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| Murray D.A. — Differential and integral calculus |
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| Предметный указатель |
Examples concerning, Spirals, logarithmic see "Equiangular"
Examples concerning, Spirals, parabolic (or lituus) 90
Examples concerning, Spirals, reciprocal see "Hyperbolic"
Examples concerning, the witch 86 159 203
Examples concerning, tractrix 426
Expansion of  , exponential series 249
Expansion of  351
Expansion of  , Gregory's series 350
Expansion of cos x 245 248
Expansion of functions by algebraic methods 249
Expansion of functions by differentiation 240
Expansion of functions by integration 350
Expansion of functions by Maclaurin's series 247—249
Expansion of functions by Taylor's series 243—247
Expansion of log (1+x), logarithmic series 244 352
Expansion of sin x 245 248
Explicit function 16
Exponential curve see "Examples"
Exponential curve and trigonometric, relations between 250
Exponential curve, expansion of 249
Exponential curve, function 17
Extended Theorem of Mean Value 177
Family of curves 190
Fermat 120 270 372
Fluent, fluxion 39
Folium of Descartes see "Examples"
Forms, indeterminate 180
Formulas of reduction 334 339
FOURIER 276
Fractions, rational, integration of 305
Frost, Curve Tracing 204 206 212
Function 14
Function of a function 54 55
Function of two variables 16 128
Function, algebraic 17 56 342
Function, circular 342
Function, classification 16
Function, continuous 18 25 35 129
Function, derived 32 34
Function, discontinuous 18 25 27
Function, elliptic 279 342
Function, explicit 16
Function, exponential 17 61
Function, graphical representation 19 20 128
Function, homogeneous, Euler's theorem on 139
Function, hyperbolic 304 342 413
Function, implicit 16 75 137
Function, increasing and decreasing 113
Function, inverse 15 56 71
Function, irrational 17 327
Function, logarithmic 17 61
Function, many-valued 15
Function, march of a 121
Function, maximum and minimum values of 114
Function, notation for 18
Function, one-valued 15
Function, periodic 312
Function, rational 17
Function, transcendental 17
Function, trigonometric and anti-trigonometric 17 66 336
Function, turning values of 115
Function, variation of 115
Gauss 234
General integral see "Integral"
General integral, spiral see "Examples"
Generalized Theorem of Mean Value 182
Geometric derivatives and differentials 95—102
Geometrical interpretation, a certain 336
Geometrical representation of derivatives, ordinary 37
Geometrical representation of derivatives, partial 130
Geometrical representation of function of a function 55
Geometrical representation of functions of one variable 19
Geometrical representation of functions of two variables 128
Geometrical representation of integrals, definite 284
Geometrical representation of integrals, indefinite 287
Geometrical representation of total differential 135
Gibson see "Calculus"
Glaisher, Elliptic Functions 343
Goursat — Hedrick, Mathematical Analysis 170
Graphical representation of functions 19
Graphical representation of real numbers 13
Graphs, sketching of 121
Gregory 235 351
Gregory's series 351
Gyration, radius of 390
Harkness and Morley, Analytic Functions 233
Harkness and Morley, Theory of Functions 35
Harmonic curve 448
Harmonic motion 78 107
Harmonic series 234
Harnack see "Calculus"
Hele Shaw, Mechanical Integrators 349
Helix 258 428
Henrici, Report on Planimeters 349
Herschel 19 40
Hobson, Trigonometry 233 352 423
Homogeneous, differential equations 396
Homogeneous, functions, Euler's theorem 139
Homogeneous, linear equation 397 406 408
Horner, Horner's process 247 256
Hutchinson see "Calculus"
Huylien's rule for circular arcs 249
Hyperbola see "Examples"
Hyperbolic functions 304 342 413
Hyperbolic functions, spiral see "Examples"
Hypocycloid see "Examples"
Implicit functions 16
Implicit functions, differentiation 75 137
Increasing function 113
Increment, notation for 4 30 31
Indefinite integral see "Integral"
Indeterminate forms 180
Inertia, centre of 386
Inertia, moment of 390
Infinite numbers 14 28 29
Infinite numbers, orders of 29
Infinite series 230 see
Infinite series, algebraic properties 234
Infinite series, differentiation of 232 240
Infinite series, general theorems 235
Infinite series, integration in 353
Infinite series, integration of 232 350
Infinite series, limiting value of 231
Infinite series, Osgood, article and pamphlet 233 236 237
Infinite series, questions concerning 231
Infinite series, remainder 236
Infinite series, study of 233
Infinitesimal 1 28 43 45
Infinitesimal differential 276
Infinitesimals 28
Infinitesimals, orders 29
Infinitesimals, summation 271
Inflexion, points of 116 125 127
Inflexional tangent 127
integral see "Calculus"
Integral curves 289 290
Integral, definite, approximation 344 353
Integral, definite, approximation, definition, representation of, properties 275—279 284 285
Integral, double 355
Integral, element of 276
Integral, elementary 293 301
Integral, elliptic 279 342 354 373
Integral, general 283
Integral, indefinite 281 283
Integral, indefinite, representation of 287
Integral, multiple 356
Integral, particular 283
Integral, precautions in finding 319
Integral, triple 355
integrand 271
| Integraph 290 348 349
Integrating factors 396
Integration 269 291
Integration as inverse of differentiation 281 291
Integration as summation 275 291
Integration by infinite series 350 353
Integration by mechanical devices 318
Integration by parts 298
Integration by substitution 296 304 328 336
Integration of infinite series 232 350
Integration of irrational functions 327
Integration of rational fractions 305
Integration of total differential 309
Integration of trigonometric functions 336 see
Integration, constant of 281 283 287
Integration, general theorems in 294
Integration, successive 355 357
Integrators 348 349
Interpolation 256
Intrinsic equation 374 423
Invention of the calculus 1 270
Inverse functions 15 56 71
Involutes 164
Irrational functions, integration 327
Isolated points 206 208
jacobi 131
Kepler 120
Klein 62
Lagrange 36 249 270
Lagrange's form of remainder 250
Lamb see "Calculus"
Laplace 270
legendre 354
Leibnitz 36 39 135 270 271 351
Leibnitz, theorem on derivative of product 110
Lemniscate see "Examples"
Lengths of curves 370 373 427
Lengths of tangents and normals 84 88
Limacon see "Examples"
Limits in integration 276
Limits of a series 231
Limits, limiting value 20 23 36
Linear differential equations of first order 397
Linear differential equations with constant coefficients 406
Linear differential equations, homogeneous 408
Linebarger see "Calculus"
Lituus see "Examples"
Locus of ultimate intersections 191
Logarithmic, differentiation 63
Logarithmic, function 17 62
Logarithmic, series 244 352
Logarithmic, spiral see "Examples"
Loria, Special Plane Curves 212
Machin 351
Maclaurin 250
Maclaurin, theorem and series 247 252
Magnitude, orders of 29
Mass, centre of 385
Mathews, G.B. 235
Maxima and minima 113
Maxima and minima by calculus 114—120
Maxima and minima by other methods 120
Maxima and minima of functions of several variables 120
Maxima and minima, practical problems 121
McMahon, proof 138 see
Mean value theorems, differentiation 164 169 174—179 182
Mean value theorems, integration 286 380
Mean values 380
Mechanical integrators 348
Mechanics 385
Mellor, Higher Mathematics 431
Mercator 352
Minima see "Maxima"
Moment of inertia 390
Morley see "Harkness"
Motion, applications to 214
Motion, simple harmonic 78 107
Muir, on notation 131
Multiple, angles in integration 338
Multiple, integrals 356
Multiple, points 206 209
Multiple, roots 93
Neil 371
Newton 39 171 351
nodes 207
Normal, equation of 83
Normal, length 84 88
Notation for absolute value 14
Notation for derivatives 35 39 103
Notation for differentials 42
Notation for functions 18
Notation for increment 4
Notation for infinite numbers 14
Notation for integration 270 283 284 358
Notation for inverse functions 19 56
Notation for limits 23
Notation for partial derivatives 76 129 131 135
Notation for summation 276
Notation, remark on 36
Numbers 13
Numbers, e and  62 328
Numbers, finite, infinite, infinitesimal 14 28
Numbers, graphical representation 13 14
Numbers, transcendental 62
Oblique axes 314
Order of, contact 149
Order of, derivative, differential 104 256
Order of, differential equation 394
Order of, infinite 29
Order of, infinitesimal 29 256
Order of, magnitude 29
Orthogonal trajectories 401 403
Oscillatory series 234
Osculating circle 152 159
Osgood, W.F., pamphlet 233 etc. see
parabola see "Examples"
Parabolic rule 346
Parabolic spiral see "Examples"
Parallel curves 164
PARAMETER 190 257
Partial derivative see "Derivative"
Partial fractions 305
Particular integral see "Integral"
Pendulum time of oscillation 354
Periodic functions 342
Perry, on notation 131 see
Picard 277
Pierpont, Theory of Functions 14 27 131 167
Planimeters 348 349
Planimeters, Henrici, Report on 349
POINTS see "Critical" "Double" "Isolated" "Multiple" "Salient" "Singular" "Stop" "Triple" "Turning"
Power series 237 240 350
Precautions in integration 319
Probabilities 249
Probability curve see "Examples"
Progressive derivative 167
Radius of curvature 156 159
Radius of gyration 390
Rate of change 11 39 40 41 90
Rate of change, variation 132
Rational fraction, integration 305
Reciprocal spiral see "Examples"
Rectification of curves 371
Reduction formulas 334 339
Regressive derivative 167
Relative error 92
Remainder after n terms 236
Remainders in Taylor's and Maclaurin's series 243 246 250
Right- and left-hand derivatives 167
Ring 323
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