Авторизация
Поиск по указателям
Widder D.V. — Advanced calculus
Обсудите книгу на научном форуме Нашли опечатку?
Название: Advanced calculusАвтор: Widder D.V. Аннотация: Classic text leads from elementary calculus into more theoretic problems. Precise approach with definitions, theorems, proofs, examples and exercises. Topics include partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Numerous graded exercises with selected answers.
Язык: Рубрика: Математика /Анализ /Учебники по элементарному анализу /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1947Количество страниц: 432Добавлена в каталог: 18.04.2005Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
7 11 330 (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, 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 ( 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
Реклама
, definition of class 
, definition of class 
, E, P, etc. 
) 
-neighborhood) 
, 
, 
, 
) 
|
|
О проекте