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| Anthony G. — Elements of differential and integral calculus |
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| Предметный указатель |
Absolute convergence 220
Acceleration 92
Approximate formulas 237
Archimedes, spiral of 274
Area, center of 408
Area, moment of 408
Areas of plane curves, polar coordinates 370 406
Areas of plane curves, rectangular coordinates 365 402
Areas of surfaces 381 413
Asymptotes 249
Auxiliary equation 434
Bending 113
Binomial differentials 340
Binomial theorem 1 99
Cardioid 273
Catenary 272
Cauchy's ratio test 218
Center, of area 408
Center, of gravity 409
Change of variables 148
Circle of curvature 178
Cissoid 271
Computation by series of  235
Computation by series of e 233
Computation by series of logarithms 235
Concave down 126
Concave up 126
Conchoid of Nicomedes 272
Conditional convergence 221
Cone 2
Conjugate points 260
Constant 8
Constant of integration 307
Constant, absolute 8
Constant, arbitrary 8
Constant, numerical 8
Continuity of functions 14
Convergency 214
Coordinates of center of curvature 178
Cosine curve 237
Critical values 110
Cubical parabola 271
Curvature, center of 178
Curvature, circle of 178
Curvature, definition 155
Curvature, radius of 155
Curve tracing 128
Curves in space 262
Cusp 259
Cycloid 82 272
Cylinder 2
Decreasing function 106
Definite integration 314
Degree of differential equation 426
Derivative of arc 134
Derivative, definition 27
Differential coefficient 27
Differential equations 421
Differential of an area 314
Differentials 141
Differentiation 29
Differentiation of constant 36
Differentiation of exponentials 48
Differentiation of function of a function 44
Differentiation of implicit function 69
Differentiation of inverse circular functions 61
Differentiation of inverse function 45
Differentiation of logarithm
Double point 256
Envelopes 205
Equiangular spiral 274
Evolute of a curve 182
Expansion of functions 227
Exponential curve 275
Family of curves 205
Fluid pressure 388
Fluxions 25
Folium of Descartes 273
Formulas for reference 1
Function, continuity of 14
Function, definition 7
Function, graph of 16
Function, implicit 69
Function, increasing, decreasing 106
Function, inverse 45
Function, many-valued 17
Function of a function
Gravity, center of 409
Greek alphabet 3
Helix 263
Homogeneous differential equation 426
Hyperbolic spiral 274
Hypocycloid 273
Increasing functions 106
Increments 25
Indeterminate forms 170
Infinitesimal 13 132
infinity 13
Inflection 125
Integral curves 446
Integral curves, definition 314
Integral curves, indefinite 281
Integraph 443
Integration, by parts 347
Integration, by rational fractions 325
Integration, by rationalization 335
Integration, by transformation 343
Integration, definition 279
| Integration, mechanical 443
Interpolation 237
Involute 187
Laplace 25
Leibnitz 32
Leibnitz formula 99
Lemniscate 272
Length of curves 375
Limacon 274
Limit, interchange of 320
Limit of a variable
Limit, theory of 11
Linear differential equation 427
Lituus 274
Logarithmic curve 275
Logarithmic curve, spiral 274
Logarithms, Briggs's 237
Logarithms, common 237
Logarithms, Napierian 237
Maclaurin's Theorem and Series 230
Maxima and minima 103
Mean value, extended theorem of 166
Mean value, theorem of 165
Mechanical integration 443
Moment of area 408
Moment of inertia 410
Multiple roots 69
Natural logarithms 4
Newton 25
Node 258
normal 76
Normal line 266
Normal plane 262
Order of differential equations 426
Ordinary point 255
Osculation 259
Osgood 215
parabola 277
Parabola, cubic 271
Parabola, semicubical 271
Parabola, spiral 275
Parabolic rule 449
PARAMETER 6 205
Parametric equations 79
Partial derivatives 191
Partial derivatives, integration 393
Pierpont 245
Planimeter, polar 446
Points, conjugate 260
Points, end 260
Points, isolated 260
Points of inflection
Points, salient 260
Points, singular 255
Points, turning 108
Polar planimeter 446
Pressure, fluid 388
Probability curve 275
Quadratic equation 1
Radius of curvature 159
Rates 141
Rational fractions 325
Reciprocal spiral 274
Reduction formulas 350
Rolle's theorem 164
Secant curve 275
Semicubical parabola 271
Series, alternating 220
Series, arithmetical 1
Series, convergent 214
Series, divergent 214
Series, geometrical 1
Series, infinite 213
Series, nonconvergent 214
Series, oscillating 215
Series, power 223
Signs of trigonometric functions 3
Simpson's rule 449
Sine curve 273
Singular points 255
Slope of curve 73
Solution of differential equations 422
Sphere 2
Stirling 230
Strophoid 274
Subnormal 77
Subtangent 77
Successive differentiation 97
Successive integration 393
Surface, area of 381 413
Tangent curve 275
Tangent line to surface 264
Tangent plane 264
Tangent, to plane curves 76
Tangent, to space curves 262
Taylor's Series, Theorem 228
Test, comparison 217
Total differentiation 194
Trajectory, orthogonal 308
Trapezoidal rule 448
Triple integration 417
Variable, definition 6
Variable, dependent 7
Variable, independent 7
Velocity 90
Volumes of solids 377 417
Witch of Agnesi 271
Work 389
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