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Murray D.A. — Differential and integral calculus
Murray D.A. — Differential and integral calculus



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Название: Differential and integral calculus

Автор: Murray D.A.

Аннотация:

This volume is produced from digital images from the Cornell University Library Historical Mathematics Monographs collection.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1908

Количество страниц: 491

Добавлена в каталог: 01.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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