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| Murray D.A. — Differential and integral calculus |
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| Предметный указатель |
Rolle 169
Rolle's theorem 166 168
Roots of equations 94 171
Rouche et Comberousse 371
Rules for approximate integration 344 346 348
Salient points 208
Schloemilch — Roche's form of remainder 250
Second derivative, geometrical meaning 104
Second derivative, physical meaning 105
Semi-cubical parabola 371 see
Series 65 see "Expansion" "Infinite "Power
Series, absolutely convergent 235
Series, conditionally convergent 235
Series, convergent 234
Series, divergent 234 235
Series, harmonic 234
Series, oscillatory 234
Serret 320
Sign of area 318 370
Simpson, Simpson's rule 346
Sin x,  , expansions 245 248 351
Singly periodic functions 342
Singular points 206 208
Singular solution 400
Sinusoid see "Examples"
Skew curves, tangent line, and normal plane 258—261 266—268
slope 5 6 11 38 79 87
Slopes, curve of 38
Smith, C., Solid Geometry 212 378
Smith, W.B., Infinitesimal Analysis 133
Snyder see "Calculus"
Solution see "Differential Equation"
Speed 2 3 4 214
Sphere, surface 377 379
Sphere, volume 324 362 363
Spiral see "Examples"
Stationary tangent 127
Stirling 250
stop points 208
Subnormal, polar 88
Subnormal, rectangular 84
Substitutions in integration 296 304 328 336
Subtangent, polar 88
Subtangent, rectangular 84
Successive differentiation 103
Successive differentiation of a product 110
Successive differentiation, derivatives 103 108
Successive differentiation, differentials 109
Successive differentiation, integration 355 357
Successive differentiation, total derivatives 134
Summation, examples 271
Summation, integration as 275
Surfaces, applications of differential calculus, tangent lines, tangent plane, normal 262—265
Surfaces, areas of 374 378
Surfaces, volumes 320 360 363 365
Tangent 5
Tangent to surface 262
| Tangent to twisted curve 259 266
Tangent, equation of 83
Tangent, inflexional 127
Tangent, length 84 88
Tangent, stationary 127
Tanner see "Analytic Geometry"
Taylor's theorem and series for functions of one variable 44 242 243 246 252
Taylor's theorem and series for functions of several variables 250
Taylor's theorem and series, applications to algebra 256
Taylor's theorem and series, applications to calculation 44 135 245 246 247
Taylor's theorem and series, applications to contact of curves 255
Taylor's theorem and series, applications to maxima and minima 254
Taylor's theorem and series, approximations by 44 135 245
Taylor's theorem and series, expansions by 244—247
Taylor's theorem and series, forms of 243 244 246
Taylor's theorem and series, historical note 249
Taylor, F.G. see "Calculus"
Test-ratio 238
Time-rate of change 39 133
Todhunter see "Calculus"
Total derivative 134
Total derivative, differential 134
Total derivative, rate of variation 132
Tractrix see "Examples"
Trajectories, orthogonal 401 403
Transcendental functions 17
Transcendental functions, numbers 13
Trapezoidal rule 344
Trigonometric functions, differentiation of 66—75
Trigonometric functions, direct and inverse 17 71
Trigonometric functions, integration of 336
Trigonometric functions, relations with exponential 250
Trigonometric functions, substitutions by 328
Trigonometry, Hobson 233 352 423
Trigonometry, Murray 71 etc.
Triple points 207
Turning points, values 115
Twisted curves see "Skew curves"
Undulation, points of 126
Value see "Average" "Limits" "Maximum" "Mean" "Turning"
Value of  , computation of 351 352
Van Vleck, E.B. 235
Variable, change of 143
Variable, dependent, independent 13 15
Variation of functions 113
Variation of functions, total rate of 132
Variation, continuous variation, interval of variation 24
Veblen — Lennes, Infinitesimal Analysis 14 27 etc.
Velocity 91 214—222
Volumes, methods of finding 320 360 363 365
Wallis 270 371
Wentworth see "Analytic Geometry"
Whittaker, Modern Analysis 234 239
Williamson see "Calculus"
Witch of Agnesi see "Examples"
Wren 372
Young see "Calculus"
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