Widder D.V. — Advanced calculus :: Электронная библиотека попечительского совета мехмата МГУ

Главная Ex Libris Книги Журналы Статьи Серии Каталог Wanted Загрузка ХудЛит Справка Поиск по индексам Поиск Форум

Авторизация

Поиск по указателям

Widder D.V. — Advanced calculus

Обсудите книгу на научном форуме

Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter

Название: Advanced calculus

Автор: 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: 1947

Количество страниц: 432

Добавлена в каталог: 18.04.2005

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

Предметный указатель

Line integral      see Integral
Linear differential equations      404—415
Linear differential equations, homogeneous      408—412
Linear differential equations, nonhomogeneous      412—415
Logical symbols, definition of      6
Loxodromo      94
Maclaurin series      240 355 359 360 418
Maclaurin's integral test      249
Mass: of a material curve (wire)      141
Mass: of a solid body      178
Maximum and minimum: absolute, definition of      101
Maximum and minimum: of a continuous function      147
Maximum and minimum: of functions of a single variable      98—100
Maximum and minimum: of functions of several variables      98 101—107 111—118
Maximum and minimum: relative, definition of      101
Mean, law of the      8 72 210 218
Mean-value theorem: first, for Riemann integrals      34
Mean-value theorem: first, for Stieltjes integrals      137
Mean-value theorem: for functions of two variables      11
Mean-value theorem: second, for Riemann integrals      138
Mean-value theorem: second, for Stieltjes integrals      138
Mercator map      94 96
Moment of inertia      126 142 170 178
Multiple integral      see Integral
Newton's law      345
Nonhomogeneous linear differential equation      412—416
Norm of a subdivision      72 127 154
Normal line to a surface      87
Normal plane to a space curve      74 78
Open square      10
Orthogonal functions      325
Oscillating integrand      270 282
Osculating piano      70 78 124
Osgood, W.F.      184 193
Overtone      349
P, definition of class P      329
Pappus, theorem of      200
Parseval's theorem      354 357 359
Partial derivatives, definitions of      1 11
Partial differential equations      420
Partial differentiation      1—19
Partial summation      135
Plane curves, family of      118
Plane: osculating      76 78 124
Plane: rectifying      78
Plane: tangent, to a surface      88
Plucked string      422
Point set: boundary of      10
Point set: closed      10
Point set: interior point of      10
Point set: open      10
Point: of inflection of a curve      100
Point: regular, on a surface      03
Point: saddle      100
Point: singular, on a surface      63 74
Polar coordinates for double integrals      162 166
Polar developable surface      124
Polynomial, homogeneous      3
Power series transform      417
Power series, convergence of      309
Probability integral      306
Proper integral: function defined by      see Function
Proper integral: properties of      291 294
Quadratic form: in three variables      110
Quadratic form: negative definite, positive definite, positive semidefinite      110
Ratio test for infinite series      212
Rectifying plane      7s
Refinement: of a subdivision of a region      183
Refinement: of a subdivision of an interval      151
Region: area of a      181 193
Region: closed      10
Region: definition of a,      10
Region: diameter of a      164
Region: in cylindrical coordinates      179
Region: in polar coordinates      162
Region: in rectangular coordinates      153 170
Region: in spherical coordinates      180
Region: multiply connected      107
Region: regular      187
Region: simply connected      154 195 213
Region: solid      213
Region: subdivision of a      154
Regularity of summability      204
Remainder: Cauchy      35
Remainder: Lagrange      35
Remainder: Taylor      34
Resultant: bilateral      300
Resultant: convolution      380
Resultant: definition of      380
Resultant: faltung      380
Rhumb line      94
Riemann integral      120 132 136 137 138 147 108 185 180 188 199
Riemann — Lebesgue theorem      334
Riemann's theorem      338 339

Rolle's theorem      7 45
Saddle-point      100
Schwarz, H.A.      174
Second fundamental form of a surface      91
Second mean-value theorem for Riemann integrals      138
Second mean-value theorem for Stieltjes integrals      138
Sequence: bounded      233
Sequence: determining      417
Sequence: limit point of a      233
Series      See also Infinite series
Series: Dirichlet      300 309 307
Series: Fourier      324—304
Series: Maclaurin      249 355 359 366 418
Series: power      369
Series: Taylor's      34. 180 200 300
Series: trigonometric      324 350
Simply connected region      154 195 21&
Sino integral, SI(x)      383 385 400 403
Spherical coordinates for triple integrals      180
Stieltjes integral      120—152 188
Stieltjes integral, definition of      127
Stieltjes integral, properties of      131
Stieltjes transform      398
Stirling's formula      317 310 320 391
Stoke's theorem      210—215
Subdivision: norm of a      72 127 154
Subdivision: of a region      154 183
Subdivision: of an interval      72 127 151
Subdivision: refinement of      151 183
Subregion      154
Summability: Abel      265 301
Summability: Cesaro      202 265 300 361
Summability: Hoelder      265
Summability: of Fourier series      351—353
Summability: of improper integrals      300—302
Summability: of infinite series      201—265
Summability: regular      264
Summation processes of infinite series      see Summability
Superior limit      233
Surface: area of      172 173
Surface: integral      180 109—204
Surfaces: developable      123 124
Surfaces: envelope of a family of      122
Symbols, definition of logical      5
Tangent line to a space curve      74
Tangent plane to a surface      88
Taylor's formula with remainder      34 228 294
Taylor's series      34 180 260 366
Torsion      80
Torus      62
Transform: Fourier      362
Transform: Fourier cosine      362
Transform: Fourier sine      362
Transform: Laplace      see Laplace transform
Transform: power series      417
Transform: Stieltjes      308
Transformation      23
Transformation, inverse of a      23 38
Trigonometric approximation      354
Trigonometric series      324 350
Trihedral at a point      78
Triple integral: definition of      170
Triple integral: iteration of: in cylindrical coordinates      180
Triple integral: iteration of: in spherical coordinates      180
Twisted cubic      58
Two-dimensional interval      10
Uniform continuity: for functions of a single variable      147
Uniform continuity: for functions of two variables      183
Uniform convergence: of improper integrals      288—290 290—209
Uniform convergence: of infinite series      252—255
Vallee Poussin, de la      186 208
Variable, dependent and independent      1 25—28
Vector      50—71
Vector form: of Green's theorem      214
Vector form: of Stoke's theorem      214
Vector, binomial      78
Vector, definition of      50
Vector, normal      87
Vector, principal normal      78
Vector, symbolic, $\nabla$       65
Vector, tangent      78
Vectors: algebra of      51
Vectors: inner or scalar product of      51 69
Vectors: outer or vector product of      61 70
Vibrating string      343 420
Vibrating string, differential equation of      344
Volume given by a double integral      157 158
Wallis's product      311
Weierstrass form of Bonnet's theorem      138
Weierstrass M-test for uniform convergence: of improper integrals      289 362 375
Weierstrass M-test for uniform convergence: of infinite series      254
Weierstrass theorem on polynomial approximation      355
Work given by a line integral      189
Zero of order n      70

1 2

О проекте