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Язык: Рубрика: Математика/Анализ/Учебники по элементарному анализу/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1947 Количество страниц: 432 Добавлена в каталог: 18.04.2005 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель , definition of class 7 11 , definition of class 330 (C,1)      see Cesaro summability Abel summability      205 301 Abscissa: of absolute convergence for a Laplace transform      374 Abscissa: of convergence for a Laplace transform      371 Adams, J.C.      307 Angle between surface curves      91 Approximation: least square      354 350 Approximation: polynomial      355 Approximation: trigonometric      354 Arc length      90 Area: of a region      184 193 Area: of a surface      172 Arithmetic means      see Cesaro summability Attraction for a continuous distribution of mass      174 178 Bessel's function of order n      391 Bessel's inequality      333 334 337 357 Beta function, B(x, y)      308 ff 311 Bilateral convolution      300 Bilateral Laplace transform      395 398 Bilateral resultant      300 Bonnet's theorem, Weierstrass form of      138 Bound: greatest lower      149 Bound: least upper      147 149 Bound: of continuous function      146 Boundary-value problem      346 Bounded variation of a function      132 C, definition of class C      6 10 Cauchy remainder in Taylor's series      35 Cauchy's convergence test      242 Cauchy's criterion      233 235 Center of gravity      168 178 Cesaro summability      202—205 300 351 Class C, D, , E, P, etc.      see C D E P etc. Comparison tests for convergence and divergence: of improper integrals      209 280 281 Comparison tests for convergence and divergence: of infinite series      239 240 Components of a vector      50 Contact of order n      76 Continuity, uniform: for functions of a single variable      147 Continuity, uniform: for functions of two variables      183 Continuous distribution of mass      142 174 Continuous function      6 10 146—149 291 296 Convergence theorem for Fourier series      330 Convolution      380 see Cosine integral, CI(s)      383 385 400 404 Cramer's rule      21 Cross derivatives, equality of      41—43 Curl      65 Curvature      80 Curvature, mean      93 Curvature, normal      92 Curvature, total, or Gaussian      03 Curve in space: arc length of      72 Curve in space: normal plane to      74 Curve in space: tangent line to      73 Curves: closed      180 Curves: family of plane      118 Curves: Jordan      184 180 187 Curves: regular      180 Curves: sectionally smooth      180 Curvilinear integral      see Integral Cylindrical coordinates for triple integrals      179 D'Alembert's ratio tent      242 D, definition of class D      330 Definite integrals, evaluation of      313—315 Del ( )      65 Delta-neighborhood ( -neighborhood)      10 Density of a continuous distribution      142 Derivative: directional      30 66 Derivative: of higher order      3 16 20 Derivative: on the left      6 Derivative: on the right      6 Derivatives: cross, equality of      41—43 Derivatives: partial, definitions of      1 11 Determining function      402 Determining function, definition of      367 Determining sequence      417 Developable surface      123 Developable surface, polar      124 Developable surface, rectifying      124 Diameter of a region      154 Dienes, P.      180 Difference equations      410 Differential equation: exact      196 Differential equation: homogeneous linear      408 Differential equation: linear      404 Differential equation: nonhomogeneous linear      412 Differential equation: of hyperbolic typo      346 Differential equation: of vibrating string      344 Differential equation: partial      420 Differential: definition of      20 Differential: exact      213 Differential: existence of exact      195 Differentiation: of a function defined by a proper integral      291—293 Differentiation: of a function defined by an improper integral      298 313 Differentiation: of implicit functions      10 Differentiation: of in finite series      259 Differentiation: partial      1—19 Directional derivative      30 66 Dirichlet formula      166 100 Dirichlet series      300 360 397 Divergence, Div      65 Divergent integrals      300—302 Divergent series      201—265 Domain      10 Domain, bounded      153 Double integral: applications of      108 Double integral: definition of      154 Double integral: existence of      182 Double integral: iteration of; in polar coordinates      102—104 Double integral: iteration of; in rectangular coordinates      159—161 Double integral: properties of      156 Duhamel's theorem      72 132 144 147 168 181 183 185 188 190 200 E, definition of class E      409 Eider's constant      307 321 Eider's theorem      15 Envelope      118 Envelope, of families of surfaces      122 Envelope, of normals      120 Envelope, of tangents      120 Equations: difference      416 Equations: simultaneous      21 47 Error function (err)      383 385 399 Exponential integral, EI(x)      383 384 400 401 403 extrema      105. See also Maximum and minimum Faltung      380. See also Resultant Fejer's theorem      352 354 355 Fejer, L.      351 Field of force, conservative      190 First fundamental form of a surface      90 First mean-value theorem for Riemann integrals      34 First mean-value theorem for Stieltjes integrals      137 Fourier coefficients      324 327 Fourier cosine transform      302 Fourier integral      324 359 Fourier integral, convergence theorem for      302 Fourier series: convergence of      333 Fourier series: convergence theorem for      336 Fourier series: definition of      324 Fourier series: for an arbitrary interval      343 Fourier series: summability of      351 Fourier sine transform      362 Fourier transform      302 Frenet — Serret formulas      83 92 124 Function: Bessel's, of order n      394 Function: beta      308 341 Function: composite      12 Function: continuous      6 10 145—149 Function: defined by a proper integral: continuity of      291 292 Function: defined by a proper integral: differentiation of      291—293 Function: defined by a proper integral: integration of      159 162 165 166 Function: defined by an improper integral: continuity of      296 Function: defined by an improper integral: differentiation of      208 313 Function: defined by an improper integral: integration of      297 Function: determining: differentiation of      374 Function: determining: product of      380 Function: error, (erf)      383 385 399 Function: even      327 Function: gamma      303 341 308 398 300 Function: generating      see Generating function Function: homogeneous      14—10 Function: implicit      2 18 38 44 Function: integrator      120 Function: limit of a      4 9 Function: multiple-valued, single-valued      1 Function: normed      325 Function: odd      327 Function: of bounded variation      132 Function: of class 7 11 Function: of class C      6 10 Function: of one variable      4—8 Function: of several variables      6—13 Function: uniformly continuous: in a region      183 Function: uniformly continuous: on an interval      147 Functional dependence      45 Functions, orthogonal      325 Fundamental form of a surface: first      90 Fundamental form of a surface: second      91 Gamma function, 303 ff 341 308 398 399 Gauss's theorem      101 197 307 Generating function: definition of      307 Generating function: differentiation of      374 Generating function: of a sequence      417 Generating functions, product of      380 Gradient, Grad      32 05 00 Gravitational attraction      see Attraction Greatest lower bound      149 Green's theorem: in three dimensions      200—202 206 213—215 Green's theorem: in two dimensions      191—199 210 Gyration, radius of      171 Harmonic analysis      343 350 Harmonic series      240 Heine — Borel theorem      115 140 185 Helix      58 Hoelder summability      205 Homogeneous function      14 Homogeneous linear differential equation      408—412 Homogeneous polynomial      3 Hyperbolic type, differential equation of      340 Implicit function theorem      44 Improper integrals: absolute convergence of      270 281 285 Improper integrals: classification of      267 285 280 Improper integrals: comparison teats for      209 280 Improper integrals: conditional convergence of      270 276—278 Improper integrals: convergence of Type I      208 Improper integrals: convergence of Type III      280 Improper integrals: convergence of Types II and IV      284 Improper integrals: divergence of      208 285 300—302 Improper integrals: functions defined by      see Function Improper integrals: limit tests for      273 281 285 Improper integrals: summability of divergent      300—302 Improper integrals: uniform convergence of      288—290 296—299 Improper integrals: Weierstrass M-test for uniform convergence of      280 302 375 Indeterminant form: evaluation by orders of infinity      230 Indeterminant form: evaluation by series      228 Indeterminant form: L'Hospital's rule      218 221 225 227 Indeterminant form: type 210 Indeterminant form: type 220 Indeterminant form: types , , 220 Indeterminant form: types , 225 Inertia, moment of      120 142 170 Inferior limit      233 Infinite series: absolute convergence of      245—240 255 Infinite series: alternating      245—247 Infinite series: comparison tests for      230—240 Infinite series: conditional convergence of      240 Infinite series: continuity of the sum of an      257 Infinite series: convergence tests for      239 240 242—244 240—251 254 Infinite series: definition of convergence, and divergence of      298 Infinite series: differentiation of      250—201 Infinite series: integration of      257—250 Infinite series: method of, for evaluation of definite integrals      315 Infinite series: summation of divergent      201—205 Infinite series: uniform convergence of      252—255 Infinitesimal      231 Infinities, table of      230 Infinity, definition of orders of      230 Integral: change of variable in      204 Integral: curvilinear      185 Integral: divergent      300—302 Integral: double      see Double integral Integral: Fourier      324 359 362 Integral: improper      see improper integral Integral: iterated      157 165 176 Integral: Lebesgue      185 Integral: line: in a plane      180—198 Integral: line: in space      210—214 Integral: Maclaurin's integral test for infinite series      243 Integral: multiple      see Double integral Triple Integral: proper: function defined by      see Function Integral: proper: properties of      291—294 Integral: proper: Riemann      see Riemann integral Integral: proper: Stieltjes      see Stieltjes integral Integral: proper: surface      186 199—204 Integral: proper: triple      see Triple integral Integrals, definite; evaluation of      313—315 Integration: by parts      134 Integration: change in order of      105—107 297 Integration: of a function defined by a proper integral      159 102 165 166 Integration: of a function defined by an improper integral      297 Integration: of infinite series      257 Integrator function      120 Invariants      68—70 Jacobian      22 38 200 208 209 Jordan curves      184 180 187 Just scale      349 l'Hospital's rule      218 221 225 227 Lagrange identity      51 108 Lagrange remainder      35 Lagrange's multipliers      113 Laguerre polynomial, 384 385 390 Lamina: attraction of, on a unit particle      174 Lamina: center of gravity of      168 Lamina: moment of inertia of      144 Lapiace — Stieltjes transform      307 Laplace transform      365—423 Laplace transform table of      399 Laplace transform, bilateral      395 398 Laplace transform, definition of      314 307 Laplace transform, inversion formula for      390 Laplace transform, operational properties of      370 Laplace transform, unilateral      305 Laplace's method      21 Laplacian, ( )      65 Law of the mean      8 72 2J0 Law of the mean, generalized      218 Least square approximation      354 350 Least squares, method of      108 Least upper bound      149 Lebesgue H.      334 Lebesgue integral      185 Leibniz's rule      409 Leibniz's theorem on alternating series      245 247 248 276 Limit inferior and superior: definition of      233 Limit inferior and superior: properties of      234 Limit point: of a point set      10 Limit point: of a sequence      233 Limit tests: for convergence and divergence of improper integrals      273 281—283 285 Limit tests: for convergence and divergence of infinite series      249 250
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