Osborne G.A. — Differential and integral calculus, with examples and applications :: Электронная библиотека попечительского совета мехмата МГУ

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Osborne G.A. — Differential and integral calculus, with examples and applications

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Название: Differential and integral calculus, with examples and applications

Автор: Osborne G.A.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1908

Количество страниц: 404

Добавлена в каталог: 17.04.2008

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

Предметный указатель

Acceleration      18
Angles with coordinate planes      133
Angles, between two curves      174 183
Arc, derivative of      186 187
Area, derivative of      241
Area, of any surface      355
Area, of curves      242 306 320 325 349
Area, of surface of revolution      337 353
Astroid      166 393
Asymptotes      179
Attraction at a point      376
Cardioid      170 392
Cauchy’s test for convergence      82
Centre, of curvature      200
Centre, of gravity      365
Centre, of pressure      374
Change of variable      57 58 148 299 304 317
Circle, of curvature      195 200
Circle, osculating      209
Comparison test for convergence      80
Computation, of $\pi$       96
Computation, of logarithms      94
Constant, definition of      1
Constant, derivative of      26
Constant, of integration      224 310
Contact, order of      206 207 209
Convergence, absolute and conditional      78
Convergence, interval of      86
Convergence, tests for      79
Curvature, centre of      200
Curvature, circle of      195 200
Curvature, direction of      189
Curvature, radius of      195 196 197
Curvature, uniform      193
Curvature, variable      194
Curves, angle of intersection of      174 183
Curves, area of      242 306 320 325 349
Curves, continuous and discontinuous      22
Curves, direction of      16 173 182
Curves, for reference, higher plane      162
Curves, length of      327 330
Curves, osculating      208
Cycloid      385
Definite integral      307
Definite integral, as a sum      319
Definite integral, change of limits      317
Definite integral, definition of      310
Definite integral, double      343
Definite integral, infinite limits      315
Definite integral, infinite variables      315
Definite integral, sign of      314
Derivative, definition      11
Derivative, general expression of      12
Derivative, illustrations of      13 16 17 18
Derivative, of an arc      186 187
Derivative, of area      241 336
Derivative, of function of a function      58
Derivative, partial      131
Derivative, partial, of higher orders      136 137
Derivative, relation between $\frac{dy}{dx}$ and $\frac{dx}{dy}$       57
Derivative, total      140
Differential coefficient      12
Differentials, definition of      68 70
Differentials, formulae for      71
Differentiation, algebraic formulae      26
Differentiation, definition of      26
Differentiation, inverse trigonometric formulae      51
Differentiation, logarithmic and exponential formulae      39
Differentiation, order of partial      137
Differentiation, partial      130
Differentiation, successive      61
Differentiation, trigonometric formulae      45
Element of an integral      319
Envelope, definition of      214 215
Envelope, equation of      215
Envelope, of normals      217
Epicycloid      390
Equation, of envelope      215
Equation, of evolute      201
Equation, of normal      176
Equation, of tangent      176
Equation, parametric      324
Evolute      201
Evolute, an envelope of normals      217
Evolute, equation of      201
Evolute, properties of      202 204
Functions of two or more variables      130
Functions, algebraic      2
Functions, continuous      22 315
functions, definition      1
Functions, discontinuous      22
Functions, expansion of      88
Functions, hyperbolic      379
Functions, implicit, differentiation of      75 144
Functions, increasing and decreasing      21
Functions, inverse trigonometric      51
Functions, logarithmic      39
Functions, transcendental      2
Functions, trigonometric      45
Gravity, centre of      365

Higher plane curves      162
Huyghens’s approximate length of arc      93
Hyperbolic functions      379
Hypocycloid      391
Increment      11
Indefinite integral      309
Indeterminant forms      106
Inertia, moment of      346 363
Infinitesimals, order of      73
Inflexion, points of      190
Integrals for reference      396
Integrals, containing $(ax+b)^{\frac{p}{q}}$       263
Integrals, containing $(ax+b)^{\frac{p}{q}}$ , $(ax+b)^{\frac{r}{s}}$       264
Integrals, containing $\sqrt{a^{2}-x^{2}}$ , $\sqrt{x^{2} \pm a^{2}}$       296
Integrals, containing $\sqrt{\pm x^2+ax+b}$       266
Integrals, definite      307
Integrals, double      343 347 349 350
Integrals, fundamental      225
Integrals, indefinite      309
Integrals, triple      344 361 363
Integration between limits      309
Integration by algebraic substitution      299
Integration by parts      279
Integration by substitution      295
Integration of $e^{ax}sin(nx)dx$ , $e^{ax}cos(nx)dx$       283
Integration of $f(x^{2})xdx$       295
Integration of $sec^{n}(x)dx$ , $cosec^{n}(x)dx$       274
Integration of $sin^{m}(x)cos^{n}(x)dx$       271 276 291
Integration of $sin^{n}(x)dx$ , $cos^{n}(x)dx$       270
Integration of $tan^{n}(x)dx$ , $cot^{n}(x)dx$       273
Integration of $tan^{n}(x)sec^{n}(x)dx$ , $cot^{n}(x)cot^{n}(x)dx$       274 291
Integration of $x^{m}(a+bx^{n})^{p}$       284
Integration of rational fractions      249
Integration, as a summation      306
Integration, constant of      224 310
Integration, definition of      223
Integration, successive      343
Intercepts of tangent      173
Involute      201
Involute, properties of      202 204
Leibnitz’s theorem      65
Length of curves      93 327 330
Limit, definition of      8
Liquids, pressure of      371
Logarithmic functions      2 39
Logarithms, computation of      94
Maclaurin’s theorem      89
Maxima and minima      114 155
Moment of inertia      346 363
Napierian base      16
Normal, equation of      176
Order, of contact      206
Order, of differentiation      137
Osculating circle, coordinates of centre      209
Osculating circle, radius of      209
Osculating curves      208
Osculating curves, order of contact of      209
Pappus, theorems of      369
PARAMETER      214 324
Parametric equations      324
Power series      85
Pressure of liquids      371
Pressure, centre of      374
Rates of increase      18
Reduction formulae      284 291
Remainder, Taylor’s theorem      105
Series of positive and negative terms      78
Series, computation by      94
Series, convergence of power      85
Series, convergent and divergent      78
Series, power      85
Slope of a curve      16
Slope of a line      16
Slope of a plane      133
Subnormal      173 183
Subtangent      173 183
Surface of revolution, area of      337 353
Surface, area of any      355
Surfaces of revolution, derivative of area of      336
Surfaces of revolution, volumes of      333 353
Tangent plane, equation of      133
Tangent, equation of      176
Tangent, intercept of      173
Taylor’s Theorem      97 103 145
Theorem, Leibnitz’s      65
Theorem, Maclaurin’s      89
Theorem, mean value      101
Theorem, Rolle’s      101
Theorem, Taylor’s      97 103 145
Transformation of partial derivatives      152 153
Trigonometric functions      2 45
Trochoid      388
Uniform curvature      193
Variable, change of      57 58 148 299 304 317
Variable, definition of      1
Variable, dependent and independent      2
Velocity      17
Volumes by area of section      340
Volumes, of any solid      361
Volumes, surfaces of revolution      333 358

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