, 49
negativen,29
non-integraln,29
binomial distribution Bin(n, p), 1168–1171
and Gaussian distribution, 1185
and Poisson distribution, 1174, 1177
mean and variance, 1171
MGF, 1170
recurrence formula, 1169
binomial expansion, 25–30, 140
binormal to space curves, 342
birthdays, different, 1134
bivariate distributions, 1196–1207
conditional, 1198
continuous, 1197
correlation, 1200–1207
and independence, 1200
matrix, 1203–1207
positive and negative, 1200
uncorrelated, 1200
covariance, 1200–1207
matrix, 1203
expectation (mean), 1199
independent, 1197, 1200
marginal, 1198
variance, 1200
Boltzmann distribution, 171
bonding in molecules, 1103, 1105–1108
Born approximation, 149, 575
Bose–Einstein statistics, 1138
boundary conditions
and characteristics, 700
and Laplace equation, 764, 766
for Green’s functions, 512, 514–516
inhomogeneous, 515
for ODE, 468, 470, 501
for PDE, 681, 685–687
for Sturm–Liouville equations, 564
homogeneous and inhomogeneous, 685, 723,
752, 754
superposition solutions, 718–724
types, 702–705
bra vector〈ψ|, 649
brachistochrone problem, 784
Bragg formula, 237
branch cut, 835
branch points, 835
Bromwich integral, 884
bulk modulus, 980calculus of residues,seezeros of a function of a
complex variableandcontour integration
calculus of variations
constrained variation, 785–787
estimation of ODE eigenvalues, 790
Euler–Lagrange equation, 776
Fermat’s principle, 787
Hamilton’s principle, 788
higher-order derivatives, 782
several dependent variables, 782
several independent variables, 782
soap films, 780
variable end-points, 782–785
calculus, elementary, 41–76
cancellation law in a group, 1046
canonical form, for second-order ODE, 516
card drawing,seeprobability
carrier frequency of radio waves, 445
Cartesian coordinates, 217
Cartesian tensors, 930–955
algebra, 938–941
contraction, 939
definition, 935
first-order, 932–935
from scalar, 934
general order, 935–954
integral theorems, 954
isotropic, 944–946
physical applications, 934, 939–941, 950–954
second-order, 935–954, 968
symmetry and antisymmetry, 938
tensor fields, 954
zero-order, 932–935
from vector, 935
Cartesian tensors, particular
conductivity, 952
inertia, 951
strain, 953
stress, 953
susceptibility, 952
catenary, 781, 787
Cauchy
boundary conditions, 702
distribution, 1152
inequality, 853
integrals, 851–853
product, 131
root test, 129, 831
theorem, 849
Cauchy–Riemann relations, 827–830, 849, 873,
875
in terms ofzandz∗, 829
central differences, 1019