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Wrede R.C., Spiegel M. — Theory and problems of advanced calculus
Wrede R.C., Spiegel M. — Theory and problems of advanced calculus

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Название: Theory and problems of advanced calculus

Авторы: Wrede R.C., Spiegel M.

Язык: en

Рубрика: Математика/Анализ/Учебники по элементарному анализу/Задачники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 2002

Количество страниц: 433

Добавлена в каталог: 23.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel, integral test of      334
Abel, summability      305
Abel, theorems of      282 293
Absolute convergence, of integrals      309 312 319—321
Absolute convergence, of series      268 283 300
Absolute convergence, theorems on      269 283
Absolute maximum or minimum      42 see
Absolute value      3
Absolute value of complex numbers      6
Acceleration      74 158
Acceleration in cylindrical and spherical coordinates      181
Acceleration, centripetal      175
Acceleration, normal and tangential components of      177
Accumulation, point of      5 117 see
Addition      1
Addition of complex numbers      7 13
Addition of vectors      151 152 163
Addition, associative law of      2 8
Addition, commutative law of      2
Aerodynamics      402
Aleph-null      5
Algebra, fundamental theorem of      43
Algebra, of complex numbers      6 7 13—15
Algebra, of vectors      151 152 163—171
Algebraic functions      43
Algebraic numbers      6 13
Algebraic numbers, countability of      13
Alternating series      267 268 282
Alternating series, convergence test for      267 268
Alternating series, error in computations using      268 282
Amplitude      7
Analytic continuation, of gamma function      376
Analytic functions      393
Analytic part, of a Laurent series      395
Anti-derivatives      94
Approximations      see "Numerical methods"
Approximations to irrational numbers      9
Approximations, by partial sums of Fourier series      352
Approximations, by use of differentials      78 79 130 131
Approximations, least square      201
Approximations, using Newton's method      74
Approximations, using Taylor's theorem      274—275
Arc length      99 109
Arc length element      157 161 174
Archimedes      90
Area      100 109
Area, expressed as a line integral      242
Area, of a parallelogram      155 168
Area, of an ellipse      205
Argand diagram      7
Argument      7
Arithmetic mean      10
Associative law      2 4
Associative law, for vectors      152 155
Asymptotic series or expansions, for gamma function      286 292
Axiomatic foundations, of complex numbers      6 7
Axiomatic foundations, of real number      4
Axiomatic foundations, of vector analysis      155
Axis, real      2
Axis, x, y and z      121
Base, of logarithms      4
Bases, orthonormal      152
Bernoulli numbers      304
Bernoulli's inequality      16
Bernoulli, Daniel      336
Bessel differential equation      276
Bessel functions      276
Beta functions      375 378 379 382 384
Beta functions, relation, to gamma functions      379
Bilinear transformation      422 see
Binary scale      16 21
Binary scale system      2
Binomial coefficients      21
Binomial coefficients, series      275
Binomial coefficients, theorem      21
Bolzano — Weierstrass theorem      6 12 19 117
boundary conditions      339
Boundary point      117
Boundary-value problems, and Fourier integrals      371
Boundary-value problems, and Fourier series      339 356 357
Boundary-value problems, in heat conduction      356 357
Boundary-value problems, in vibration of strings      361
Boundary-value problems, separation of variables method for solving      356
Bounded functions      40 41
Bounded sequences      24 30—32 36
Bounded sets      6
Bounds, lower and upper      6 12 13
Box product      155
Branch line      417
Branch point      396 417
Branches of a function      41
Calculus, fundamental theorem of integral      94 95 104
Cardinal number of the continuum      5
Cardioid      114
Catenary      113
Cauchy principal value      310 321
Cauchy — Riemann equations      393 400—403
Cauchy — Riemann equations, derivation of      401
Cauchy — Riemann equations, in polar form      422
Cauchy's convergence criterion      25 33
Cauchy's form of remainder in Taylor's theorem      274 296
Cauchy's generalized theorem of the mean      72 82
Cauchy's inequality      422
Cauchy's integral formulas      394 403—406
Cauchy's theorem      394 403—406
centripetal acceleration      175
Chain rules      69 122 133
Chain rules, for Jacobians      124
Circle of convergence      276
class      1 see
Closed interval      5
Closed region      117
Closed set      6 12 13 117
Closure law or property      2
Cluster point      5 117 see
Collection      1 see
Commutative law      2
Commutative law, for dot products      153
Commutative law, for vectors      154 166 167
Comparison test, for integrals      308 311 319
Comparison test, for series      267 279 280
Completeness, of an orthonormal set      310
complex numbers      6 13 14
Complex numbers, absolute value of      6
Complex numbers, amplitude of      7
Complex numbers, argument of      7
Complex numbers, as ordered pairs of real numbers      7
Complex numbers, as vectors      20
Complex numbers, axiomatic foundations of      7
Complex numbers, conjugate of      6
Complex numbers, equality of      6
Complex numbers, modulus of      6
Complex numbers, operations with      6 13 14
Complex numbers, polar form of      7 14
Complex numbers, real and imaginary parts of      6
Complex numbers, roots of      7 13
Complex plane      7
Complex variable      392 393 see
Components, of a vector      153
Composite functions      47
Composite functions, continuity of      47
Composite functions, differentiation of      69 132—135
Conditional convergence, of integrals      309 312 319 320
Conditional convergence, of series      268 300
Conductivity, thermal      357
Conformal mapping or transformation      417 see
Conjugate, complex      6
connected region      237
Connected region, set      117
Conservative field      233
Constants      5
Constraints      188
Continuity      46—64 119 127 128 399
Continuity and differentiability      66 72 73 120 121
Continuity, definition of      46 47
Continuity, in a region      119
Continuity, in an interval      47
Continuity, of an infinite series of functions      271 272 288
Continuity, of functions of a complex variable      393 399 400
Continuity, of integrals      99 314
Continuity, of vector functions      156
Continuity, piecewise      48
Continuity, right- and left-hand      47
Continuity, theorems on      47 48
Continuity, uniform      48 119
continuous      see "Continuity"
Continuous differentiability      67 121
Continuously differentiable functions      66 67 120
Continuum, cardinality of      5
Contour integration      398
Convergence, circle of      276
Convergence, criterion of Cauchy      33 37
Convergence, domain of      272
Convergence, interval of      25 272
Convergence, of Fourier integrals      see "Fourier's integral theorem"
Convergence, of Fourier series      338 354—356
Convergence, of improper integrals      see "Improper integrals"
Convergence, of infinite series      see "Infinite series"
Convergence, of series of constants      278—285
Convergence, radius of      272 276
Convergence, region of      117
Convergent      see "Convergence"
Convergent, integrals      306—309 see
Convergent, sequences      23 269 see
Convergent, series      25 see
Convolution theorem, for Fourier transforms      365
Convolution theorem, for Laplace transforms      334
Coordinate curve      160
Coordinates, curvilinear      139 160 see
Coordinates, cylindrical      161 174
Coordinates, hyperbolic      218
Coordinates, polar      7
Coordinates, rectangular      152
Coordinates, spherical      162 190
Correspondence      2 11 23 39 160
Correspondence, one to one      2 11
Countability      5 11 12
Countability, of algebraic numbers      13
Countability, of rational numbers      11 12
Countable set      5 11 12
Countable set, measure of a      91 103
Critical points      73
Cross products      154 166—169
Cross products, proof of distributive law for      166
Curl      158 159 172—174
Curl, in curvilinear coordinates      161
Curvature, radius of      177 181
Curve, coordinate      150
Curve, simple closed      117 232 242
Curve, space      157
Curvilinear coordinates      125 139
Curvilinear coordinates, curl, divergence, gradient, and Laplacian in      161 162
Curvilinear coordinates, Jacobians and      161 162
Curvilinear coordinates, multiple integrals in      207—228
Curvilinear coordinates, orthogonal      207—228
Curvilinear coordinates, special      161 162
Curvilinear coordinates, transformations and      139 140 160
Curvilinear coordinates, vectors and      161 162
Cut      see "Dedekind cut"
Cycloid      99
Cylindrical coordinates      161
Cylindrical coordinates, arc length element in      161
Cylindrical coordinates, divergence in      175
Cylindrical coordinates, gradient in      175
Cylindrical coordinates, Laplacian in      161 173
Cylindrical coordinates, multiple integrals in      222
Cylindrical coordinates, parabolic      180
Cylindrical coordinates, volume element in      161 175
De Moivre's theorem      7 15
Decimal representation of real numbers      2
Decimals, recurring      2
Decreasing functions      41 47
Decreasing functions, monotonic      41
Decreasing functions, strictly      41 47
Decreasing sequences, monotonic and strictly      24
Dedekind cuts      4 16
Definite integrals      90—95 103 see
Definite integrals, change of variable in      95 105—108
Definite integrals, definition of      90 91
Definite integrals, mean value theorems for      92 93 104
Definite integrals, numerical methods for evaluating      98 108 109
Definite integrals, properties of      91 92
Definite integrals, theorem for existence of      91
Definite integrals, with variable limits      95 186 313 314
Degree, of a polynomial equation      6
Degree, of homogeneous fuctions      122
Del ($\nabla$)      159
Del ($\nabla$), formulas involving      159
Del ($\nabla$), in curl, gradient, and divergence      159
Deleted neighborhood      6 117
Dense, everywhere      2
Denumerable set      see "Countable set"
Dependent variable      39 116
derivatives      65—89 75—79 see
Derivatives, chain rules for      70 124
Derivatives, continuity and      66 72 121 130
Derivatives, definition of      65 66
Derivatives, directional      186 193 202
Derivatives, evaluation of      71 75—89
Derivatives, graphical interpretation of      66
Derivatives, higher order      71 120
Derivatives, of elementary functions      71 78—80
Derivatives, of functions of a complex variable      393 400—403
Derivatives, of infinite series of functions      269 400—403
Derivatives, of vector functions      157 171 172
Derivatives, right- and left-hand      67 77 78 86
Derivatives, rules for finding      70
Derivatives, table of      71
Determinant, for cross product      154
Determinant, for curl      159
Determinant, for scalar triple product      155
Determinant, Jacobian      see "Jacobian"
Dextral system      152
Difference equations      65
Differentiability      66 67 121
Differentiability, and continuity      66 72 73
Differentiability, continuous      66
Differentiability, piecewise      66
Differential equation, Gauss'      276
Differential equation, solution of, by Laplace transforms      314 330
Differential geometry      158 181
Differential, as a linear function      68 121
Differential, elements of area, of volume      160 163 212 213 233
Differentials      67 68 69 78 120—122
Differentials, approximations by use of      78 79 120
Differentials, exact      122 131 132
Differentials, geometric interpretation of      68 69 121
Differentials, of functions of several variables      120 130
Differentials, of vector functions      156
Differentials, total      120
Differentiation      see also "Derivatives"
Differentiation, of Fourier series      339 353
Differentiation, rules for      70 78—80 87
Differentiation, under the integral sign      186 194 203
Diffusivity      357
Directed line segments      150
Directional derivatives      186 193 202
Dirichlet conditions      337 345
Dirichlet integrals      379 385 389
Dirichlet's test, for integrals      314
1 2 3 4
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