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| Murray D.A. — A first course in infinitesimal calculus |
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| Предметный указатель |
Abdank — Abakanowicz 169
Absolute, constants 16
Absolute, value 14
Acceleration 109
Adiabatic curves 87
Aldis, Solid Geometry 299
Algebra, Chrystal's 14 29 67 70
Algebra, Chrystal's Introduction to 19
Algebra, Hall and Knight's 70 303
Algebra, Hall's Introduction to Graphical 19
Algebraic equations, theorems 98 99
Algebraic functions 17 61 98
Allen see "Analytic Geometry"
Amsler's planimeter 229
Analytic Geometry, Ashton 131
Analytic Geometry, Candy 5
Analytic Geometry, Tanner and Allen 19 131
Analytic Geometry, Wentworth 131
Analytical Society 45
Anti-derivatives 50 53
Anti-differentials 50 170 171
Anti-differentiation 148 170
Anti-trigonometric functions 17
Applications of differentiation in series 313
Applications of integration 192
Applications of integration in series 313
Applications of partial differentiation 141
Applications of successive integration 235
Applications of Taylor's theorem 322 331 332
Applications, elimination 114
Applications, equations 98 99
Applications, geometrical 84
Applications, physical 84
Applications, rates 91
Approximate integration 223
Approximations, to areas and integrals 157 223 316
Approximations, to small errors and corrections 96 138
Approximations, to values of functions 49
Arbitrary constants 16
Arbogaste 42
Arc, derivative 102 103
Arc, Huyghen's approximation 326
Arc, length 245 248
Archimedes see "Spiral"
Area derivative, differential 99 101
Area of a closed curve 198 245
Area of curves 192 242 244
Area of other surfaces 253
Area of surfaces of revolution 249
Area, approximation to 223 225
Area, mechanical measurement 228 229
Area, precautions in finding 198
Area, sign of 197 245
Area, swept over by a moving line 245
Argument of function 15
Ashton see "Analytic Geometry"
Astroid see "Examples"
Asymptotes 286
Asymptotes parallel to axes 288
Asymptotes, circular 292
Asymptotes, curvilinear 291
Asymptotes, oblique 290
Asymptotes, polar 292
Asymptotes, various methods of finding 291
Asymptotic circle 292
Average value 259
Beman, Famous Problems 13
bernoulli 150
Binomial theorem 322
Bitterli 169
Borel, divergent series 305
Burmann 18
Byerly see "Calculus"
Cajori, History of Mathematics 42 46 149 204 222
Calculation of small corrections 96
Calculus 1
Calculus, differential 11 39 149
Calculus, fundamental theorems 36
Calculus, integral 11 39 50 149
Calculus, invention 1 149
Calculus, notions of 11
Calculus, references to works on, Byerly, Diff. 34
Calculus, references to works on, Byerly, Problems 111
Calculus, references to works on, Echols 41
Calculus, references to works on, Edwards, Integral 213
Calculus, references to works on, Edwards, Treatise 129
Calculus, references to works on, Gibson 29
Calculus, references to works on, Harnack 20
Calculus, references to works on, Integral 163
Calculus, references to works on, Lamb 29
Calculus, references to works on, McMahon and Snyder, Diff. 33
Calculus, references to works on, Murray, Integral 163
Calculus, references to works on, Perry 12 381
Calculus, references to works on, Smith, W.B. 135 222
Calculus, references to works on, Snyder and Hutchinson 156
Calculus, references to works on, Taylor 129
Calculus, references to works on, Todhunter, Diff. 70
Calculus, references to works on, Williamson, Diff. 70
Calculus, references to works on, Young and Linebarger 381
Candy see "Analytic Geometry"
Cardioid see "Examples"
Catenary see "Examples"
Cauchy 301
Cauchy form of remainder 327
Centre of curvature 269 270
Centre of mass of curvature 373
Change of variable, in differentiation 145
Change of variable, in integration 175
Chrystal see "Algebra"
circle see "Examples"
Circle of curvature 268
Circle, curvature of 267
Circle, osculating 264
Circular asymptotes 292
Circular asymptotes, functions and exponential functions 327
Cissoid see "Examples"
Clairaut's equation 339
Commutative property of derivatives 133 140
Comparison test for convergence 307
Complete differential 136
Compound interest law 70
Computation of  313 314
Concavity 260
Condition for total differential 141
Conjugate points 295
Conoids 241
Constant of integration 160 162 166 335
Constant, absolute 16
Constant, arbitrary 16
Constant, elimination of 114
Contact of circle 263
Contact of curves 261 280 282
Contact of straight line 262
Continuity, continuous function see "Function"
Convergence see "Series" Series"
Convergence, interval of 306
Convergence, kinds of 304 305 311
Convergence, tests for 307 308
Convexity 260
Corrections 96
Cos x, derivative of 73
Cos x, expansion for 322 325
Criterion of integrability 188
Critical point, critical value 118 120
Crossing of curves 263 332
Cubical parabola see "Examples"
Curvature at a point 266 267
Curvature circle of 268
Curvature of a circle 267
Curvature, average 266
| Curvature, centre of 269 270
Curvature, radius of 268 271
Curvature, total 266
Curve tracing 298
CURVES see "Examples"
Curves, area of 192 242 244
Curves, asymptotes 286
Curves, contact of 261 280 282
Curves, derived 44
Curves, differential 44
Curves, envelope 277
Curves, equations derived 203
Curves, evolute 272
Curves, family 277
Curves, integral 168 169
Curves, involutes 276
Curves, length 245 248
Curves, locus of ultimate intersections 278
Curves, Loria's Special Plane 299
Curves, parallel 276
Curvilinear asymptotes 291
Cusps 280 293 294 296 297
Cycloid see "Examples"
De Moivre's theorem 328
Decreasing functions 116
Definite integral see "Integral"
density 372
Derivation of equation of curves 203
Derivative, definition 38
Derivative, general meaning 46
Derivative, geometric meaning 43
Derivative, notation 41
Derivative, physical meaning 45
Derivative, progressive, regressive 93
Derivatives of a constant 52
Derivatives of a function of a function 59
Derivatives of elementary functions 61—80
Derivatives of implicit functions 80 139
Derivatives of inverse functions 61
Derivatives of sum, product, quotient 51 53—57
Derivatives, geometric 99—106
Derivatives, meanings of second 108 109
Derivatives, partial 81 130 131
Derivatives, partial, commutative property of 133 140
Derivatives, partial, geometrical representation 132
Derivatives, partial, successive 133
Derivatives, special case 60
Derivatives, successive 107 112
Derivatives, total 136
Derivatives, total, successive 143
Derived, curves 44
Derived, functions 40 41
Descartes 149
Differentiable 41
Differential calculus see "Calculus"
Differential coefficient see "Derivative"
Differential equations 114 334
Differential equations classification 334
Differential equations, Clairaut's 339
Differential equations, exact 336
Differential equations, homogeneous 336
Differential equations, linear 337 346 348
Differential equations, order 334
Differential equations, ordinary 334
Differential equations, partial 334
Differential equations, references to text-books 115 351
Differential equations, second order 349
Differential equations, solutions 114 335 340
Differential, complete 136
Differential, condition for total 141
Differential, differentials 47 49
Differential, exact 142
Differential, geometric 99—106
Differential, infinitesimal 155
Differential, integration of total 188
Differential, partial 136
Differential, successive 112
Differential, total 136 137
Differentiation 39 170 see "Derivatives"
Differentiation of series 312
Differentiation, general results 51
Differentiation, logarithmic 68
Differentiation, successive 107
Discontinuity, discontinuous functions see "Functions"
Divergent series see "Series"
Double points 280 293 294
Doubly periodic functions 221
Durand's rule 227
Echols see "Calculus"
Edwards see "Calculus"
Elementary integrals 172 180
Elimination of constants 114
ellipse see "Examples"
Ellipsoid 235
Elliptic functions 158 221
Elliptic functions integrals 158 221 317
End-values 155
Envelopes, contact property 280 282
Envelopes, definition 278
Envelopes, derivation 281 284
Equations, derivation of 203
Equations, graphical representation 19 20 130
Equations, roots of 98 99
Equiangular spiral see "Examples"
Errors, relative 96
Errors, small 96 138
Euler 142 314 328
Euler theorem on homogeneous functions 142
Evolute of the ellipse see "Examples"
Evolute, definitions 272 275 283
Evolute, properties of 273
Exact differential 142
exact differential equations 336
Examples concerning adiabatic curves 87
Examples concerning astroid (or hypocycloid) 86 102 198 203 251 270 273 345 365
Examples concerning cardioid 91 101 244 249 252 271 345 365 376 383 390 392 393 396
Examples concerning catenary 201 248 253 366 383
Examples concerning circle 86 194 202 244 249 252 271 344 375 376 378 391 393 399
Examples concerning cissoid 290 393
Examples concerning cubical parabola 92 101 102 158 166 195 198 201 270
Examples concerning cycloid 87 248 252 270 273 366
Examples concerning ellipse 86 106 200 203 248 257 276 290 374 385 390 391 393 397 399 400
Examples concerning evolute of the ellipse 273 390
Examples concerning exponential curve 86 392
Examples concerning folium of Descartes 87 244 290
Examples concerning harmonic curve 398
Examples concerning hyperbola 87 92 270 271 273 290 291 345 383 388 390 393
Examples concerning hypocycloid see "Astroid"
Examples concerning lemniscate 244 271 345 383 393
Examples concerning limacon 398
Examples concerning parabola 86 87 92 102 104 152 159 166 195 196 198 234 249 257 270 271 273 276 283 284 290 345 366 376 383 388 391 393
Examples concerning probability curve 290
Examples concerning semi-cubical parabola 86 87 159 198 270 366 391
Examples concerning sinusoid 86 159
Examples concerning Spirals, archimedes' 91 101 103 249 271
Examples concerning Spirals, equiangular (or logarithmic) 91 244 249 271 366 390
Examples concerning Spirals, general 91 271
Examples concerning Spirals, hyperbolic (or reciprocal) 91 244
Examples concerning Spirals, logarithmic see "Equiangular"
Examples concerning Spirals, parabolic (or lituus) 91
Examples concerning Spirals, reciprocal see "Hyperbolic"
Examples concerning the witch 87 271 290
Examples concerning tractrix 366 392
Expansion of  , exponential series 326
Expansion of  314
Expansion of  , Gregory's series 228 313
Expansion of cos x 322 325
Expansion of functions by algebraic methods 326
Expansion of functions by differentiation 228 315
Expansion of functions by integration 228 313
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