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Murray D.A. — A first course in infinitesimal calculus
Murray D.A. — A first course in infinitesimal calculus



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Название: A first course in infinitesimal calculus

Автор: Murray D.A.

Аннотация:

Infinitesimal calculus is the part of mathematics concerned with finding tangent lines to curves, areas under curves, minima and maxima, and other geometric and analytic problems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1903

Количество страниц: 439

Добавлена в каталог: 24.03.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\pi$      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 $e^{x}$, exponential series      326
Expansion of $sin^{-1} x$      314
Expansion of $tan^{-1} x$, 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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