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| Авторизация |
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| Woods F.S., Bailey F.H. — A Course in Mathematics. Volume II |
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| Предметный указатель |
Differentiation of exponential functions I 284
Differentiation of hyperbolic functions I 290
Differentiation of implicit functions I 188
Differentiation of inverse hyperbolic functions I 292
Differentiation of inverse trigonometric functions I 276
Differentiation of logarithmic functions I 284
Differentiation of polynomials I 103
Differentiation of trigonometric functions I 272
Differentiation partial, independent of order II 213
Differentiation successive I 187
Differentiation use of logarithm I 288 Differential)
Differentiation, collected formulas II 10
Differentiation, defined I 102
Differentiation, general formulas I 184
Direction, cosines defined II 180
Direction, cosines found from two equations of line II 186
Direction, cosines found from two equations of normal to plane II 184
Direction, cosines found from two equations of plane curve in polar coordinates I 345
Direction, cosines found from two equations of plane curvfe in rectangular coordinates I 197
Direction, cosines found from two equations of space curve II 182
Direction, cosines found from two equations of straight line in space II 180
Directrix of circle I 149
Directrix of conic I 148
Directrix of ellipse I 149
Directrix of hyperbola I 149
Directrix of parabola I 146
Discontinuity defined I 101
Discontinuity, examples of I 41 128 268 282 283 II 292 294
Discontinuity, finite defined II 291
Discriminant defined I 117
Discriminant of cubic equation I 114 117
Discriminant of quadratic equation I 73 117
Discriminant of quadratic equation in two variables I 236
Distance between two points in plane I 36
Distance between two points in space II 178
Distance of point from plane II 191
Distance of point from straight line I 63
Divergence II 279
e, the number I 280
Eccentric angle of ellipse I 304
Eccentricity of conic I 148
Eessel’s II 360
Eessel’s classes I 43
Eessel’s complementary II 349
Eessel’s conjugate II 313
Eessel’s continuous, one variable I 101
Eessel’s continuous, several variables II 200
Eessel’s decreasing I 106
Eessel’s defined by equation of second degree I 127
Eessel’s defined, one variable I 40
Eessel’s defined, several variables II 168
Eessel’s graphical representation, one variable I 44
Eessel’s graphical representation, two variables II 159
Eessel’s implicit I 188 II 210
Eessel’s increasing I 106
Eessel’s increment, one variable I 100
Eessel’s increment, several variables 11 200
Eessel’s involving fractions I 128
Eessel’s mean value II 54
Eessel’s notation I 44
Eessel’s periodic II 290
Eessel’s total differential II 200 Exponential Hyperbolic Logarithmic Transcendental Trigonometric
Eessel’s total differential, graph of Boyle-Mariotte’s law I 43
Eessel’s total differential, illustrating differential II 8
Eessel’s total differential, illustrating function II 158
Eessel’s total differential, illustrating partial derivative II 199
Eessel’s total differential, temperature-pressure-volume surface II 168
Elasticity I 204
Element of definite integral II 64
Element of determinant I 4
Eliminant I 23
Elimination I 1
Ellipse, angle between normal and focal radii I 191
Ellipse, area I 304 II 66 261
Ellipse, center of curvature I 357
Ellipse, center of gravity of segment II 96 247
Ellipse, definition and simplest equation I 139
Ellipse, evolute I 358
Ellipse, expressed by general equation of second degree I 231 235
Ellipse, length II 77
Ellipse, parametric equations I 303
Ellipse, radius of curvature I 355
Ellipse, referred to conjugate diameters I 259
Ellipse, special case of conic I 148
Ellipsoid, equation II 165
Ellipsoid, volume II 73 249
Energy, kinetic I 203
entropy II 272
Envelopes II 322
Epicycloid I 307
Epitrochoid I 309
Equations with given roots I 79
Equations, complex roots I 82
Equations, depression of I 79
Equations, differential (see Differential equations)
Equations, discriminant I 117
Equations, first degree in three variables II 161
Equations, first degree in two variables I 52
Equations, fractional roots I 90
Equations, irrational roots I 92
Equations, multiple roots I 116
Equations, Newton’s method of solution 1 114
Equations, number of roots I 80
Equations, rational roots I 89
Equations, second degree in two variables I 229
Equations, simultaneous I 161
Equations, simultaneous linear I 12
Equations, simultaneous linear homogeneous I 21
Equations, solution by factoring I 77
Equations, sum and product of roots I 82
Equations, transcendental I 293
Evolute I 357
Evolute of ellipse I 358
Exact differential in three variables II 276
Exact differential in two variables II 269
Expansion, coefficient I 204
Exponential equations I 295
Exponential function of complex number II 307
Exponential function of real number I 279
Exponential function, differentiation I 284
Exponential function, expansion II 58 308
Exponential function, integrals II 25
Factoring of quadratic polynomial 1 79
Factoring, solution of equations by I 77
Factors of polynomial I 81 83
Factors, integrating II 271 328
Factors, list of integrating II 273
Families of curves II 316
Families of curves, orthogonal II 314 327
Flow of liquid II 259 266
Focus of conic I 148
Focus of ellipse I 139
Focus of hyperbola I 142
Focus of parabola I 146
Folium of Descartes I 132
force I 202
Force, function II 266
Forms, indeterminate II 295
Fourier’s series II 290
Fractions, differentiation I 182
Fractions, integration II 113
Fractions, partial II 104
Functions, analytic II 311
General solution, linear differential equation II 350
Generators, rectilinear II 172
Graph I 40
Gravity (see Center of gravity)
Harmonic division of line I 250
Harmonic division of line, motion I 275
Harmonic division of line, property of polars I 249
| Heat, as line integral II 260
Heat, dependent on path II 267
Heat, derivatives II 269
Heat, entropy II 272
Helix, direction II 182
Helix, equation II 172
Helix, length II 180
Homogeneous differential equation II 145
Homogeneous equations I 21
homogeneous functions II 145
Horner’s method referred to I 92
Hyperbola, conjugate I 262
Hyperbola, definition and simplest equation I 142
Hyperbola, equilateral I 146
Hyperbola, referred to asymptotes I 224
Hyperbola, referred to conjugate diameters I 259
Hyperbola, second degree I 231 235
Hyperbola, special case of conic I 149
Hyperbolic functions, defined I 288
Hyperbolic functions, differentiation I 290
Hyperbolic functions, differentiation of inverse I 292
Hyperbolic functions, expansion II 63
Hyperbolic functions, integrals leading to inverse II 24
Hyperbolic functions, inverse I 291
Hyperbolic spiral I 332
Hyperboloid of one sheet II 163
Hyperboloid of two sheets II 165
Hypocycloid I 309
Hypocycloid, four-cusped I 132
Hypocycloid, Imaginary unit I 31
Hypocycloid, numbers (see Complex numbers)
Hypocycloid, surfaces II 160
Implicit functions, general discussion II 210
Implicit functions, special case I 188
Increment of function of one variable I 100
Increment of functions of several variables II 200
Indefinite integral of  II 127
Indefinite integral of  II 123
Indefinite integral of  II 29
Indefinite integral of  ,  II 129
Indefinite integral of rational fractions II 113
Indefinite integral, containing ![$\sqrt[n]{a+bx}$](/math_tex/a99454dccef2c2b4a45bf7a9317e7df782.gif) II 20 119
Indefinite integral, containing  II 121
Indefinite integral, containing  II 122
Indefinite integral, containing  II 29
Indefinite integral, containing  II 29
Indefinite integral, containing  II 29
Indefinite integral, defined II 4
Indefinite integral, fundamental formulas II 2
Indefinite integral, reduction formulas II 130 135
Indeterminate forms II 295—301
Indicator diagram II 43 54
Inertia (see Moment of inertia)
Infinitesimal, defined II 1
Infinitesimals, fundamental theorems on II 4
Infinitesimals, order of II 1
infinity I 29
Inflection, point of II 112 194
Integral, particular II 349 Indefinite and
Integrand, defined II 12
Integrand, infinite II 53
Integrating factors II 273
Integration by parts II 30 51
Integration by substitution (see Substitution)
Integration of rational fractions II 113
Integration of simple differential equations II 141
Integration, constant of II 12
Integration, definition II 12
Integration, elementary formulas II 26
Integration, fundamental formulas II 13
Integration, possibility of II 32
Integration, preliminary discussion I 205
Integration, special methods of II 119
Intercepts I 53
Intersection of plane curves I 161
Intersection, curves with common points I 171
Intersection, number of points I 169
Involute I 357
Involute of circle I 311
Isolated points, examples 1 126 11 292
kinetic energy I 203
Laplace’s equation in plane II 366
Laplace’s equation in three dimensions II 368
Latus rectum I 211
Legendre’s coefficients II 359
Legendre’s equation II 357
Lemniscate I 340
Lemniscate, area I 348
Lemniscate, Cartesian equation I 341
Length (see Arc and Distance)
Limacon I 336
Limit of ratio of arc to chord I 195
Limit, approached by variable, defined I 97
Limits of  and  I 283
Limits of  and  I 270
Limits, defined II 40
Limits, infinite II 52
Limits, of definite integral, change of II 49
Limits, theorems relating to I 178
Line integral, defined II 258
Line integral, dependent on path II 2 37
Line integral, independent of path II 2 53
Line integral, related to double integral II 261
Line, adiabatic II 207
Line, determined by point and direction in plane I 58
Line, determined by point and direction in space II 190
Line, determined by two points in space II 187
Line, direction cosines II 186
Line, direction in plane I 55
Line, direction in space II 180
Line, equation in plane I 50
Line, equations in space II 170
Line, intersection in plane I 61
Line, normal equation in plane I 64
Line, parallel lines in plane, Ir 56
Line, parallel lines in space II 183
Line, parametric equations in plane 1 302
Line, perpendicular lines in plane I 57
Line, perpendicular lines in space II 183
Line, polar equation in plane I 342
Line, satisfying two conditions in plane I 58
Line, straight, determined by two points in plane I 60
Line, tangent to plane curve I 104
Line, tangent to space curve II 189
Linear algebraic equations I 1
Linear differential equations II 146 340
Linear partial differential equations II 364
Liquid, flow of II 259 266
Locus I 45
Locus, problems I 316
Logarithm, Naperian I 280
Logarithmic function of complex number II 310
Logarithmic function of real number I 279
Logarithmic function, differentiation of I 284
Logarithmic function, expansion II 59
Maclaurin’s series II 55 287
Maxima and minima defined I 108
Maxima and minima defined, discussed by Taylor’s theorem II 60
Maxima and minima defined, for functions of two variables II 205
Maxima and minima defined, problems I 192 275
Maxima and minima defined, test by first derivative I 108
Maxima and minima defined, test by second derivative I 112
Mean value of function II 54
Mechanics and physics problems, acceleration I 202
Mechanics and physics problems, adiabatic lines II 267
Mechanics and physics problems, attraction of cylinder II 252
Mechanics and physics problems, attraction of wire II 87
Mechanics and physics problems, beams, bending moment II 149
Mechanics and physics problems, Boyle — Mariotte’s law I 43
Mechanics and physics problems, catenaiy II 142
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