|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Wrede R.C., Spiegel M. — Theory and problems of advanced calculus |
|
|
|
| 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 ( ) 159
Del (), formulas involving 159
Del (), 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
|
|
|
| Реклама |
|
|
|
|
|
О проекте