INDEX
The numbers refer to the pages
Addition rule in probability, 316 Addition theorems, 12
Advancing difference formula, 51,
61
Aitken, A. C., 131 Algebraic function, 134
Alison, S. H., 32
Angle, complementary, to
definition of, I magnitude of, 6 negative, 4
Approximate integration, 285 Approximation, successive, 89
Areas of curves, 271 Argument, 25
Asymptote, 147 Average rate, 136
Backward formula, Gauss, 71, 126 Bernouilli, 332
Bernouilli's numbers, 185
Bessel's formula, 71
Beta function, 270
Binomial theorem, 32
Buchanan, J., 122, 219
Calculus, differential, 150 integral, 223
Cauchy, 18o
Central differences, 68, 123 Chance, 317
Change of origin, 49, 290 Change of unit, 289
Chrystal, 314
definition of probability, 314 Coefficient, differential, 159 Coefficients, detached, 40, 108 Collins, John, 47
Complementary angle, to Compound function, 116 Constant, definition of, 22
of integration, finite differences,
104
of integration, integral calculus, 229
Constant rate, 136
Contact of the first order, 223 Continuous function, 139, 146
Convergent series, 144 Cosecant, 2
Cosine, 2
series for, 186
Cotangent, 2
Critical value, 191
D'Alembert, 332
Definite integral, 224, 262 Degree, 6
De Morgan, 332
Dependent events, 320 Dependent variable, 22 Derivative, 150
Derived function, 150 Detached coefficients, 40, 108 Difference table, 25 Differences, central, 68
definition of, 24
divided, 57
leading, 25
Differences of zero, 114 Differential, 237
Differential calculus, 150 Differential coefficient, 150 Differential equation, 181 Differentiation, logarithmic, 161
partial, 209
successive, 162
under the integral sign, 274 Divergent series, 144 Divided differences, 57 Double angles, 14
Double integrals, 277, 357 Double limit, 145
Duration of play, 336
Elimination of third differences, 90 Entry, 25
Equation, differential, 181
Euler, 63
Eulerian integrals, 270 Euler-Maclaurin expansion, 299 Euler's theorem, 2t2
Everett's formula, 72, 73 Expansions, 174 Expectation, 331 Explicit function, 134
398 INDEX
Factorial notation, 38 Finite differences, 22
Forward formula, Gauss, 69, 8o, 126 Fraser, D. C., 47, 76, 77, 123, 129, 130,
219
hexagon diagram, 123 Frequency, 315
relative, 315
Function, algebraic, 134 compound, 116
continuous, 139, 146 definition of, 22
explicit, 134
first derived, 150 homogeneous, 6o, 135, 212 implicit, 138
inverse, 10
parabolic, 22
periodic, 9
rational integral, 22 transcendental, 135 two variable, 118
Gamma function, 279
Gauss, backward formula, 71, 126
forward formula, 69, 8o, 126 Geometrical solutions, probability, 364 Gibson's Calculus, 208
Gradient, 152
Gregory, James, 47
Half angles, 14
Hall and Knight's Algebra, too Hardy, G. F., 131 Hardy's formulae, 295
Henry's Calculus and Probability,
249
Hexagon diagram, 123 Homogeneous function, 212 Homogeneous products, 6o, 135 Huyghens' problem, 326
Identities, trigonometrical, 5 Implicit function, 135 Indefinite integral, 225 Independent events, 319 Independent variable, 22 Indeterminate forms, 206 Induction, method of, 333 Inflexion, point of, 196 Integral calculus, 223 Integral, definite, 224, 262
double, 277, 357
Eulerian, 270
indefinite, 225
Integration, approximate, 285
by parts, 249, 267
Interpolation, 44, 57
formulae of, 47, 58, 62, 69, 71, 72 inverse, 84
osculatory, 216
Intervals, equidistant, 44 subdivision of, 51 unequal, 57
Inverse function, to Inverse interpolation, 84
King, A. E., 307 King, G., 219, 296
Lagrange, form of remainder, 179
interpolation formula, 62, 122 Leading differences, 25 Leading term, 25
Leibnitz's theorem, 164
Lidstone, G. J., 72, 77, 131, 215, 219 Limit, definition of, 140, 142
double, 145
of a sequence, 143 Limiting value, 137 Logarithmic differentiation, 161 Lubbock's formula, 392
Maclaurin's theorem, 179 Magnitude of angles, 6 Maximum value, 191 Mean value, 354
Mean value theorem, 176, 197 Minimum value, 191 Most probable value, 328 Multiplication rule, 319 Mutually exclusive events, 316
Negative angles, 4
Newton's formula, advancing differ47, 61, 126
divided differences, 58
Operators, ., E, 27
8, µ, 79
0, 104, to6
V, 127
D, 0, 213
Origin, change of, 49, 290 Osculatory interpolation, 216
Parabolic function, 22
Partial differentiation, 209 Parts, integration by, 249, 267 summation by, 102
INDEX 399
Periodic function, 9
Periodicity of trigonometrical func
tions, 7 Poincar6, 333
Point of inflexion, 196
Probability, 313, 360
application of calculus to, 360 geometrical solutions, 364
Probable value, 331
Projection, 11
Quadrature formulae, 296
Radian, 6
Rates, 135
average, 136
constant, 136
Rational integral function, 22
Ratios, trigonometrical, 2
Recurring series, 199
Reduction formulae, 252
Relative frequency, 315
Remainder term, Taylor's series, 179 Rolle's theorem, 174
St Petersburg problem, 332 Schlomilch, 18o
Secant, 2
Separation of symbols, 36 Sequence, limit of, 143 Series, convergent, 144
divergent, 144
recurring, 109
Sheppard, W. F., 76, 77, 79, 315 Sheppard's rules, 73 Simpson's rule, 286, 292, 308 Sine, 2
series for, 186
Spencer, J., 121
Sprague, Dr T. B., 219 Spurgeon's Life Contingencies, 297 Standard forms, differential calculus,
156
integral calculus, 228 Steffensen, Prof. J. F., 6o Steffensen's Interpolation, 93, 127 Stirling's formula, 71, 8o Stirling's theorem, 179
Subdivision of intervals, 51 Substitution, method of, 235 Successive approximation, 89 Successive differentiation, 162
Sum and difference formulae, 14 Summation, 97
by parts, 102 Summation n, 1 28 Symbolic notation, 24
Symbols, 0, 24 6, 79
V, 127
E, 27
2, 104, 105 12, 79
D, 213
I, 224
Symbols, separation of, 36
Tangent, z
Taylor's theorem, 65, 177
Term, leading, 25 Thiele, 44
Three-eighths rule, 293 Todhunter, R., 131 Transcendental function, 135 Trigonometrical ratios, 2
Turning value, 191
Two variables, functions of, 118
Unitary definition of probability, 314 Unit, change of, 289
Vandermonde's theorem, 166 Variable, definition of, 22 dependent, 22
independent, 22
Weddle's rule, 294
Whittaker and Robinson's Calculus of
Observations, 77, 93, 307 Whitworth's Choice and Chance, 333 Wickens, C. H., 307
Williamson's Integral Calculus, 249 Woolhouse's formula, 304
Zero, differences of, 114 Zig-zag formula, 70, 71
CAMBRIDGE: PRINTED BY
W. LEWIS, M.A.
AT THE UNIVERSITY PRESS