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| Wrede R.C., Spiegel M. — Theory and problems of advanced calculus |
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| Предметный указатель |
Rectangular neighborhood 117
Rectangular rule for integration 98
Recurring, decimal 2
Region 117
Region, closed 117
Region, connected 232
Region, multiply-connected 117
Region, of convergence 117
Region, open 117
Region, simply-connected 117 232 241
Regular summability 278 304
Relative extrema 73
Relativity, theory of 182
Removable discontinuity 56 119
Removable singularity 393 407
Residue theorem 397 398 409—412
Residue theorem, evaluation of integrals by 398 403—406
Residue theorem, proof of 409 410
Residues 397 409—412
Resultant of vectors 151 163
Reversion of series 273
Riemann integrable 91
Riemann's theorem 354 370
Riemann, axis 396
Riemann, surface 397
Right-hand continuity 47
Right-hand derivatives 67 77 78
Right-hand limits 45
Right-handed rectangular coordinate system 152 153
Rolle's theorem 72
Rolle's theorem, proof of 80
Roots of equations 43
Roots of equations, computations 59
Roots of equations, Newton's method for finding 89
Roots, of complex numbers 7 14
Roots, of real numbers 3 11
Saddle points 188
scalar 153
Scalar field 153
Scalar invariant 182
Scalar product see "Dot products"
Scalar triple product 155
Scale factors 160
Scale of two see "Binary scale"
Schwarz's inequality, for integrals 110
Schwarz's inequality, for real numbers 10 18
Section see "Dedekind cut"
Separation of variables in boundary-value problems 356
Sequence, Fibonacci 35
Sequences 23—38 269
Sequences, bounded, monotonic 24 30—32
Sequences, convergent and divergent 23 269
Sequences, decreasing 25
Sequences, definition of 23
Sequences, finite and infinite 269
Sequences, increasing 25
Sequences, limits of 23 27 269
Sequences, of functions 269
Sequences, terms of 26
Sequences, uniform convergence of 269
Series see "Infinite series"
Series, binomial 275
Series, double 277
Series, geometric 25 266
Series, harmonic 266
Series, Laurent's 395 407 408 420
Series, Maclaurin 274
Series, of functions of a complex variable 406—409
Series, partial sums of 25 266
Series, reversion of 273
Series, sum of 25 266
Series, telescoping 278
Series, terms of 266
Series, test for integrals 280
Sets 1
Sets, bounded 6
Sets, closed 6 12 13
Sets, connected 117
Sets, countable or denumerable see "Countable set"
Sets, defined from Laurent series 395
Sets, elements of 1
Sets, essential 395 407
Sets, everywhere dense 2
Sets, intersection of 12
Sets, Isolated 395
Sets, orthonormal 337 342
Sets, point 117
Sets, removable 395 407
Sets, union of 12
Simple closed curves 117 232 241
Simple poles 395
Simply connected region 117 232 241
Simply-connected region 117 232
Simpson's rule 98 108 109
Single-valued function 39 116 392
Singular points or singularities 395—398 406—409
Sink 259
slope 66
Smooth function see "Piecewise differentiability"
Solenoidal vector fields 259
Source 259
Space curve 157
Specific heat 356 357
Spherical coordinates 162 174 175
Spherical coordinates, arc length element in 162 174
Spherical coordinates, Laplacian in 162 176
Spherical coordinates, multiple integrals in 222
Spherical coordinates, volume element in 162 175
Staircase or step function 51
Stirling's asymptotic formula and series 378 384
Stokes' theorem 237 252—257
Stokes' theorem, proof of 252 253
Stream function 402
Subset 1
Subtraction 2
Subtraction, of complex numbers 13 14
Subtraction, of vectors 151
SUM 2
Sum, of series 25 266
Sum, of vectors 151 163
Sum, partial 25 266
Summability 278 296 304
Summability, Abel 305
Summability, Cesaro 278 296
Summability, regular 278 304
Superposition, principal of 357
surface 116
| Surface integrals 233—236 245—249 261
Surface, equipotential 186
Surface, level 144 186
Surface, normal line to see "Normal line"
Surface, orientable 248
Surface, tangent place to see "Tangent plane"
Tangent line, to a coordinate curve 84
Tangent line, to a curve 65 184 202
Tangent plane 183 189—191 200
Tangent plane, in curvilinear coordinates 201 202
Tangent vector 157 177
Tangential component of acceleration 180 181
Taylor polynomials 273
Taylor series, in one variable 274 see
Taylor series, in several variables 276
Taylor series, of functions of a complex variable 395
Taylor's theorem 273 297 see
Taylor's theorem, for functions of one variable 273
Taylor's theorem, for functions of several variables 276 277
Taylor's theorem, proof of 297 407 408
Taylor's theorem, remainder in 274
Telescoping series 278
Tensor analysis 182
Term, of a sequence 23
Term, of a series 266
Terminal point of a vector 150
thermal conductivity 356 357
Thermodynamics 148
Torsion, radius of 181
Total differential 122 see
Trace, on a place 127
Transcendental functions 45 46
Transcendental numbers 6 13
Transformations 124 139 140
Transformations and curvilinear coordinates 139 140 160
Transformations, conformal 417
Transformations, Jacobians of 125 160
Transformations, of integrals 95 105—108 211—213 216—219
transforms see "Fourier transforms" "Laplace
Transitivity, law of 2
Trigonometric functions 46 96
Trigonometric functions, derivatives of 71
Trigonometric functions, integrals of 95 96
Trigonometric functions, inverse 44
Triple integrals 210 219—221
Triple integrals, transformation of 221—225
Triple products, scalar 155
Triple products, vector 155
Unbounded interval 5
Uniform continuity 48 58 63 119
Uniform convergence 269 270 287 288
Uniform convergence, of integrals 313 314
Uniform convergence, of power series 272
Uniform convergence, of sequences 269
Uniform convergence, of series 269 270
Uniform convergence, tests for integrals 313 314
Uniform convergence, tests for series 270
Uniform convergence, theorems for integrals 314
Uniform convergence, theorems for series 270 271 272
Uniform convergence, Weirstrass M test for see "Weirstrass M test"
Union of sets 12
Unit tangent vector 157
Unit vectors 152 342
Unit vectors, infinite dimensional 342
Unit vectors, rectangular 152
Upper bound 6
Upper bound, of functions 40 41
Upper bound, of sequences 24
Upper limit see "Limit superior"
Variable 5 39
Variable, change of, in differentiation 69
Variable, change of, in integration 95 105—108 211
Variable, complex 392 393 see
Variable, dependent and independent 40 116
Variable, dummy 94
Variable, limits of integration 94 186 194 313
Vector algebra 151 152 161—165
Vector analysis see "Vectors"
Vector field 156
Vector field, solenoidal 259
Vector functions 156
Vector functions, limits, continuity and derivatives of 156 171 172
Vector product see "Cross products"
Vector triple product 155 169—171
Vector, bound 150
Vector, free 150
Vectors 20 150—182
Vectors, algebra of 151 152 178
Vectors, axiomatic foundations for 155
Vectors, complex numbers as 20
Vectors, components of 153
Vectors, curvilinear coordinates and 161 162
Vectors, equality of 150
Vectors, infinite dimensional 342
Vectors, Jacobians interpreted in terms of 160
Vectors, length or magnitude of 150
Vectors, normalized 342
Vectors, null 151
Vectors, position 153
Vectors, radius 153
Vectors, resultant or sum of 151 163
Vectors, scalar product 153
Vectors, tangent 157 177 179
Vectors, unit 152 153 342
Velocity 74 177
Velocity, of light 181
Velocity, potential 402
Vibrating string, equation of 361
Volume 100
Volume of revolution, disk method 100
Volume of revolution, shell method 101
Volume, element of 161 162 175
Volume, of parallelepiped 161 169
Wallis' product 359
Wave equation 361
Weierstrass M test, for integrals 313 324—329
Weierstrass M test, for series 270 289
Wilson, E.B. 150
Work, as a line integral 239
x-axis 116
z-axis 116
z-axis, intercept 126
Zeno of Elea 265
Zero 1
Zero, division by 8
Zero, measure 91 103
Zero, vector 151
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