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| Murray D.A. — A first course in infinitesimal calculus |
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| Предметный указатель |
Expansion of functions by Maclaurin's series 325
Expansion of functions by Taylor's series 321
Expansion of log (1+x), logarithmic series 315 321
Expansion of sin x 322 325
Explicit function 17
Exponential curve see "Examples"
Exponential curve and trigonometric, relations between 327
Exponential curve, expansion of 326
Exponential curve, function 17
Family of curves 277
Fermat 122 149 247
Fluent, fluxion 45
Folium of Descartes see "Examples"
Forms, indeterminate 367
Formulas of reduction 213 218
FOURIER 155
Fractions, rational, integration of 184
Frost, Curve Tracing 291 293 299
Function 15
Function of a function 59 60
Function of two variables 130
Function, algebraic 17 61 221
Function, circular 221
Function, classification 17
Function, continuous 25 28 41 130
Function, derived 40 41
Function, discontinuous 25 27
Function, elliptic 158 221
Function, explicit 17
Function, exponential 17 70
Function, graphical representation 19 20 130
Function, homogeneous, Euler's theorem on 142
Function, hyperbolic 183 221 353
Function, implicit 17 80
Function, increasing and decreasing 116
Function, inverse 18 76
Function, irrational 206
Function, logarithmic 17 67
Function, march of a 123
Function, maximum and minimum values of 117
Function, notation for 17 18
Function, periodic 221
Function, transcendental 17
Function, trigonometric and anti-trigonometric 17 71 215
Function, turning values of 117
Function, variation of 116
Gauss 304
General integral see "Integral"
General integral spiral see "Examples"
Geometric derivatives and differentials 99—106
Geometrical interpretation, a certain 215
Geometrical representation of derivatives, ordinary 43
Geometrical representation of derivatives, partial 132
Geometrical representation of function of a function 60
Geometrical representation of functions of one variable 19 20
Geometrical representation of functions of two variables 20 130
Geometrical representation of integrals, definite 163
Geometrical representation of integrals, indefinite 166
Geometrical representation of total differential 137
Geometry, Famous Problems in 13
Gibson see "Calculus"
Glaisher, Elliptic Functions 222
Graph of a function 19
Graphical Algebra, Hall 19
Graphs, sketching of 123
Gregory 305 313
Gregory's series 313
Gyration, radius of 377
Hardy, infinitesimals 38
Harkness and Morley, Analytic Functions 15 29 303
Harkness and Morley, Theory of Functions 41
Harmonic curve 398
Harmonic motion 83 110
Harmonic series 304
Harnack see "Calculus"
Hele Shaw, Mechanical Integrators 229
Henrici, Report on Planimeters 229
Herschel 18 46
Hobson, Trigonometry 303 314 363
Homogeneous functions, Euler's theorem 142
Homogeneous, differential equations 336
Homogeneous, linear equation 348
Horner, Horner's process 324 333
Hutchinson see "Calculus"
Huyhen's rule for circular arcs 326
Hyperbola see "Examples"
Hyperbolic functions 183 221 328 353
Hyperbolic spiral see "Examples"
Hypocycloid see "Examples"
Implicit functions, differentiation 80 139
Increasing function 116
Increment, notation for 4
Indefinite integral see "Integral"
Indeterminate forms 296 367
Inertia, centre of 373
Inertia, moment of 377
Infinite numbers 14 30 31
Infinite numbers, orders of 31
Infinite series 300 see
Infinite series, algebraic properties 304
Infinite series, differentiation of 302 312
Infinite series, general theorems 305
Infinite series, integration in 227 316
Infinite series, integration of 302 310
Infinite series, limiting value of 301
Infinite series, Osgood, article and pamphlet 303 306 307
Infinite series, questions concerning 301
Infinite series, remainder 306
Infinite series, study of 303
Infinitesimal 1 48 49
Infinitesimal differential 155
Infinitesimals 30
Infinitesimals summation 150
Infinitesimals, Hardy 38
Infinitesimals, orders 31
Infinitesimals, theorems 33 35
Inflexion, points of 118 127 261
Inflexional tangent 129
integral see "Calculus"
Integral curves 168 169
Integral, definite, approximation 223 316
Integral, definite, definition, representation of, properties 154—158 163 164
Integral, double 230
Integral, element of 155
Integral, elementary 172 180
Integral, elliptic 158 221 248 317
Integral, general 162
Integral, indefinite 162
Integral, indefinite, representation of 166
Integral, multiple 231
Integral, particular 162
Integral, precautions in finding 198
Integral, triple 230
integrand 150
Integraph 169 228 229
Integrating factors 336
Integration 148 170
Integration as inverse of differentiation 160
Integration as summation 154 170
Integration of see "Applications"
Integration of infinite series 302 310
Integration of irrational functions 206
Integration of rational fractions 184
Integration of total differential 188
Integration of trigonometric functions 215
Integration, by infinite series 227 316
Integration, by mechanical devices 228
Integration, by parts 177
Integration, by substitution 175 183 215
Integration, constant of 160 162 166
| Integration, general theorems in 173
Integration, successive 230 232
Integrators 228 229
Intrinsic equation 249 363
Invention of the calculus 1 149
Inverse functions 18 61 76
Involutes 276
Irrational functions, integration 206
Isolated points 295 296
jacobi 133
Kepler 122
Klein 13 67
Lagrange 42 149 326
Lagrange's form of remainder 323
Lamb see "Calculus"
Laplace 149
legendre 317
Leibnitz 1 42 45 149 150 282 313
Leibnitz theorem on derivative of product 113
Lemniscate see "Examples"
Lengths of curves 245 248
Limacon see "Examples"
Limits in integration 155
Limits of a series 301
Limits, Hardy 38
Limits, limiting value 20 23 42
Limits, theorems 35
Linear differential equations of first order 337
Linear differential equations with constant coefficients 346
Linear differential equations, homogeneous 348
Linebarger see "Calculus"
Lituus see "Examples"
Locus of ultimate intersections 278
Logarithmic spiral see "Examples"
Logarithmic, differentiation 68
Logarithmic, function 17 67
Logarithmic, series 315 321
Loria, Special Plane Curves 299
Machin 314
Maclaurin 327
Maclaurin theorem and series 324 328
Magnitude, orders of 31
Mass, centre of 372
Mathews, G.B. 305
Maxima and minima 116
Maxima and minima by calculus 117—122
Maxima and minima by other methods 122
Maxima and minima of functions of several variables 122
Maxima and minima, practical problems 123
McMahon see "Calculus"
McMahon, proof 142
Mean square value 259
Mean value theorems, differentiation 84 94 95 318
Mean value theorems, integration 165 255
Mean values 255
Mechanical integrators 228
Mechanics 372
Mellor, Higher Mathematics 381
Mercator 315
Minima see "Maxima"
Moment of inertia 377
Morley see "Harkness"
Motion, simple harmonic 83 110
Muir, on notation 133
Multiple integrals 231
Multiple points 293 296
Multiple roots 98
Multiple, angles in integration 217
Neil 246
Newton 1 45 149 314
nodes 294
Normal, polar 89
Normal, rectangular 84
Notation for absolute value 14
Notation for derivatives 41 46 107
Notation for differentials 47
Notation for functions 17
Notation for increment 4
Notation for infinite numbers 15
Notation for integration 149 162 163 233
Notation for inverse functions 18 61
Notation for limits 24
Notation for partial derivatives 81 131 133 137
Notation for summation 155
Notation, remark on 42
Numbers 13
Numbers, algebraic 13
Numbers, e and  67 328
Numbers, finite, infinite, infinitesimal 14 30
Numbers, graphical representation 13 14
Numbers, transcendental 13 67
Oblique axes 193
Order of derivative, differential 108 333
Order of differential equation 334
Order of infinite 31
Order of infinitesimal 31 333
Order of magnitude 31
Order of, contact 261
Orthogonal trajectories 341 343
Oscillatory series 304
Osculating circles 264 271
Osgood, W.F., article 311 313
Osgood, W.F., pamphlet 303
parabola see "Examples"
Parabolic rule 225
Parabolic spiral see "Examples"
Parallel curves 276
PARAMETER 277
Partial derivative see "Derivative"
Partial fractions 184
Particular integral see "Integral"
Pendulum time of oscillation 317
Periodic functions 221
Perry, on notation 133 see
Picard 156
Planimeters 228 229
Planimeters, Henrici, Report on 229
POINTS see "Critical" "Multiple" "Salient" "Singular" "Stop" "Triple" "Turning"
Power series 307 310 312 313
Precautions in integration 198
Probabilities 326
Probability curve see "Examples"
Progressive derivative 93
Radius of curvature 268 271
Radius of gyration 377
Rate of change 11 45 46 47
Rate of variation 134
Rational fraction, integration 184
Reciprocal spiral see "Examples"
Rectification of curves 246
Reduction formulas 213 218
Regressive derivative 93
Remainder after n terms 306
Remainders in Taylor's and Maclaurin's series 320 323 327
Ring 202
Rolle 99
Rolle's theorem 84 93 95 99 319
Roots of equations 98 99
Rouche et Comberousse 246
Rules for approximate integration 223 225 227
Salient points 295
Schloemilch — Roche's form of remainder 327
Second derivative, geometrical meaning 108
Second derivative, physical meaning 109
Semi-cubical parabola 246 see
Series 70 see "Expansion" "Infinite "Power
Series, absolutely convergent 305
Series, conditionally convergent 305
Series, convergent 304
Series, divergent 304 305
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