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| Murray D.A. — Differential and integral calculus |
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| Предметный указатель |
Abdank-Abakanowicz 290
Absolute, constants 16
Absolute, value 14
Acceleration 105 223—229
Adiabatic curves 86
Aldis, Solid Geometry 212
Algebra, Chrystal's 62 65 181 etc.
Algebra, Hall and Knight's 65 233
Algebraic equations, theorems 94 168
Algebraic functions 17 56 93
Allen see "Analytic Geometry"
Amsler's planimeter 348
Analytic Geometry, Ash ton 129
Analytic Geometry, Candy 5
Analytic Geometry, Tanner and Allen 129
Analytic Geometry, Went-worth 129
Analytical Society 39
Angles at which curves intersect 81
Anti-derivatives 45 48
Anti-differentials 45 291 292
Anti-differentiation 269 291
Anti-trigonometric functions 17
Applications of differentiation in series 240
Applications of integration 313 etc.
Applications of integration in series 350
Applications of successive integration 360 etc.
Applications of Taylor's theorem 244—248 254—256
Applications to motion 214
Applications, elimination 111
Applications, equations 93 94 171
Applications, geometrical 79
Applications, physical 79
Applications, rates 90
Approximate integration 344
Approximate integration by means of series 353
Approximations to areas and integrals 278 344 353
Approximations to roots of equations 171
Approximations to small errors and corrections 92 138
Approximations to values of functions 44
Arbitrary constants 16
Arbogaste 36
Arc, derivative 98 99
Arc, Huyglieus' approximation 249
Arc, length 370 375 127
Archimedes see "Spiral"
Area 10
Area of a closed curve 319 370
Area of curves 313 367 369
Area of other surfaces 378
Area of surfaces of revolution 374
Area, approximation to 344 346
Area, derivative, differential 95 97
Area, mechanical measurement 348 349
Area, precautions in finding 319
Area, sign of 318 370
Area, swept over by a moving line 370
Argument 142
Ashton see "Analytic Geometry"
Astroid see "Examples"
Asymptotes 199 212 213
Asymptotes, circular 205
Asymptotes, curvilinear 204
Asymptotes, oblique 203
Asymptotes, parallel to axes 201
Asymptotes, polar 205
Asymptotes, various methods of fiuding 204
Asymptotic circle 205
bernoulli 271
Binomial theorem 245
Bitterli 290
Borel, divergent series 235
Burmann 19
Byerly see "Calculus"
Cajori, History of Mathematics 36 40 270 325 343
Calculation of small corrections 92
Calculus 1
Calculus, differential 11 33 270
Calculus, integral 11 33 45 270
Calculus, invention 1 270
Calculus, notions of 11
Calculus, references to works on Byerly, Problems 108 etc.
Calculus, references to works on Campbell 225
Calculus, references to works on Echols 35 etc.
Calculus, references to works on Edwards, Integral 334 etc.
Calculus, references to works on Edwards, Treatise 127 etc.
Calculus, references to works on Gibson 41 etc.
Calculus, references to works on Harnack 170 etc.
Calculus, references to works on Integral 284 etc.
Calculus, references to works on Lamb 41 etc.
Calculus, references to works on McMahon and Snyder, Diff 41 etc.
Calculus, references to works on Murray, Integral 284 etc.
Calculus, references to works on Osgood 170 etc.
Calculus, references to works on Perry 12 431 etc.
Calculus, references to works on Smith, W.B. 133 343
Calculus, references to works on Snyder and Hutchinson 277 etc.
Calculus, references to works on Taylor 127 etc.
Calculus, references to works on Todhunter, Diff 65 etc.
Calculus, references to works on Williamson, Diff 65 etc.
Calculus, references to works on Young and Linebarger 431
Campbell see "Calculus"
Candy see "Analytic Geometry"
Cardioid see "Examples"
Catenary see "Examples"
Cauchy 234
Cauchy, form of remainder 250
Centre of curvature 157 158
Centre of mass 385
Change of variable, in differentiation 143
Change of variable, in integration 296
Changes in variable and function 30 31
Chrystal see "Algebra"
Circle of curvature 156
Circle, curvature of 155
Circle, osculating 152 159 see
Circular asymptotes 205
Circular asymptotes, functions and exponential functions 250
Cissoid see "Examples"
Clairaut's equation 399
Commutative property of derivatives 131
Comparison test for convergence 237
Complete differential 134
Compound interest law 65
Computation of ir 351
Concavity 148
Condition for total differential 138
Conjugate points 208
Conoids 366
Constant of integration 281 283 287 395
Constant, absolute 16
Constant, arbitrary 16
Constant, elimination of 111
Contact of circle 150
Contact of curves 149
Contact of straight line 151
Contact, order of 149
Continuity, continuous function see "Function"
Convergence 234 237
Convergence, interval of 237
Convergence, tests for 237 238 see "Infinite
Convexity 148
Corrections 92
Cos x, derivative of 69
Cos x, expansion for 245 248
Criterion of integrability 309
Critical point, critical value 114 116
Crossing of curves 81 151 255
Cubical parabola see "Examples"
Curvature 153
Curvature at a point 154 155
Curvature of a circle 155
| Curvature, average 154
Curvature, centre of 157 158
Curvature, circle of 156
Curvature, radius of 156 159
Curvature, total 154
Curve tracing 211
Curves of one parameter 257 260
Curves, area of 313 367 369
Curves, asymptotes 199 212 213
Curves, contact of 149
Curves, derived 38
Curves, differential 38
Curves, envelope 190
Curves, equations derived 324
Curves, evolute 160
Curves, family 190
Curves, integral 289 290
Curves, involutes 164
Curves, length 370 373 427
Curves, locus of ultimate intersections 191
Curves, Loria's Special Plane 212
Curves, parallel 164
Curves, twisted, skew 258 see
Curvilinear asymptotes 204
Cusps 193 206 207 209 210
Cycloid see "Examples"
De Moivre's theorem 251
Decreasing functions 113
Definite integral see "Integral"
density 385
Derivation of equation of curves 324
Derivative definition 32
Derivative general meaning 40
Derivative geometric meaning 37
Derivative notation 35
Derivative physical meaning 39
Derivative progressive, regressive 167
Derivative right and left hand 167
Derivatives of a constant 47
Derivatives of a function of a function 54
Derivatives of elementary functions 56—75
Derivatives of implicit functions 75 137
Derivatives of inverse functions 56
Derivatives of sum, product, quotient 46 48—52
Derivatives, geometric 95—102
Derivatives, meanings of second 104 105
Derivatives, partial 76 128 129
Derivatives, partial, commutative property of 131
Derivatives, partial, geometrical representation 130
Derivatives, partial, illustrations 139—142
Derivatives, partial, successive 131
Derivatives, special case 55
Derivatives, successive 103 108
Derivatives, total 134
Derivatives, total, successive 139
Derived, curves 38
Derived, functions 32 34
Descartes 270
Difference-quotient 32 34
Differentiable 35
Differential calculus see "Calculus"
Differential coefficient see "Derivative"
Differential equations 112 394
Differential equations, Clairaut's 399
Differential equations, classification 394
Differential equations, exact 396
Differential equations, homogeneous 396
Differential equations, linear 397 406 408
Differential equations, order 394
Differential equations, ordinary 394
Differential equations, partial 394
Differential equations, references to text-books 112 411 etc.
Differential equations, second order 409
Differential equations, solutions 112 395 400
Differential, differentials 42 44
Differential, differentials, complete 134
Differential, differentials, condition for total 138
Differential, differentials, exact 138
Differential, differentials, geometric 95—102
Differential, differentials, illustrations 139—142
Differential, differentials, infinitesimal 276
Differential, differentials, integration of total 309
Differential, differentials, partial 134
Differential, differentials, successive 109
Differential, differentials, total 134 135
Differentiation 33 291
Differentiation of series 240
Differentiation, general results 46
Differentiation, logarithmic 63
Differentiation, successive 103 see "Derivatives"
Direction cosines of a line 258
Discontinuity, discontinuous functions see "Functions"
Displacement 214 216 218
Divergent series see "Series"
Double points 193 206 207
Doubly periodic functions 342
Durand's rule 348
Echols see "Calculus"
Edwards see "Calculus"
Elementary integrals 293 301
Elimination of constants 111
ellipse see "Examples"
Ellipsoid 360
Elliptic functions 279 342
Elliptic functions, integrals 279 342 354
End-values 276
Envelopes, contact property 193 195
Envelopes, definition 191
Envelopes, derivation 194 197
Equations of tangent and normal 83
Equations, approximate solution of 171
Equations, derivation of 324
Equations, graphical representation 19 128
Equations, roots of 94 171
Equiangular spiral see "Examples"
Errors, relative 92 136
Errors, small 92 136
Euler 139 251 351
Euler, theorem on homogeneous functions 139
Evolute of the ellipse see "Examples"
Evolute, definitions 160
Evolute, properties of 161
Exact differential 138
Exact differential, equations 396
Examples concerning, adiabatic curves 86
Examples concerning, astroid (or hypocycloid) 85 98 158 161 319 324 376 405 425
Examples concerning, cardioid 90 97 159 369 374 377 389 405 425 433 446
Examples concerning, catenary 322 373 378 426 433
Examples concerning, circle 85 159 315 369 374 377 388 389 391 404 449
Examples concerning, cissoid 203
Examples concerning, cubical parabola 91 97 98 158 279 287 316 319 322
Examples concerning, cycloid 86 158 161 373 377 426
Examples concerning, ellipse 85 102 164 203 321 324 373 382 387 435 447 449 450
Examples concerning, evolute of the ellipse 161 164
Examples concerning, exponential curve 85
Examples concerning, folium of Descartes 86 203 369
Examples concerning, harmonic curve 448
Examples concerning, helix 328 329
Examples concerning, hyperbola 86 91 158 159 161 203 204 212 405 433
Examples concerning, hypocycloid see "Astroid"
Examples concerning, lemniscate 159 369 405 433
Examples concerning, limacon 448
Examples concerning, parabola 85 86 91 98 100 158 159 161 164 196 197 203 213 273 280 287 316 317 319 359 374 382 389 405 426 433
Examples concerning, probability curve 203
Examples concerning, semi-cubical parabola 85 86 158 280 319 426
Examples concerning, sinusoid 85 280
Examples concerning, Spirals, Archimedes' 90 97 99 159 374
Examples concerning, Spirals, equiangular (or logarithmic) 90 159 369 374 426
Examples concerning, Spirals, general 90 159
Examples concerning, Spirals, hyperbolic (or reciprocal) 90 369
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