|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Asmar N.H. — Partial Differential Equations with fourier series and boundary value problems |
|
|
|
| Предметный указатель |
 -periodic 11
Abel - Dirichlet test of convergence 95
Abel’s formula for the Wronskian A4 A9 A27
Abel’s kernel 555
Abel’s summation by parts formula 98
Advection equation 3 16
Aging spring problem 245
Airy’s differential equation A49
Almost periodic 23
Amplitude of normal mode 73
Analytic function 648
Analytic function and Cauchy - Riemann equations 649
Analytic function, defined by power series A29
Analytic function, examples of derivatives of 650
Analytic function, imaginary part of 649 651
Analytic function, properties of 651
Analytic function, real part of 649 651
Approximation in the mean 53
Approximation in the mean, best with Fourier series 59
Arccotangent see "Inverse cotangent"
Arctangent inverse tangent argument, function 653
Argument of complex number 646
Argument, function in Dirichlet problems 653
Argument, function, arg  646
Argument, function, constant on rays 653
Argument, function, translate 654
Argument, principal value of arg 646
Arithmetic average see "Average"
Associated homogeneous equation A5
Associated Legendre differential equation 271 272 282 321
Associated Legendre function 273 282
Associated Legendre function of negative order 319
Associated Legendre function, defined 319
Associated Legendre function, examples of 320
Associated Legendre function, order of 319
Associated Legendre function, orthogonality of 322
Associated Legendre function, Rodrigues’ formula for 319
Associated Legendre series 322
Asymptotic formula for Bessel function 264 342
Asymptotic formula for modified Bessel function 388
Average 30
Average temperature 152
Average, definite integral as an 57
Axisymmetric 199 270
Azimuthal angle 270
Backward difference approximation 524
Band limited function 547
Band limited function, approximation of functions by 554
Band limited function, example of 547
Band limited function, properties of 548
Band width 547
Basis 326
Beam 360
Beam, bending moment 361
Beam, clamped case 363
Beam, clamped-free case 365
Beam, curvature 361
Beam, simply supported case 360
Beam, transverse vibrations of 360 416 419
Bending moment 361
Bernoulli numbers 58 59
Bernoulli, Daniel (1700-1782) 13 237 346
Bessel - Fourier coefficient 253
Bessel coefficient 201 253
Bessel function 39 200 508
Bessel function and the heat equation 216
Bessel function and the Helmholtz equation 231
Bessel function and the wave equation 200 209
Bessel function integral identity 202 206 211 215 249
Bessel function integral representation 261 264
Bessel function of order  0 240 241
Bessel function of order  0 209 239
Bessel function of order 0 200
Bessel function of the second kind 241 246
Bessel function,  ,  120
Bessel function, , not an integer 240
Bessel function, asymptotic formula 264 265 342
Bessel function, definition as a series 239
Bessel function, derivatives involving 248
Bessel function, generated by Fourier series 263
Bessel function, identities involving 248 219
Bessel function, maximum and minimum of 257
Bessel function, modified 229 231 246
Bessel function, orthogonality of 250 252
Bessel function, orthogonality of with respect to a weight 330
Bessel function, recurrence relation 249
Bessel function, spherical 256 260
Bessel function, zeros of 250 265 268
Bessel series 201 210 213 252 508
Bessel series and the wave equation 201 210 213
Bessel series, defined 252
Bessel series, example of 253 238 263 264
Bessel series, Parseval’s identity for 332
Bessel series, representation theorem 253
Bessel, F. W. 237
Bessel’s equation 231 237
Bessel’s equation and the aging spring problem 245
Bessel’s equation and the Frobenius method A51
Bessel’s equation indicial equation 238
Bessel’s equation indicial root 238
Bessel’s equation with Robin condition 311
Bessel’s equation, general solution 242
Bessel’s equation, modified 229 230
Bessel’s equation, parametric form of 200 209 255
Bessel’s equation, regular singular point of 237
Bessel’s equation, solution using the Laplace transform 501
Bessel’s equation, solved by Frobenius method 237
Bessel’s inequality 56
Best approximation in the mean 59
beta function 248
Biharmonic equation 371
Biharmonic equation, cannot be separated 371
Biharmonic function 372
Biharmonic operator 371
Binomial formula 309
Binomial theorem 307
Bohr radiu,s 585
Bohr, Niels 586
Bonnet’s recurrence relation 309
Born, Max 574
Born’s statistical interpretation 574
Boundary condition 3 105
Boundary condition, decomposition of 183 184
Boundary condition, homogeneous 105
Boundary condition, linear 105
Boundary condition, radially symmetric 199
Boundary value problem 105
Branch cut 648
Buckling load 360
Buckling of columns 360 368
Buckling of columns, clamped-clamped case 368
Buckling of columns, clamped-free case 368
Buckling of columns, simply supported case 368
Cauchq sequence 98
Cauchy - Riemann equations 649
Cauchy - Schwarz inequality 593
Centered dillon-nce approximation 518 521
Centered second difference 533
Chain rule 651
Characteristic curve 6 108
Characteristic curve, the method of 5
Characteristic equation A10
Characteristic frequency 157
Characteristic interval 477
Characteristic line of the wave equation 130
Characteristic polynomial A10
Characteristic root A10
Characteristic triangle 477
Chebyshev polynomial 332 315
Chebyshev’s differential equation 315
| Compatibility condition 186 225 618 381
Complementary error function 427
Complete set of functions 173 18
Completeness property 98
Complex conjugate 615
Complex cosine function 647
Complex cosine function, derivative of 650
Complex cosine function, imaginary part of 647
Complex cosine function, real part of 647
Complex exponential function 67 647
Complex exponential function, as a conformal mapping 666
Complex exponential function, evaluating integrals with the 68
Complex exponential function, imaginary part of 617
Complex exponential function, periodicity of 67
Complex exponential function, real part of 647
Complex exponential system 65
Complex function, differentiable 618
Complex function, imaginary part 616
Complex function, real part 616
Complex logarithm, as a conformal mapping 669
Complex logarithm, branch cut of 618
Complex logarithm, continuity of 648
Complex logarithm, derivative of 650
Complex logarithm, imaginary part of 647
Complex logarithm, real part of 617
Complex number 645
Complex number, argument of 646
Complex number, conjugate of 645
Complex number, imaginary part of 645
Complex number, modulus of 615
Complex number, polar form of 646
Complex number, real part of 645
Complex sine function 647
Complex sine function, as a conformal mapping 667
Complex sine function, derivative of 650
Complex sine function, imaginary part 647
Complex sine function, real part 647
Conformal mapping 663
Conformal mapping and Green’s function 674 677 681
Conformal mapping and Laplace’s equation 664
Conformal mapping and separation of variables 669
Conformal mapping method 663
Conformal mapping of the disk onto itself 676
Conformal mapping of the disk onto the upper half-plane 678
Conformal mapping of the upper half-plane onto the disk 678
conjugate 6 15
Connected set 613
Conservation of energy 134
Convection coefficient 147 185 341 346 419
Convergence in the mean 55
Convergence, pointwise 85
Convergence, uniform 86
Convergence, weak 446
Convolution 402 421 194
Convolution integrability of 410
Convolution of generalized functions 455
Convolution of sequences 562
Convolution of step functions 456
Convolution of the indicator function 461
Convolution of two Dirac delta functions 456
Convolution with Dirac delta function 455
Convolution with Gauss’s kernel 421
Convolution with the Pois,son kernel 129
Convolution, basic properties 410
Convolution, commutative 103
Convolution, derivatives of 410
Convolution, Fourier transform of 404
Convolution, identity for 455
Cooley Tukey algorithm 546 564
Cooley, W. 564
Cosine Fourier transform, table of A68
Cosine integral function 397
Cosine series 50
Cosine series, solution of heat problems 147
Curvature of a beam 361
Curve 612
Curve of heat flow 657
Curve, closed 612
Curve, negative direction of 612
Curve, parametric 612
Curve, positive direction of 612
Curve, simple 612
Cylindrical coordinates 196
Damping 76
De la Vall e Poussin kernel, jo 5
De Moivre’s identity 68
DFT see "Discrete Fourier transform"
Diagonally dominant matrix 536
Differentiable complex function 648
Dirac delta function 446 496
Dirac delta function and Green’s function 635
Dirac delta function in Poisson’s equation 635
Dirac delta function integral involving the 115
Dirac delta function integration against the 497
Dirac delta function, as a derivative of stop function 148
Dirac delta function, as a unit for convolution 498
Dirac delta function, as a weak limit 446
Dirac delta function, convolution of two 456
Dirac delta function, derivative of higher order 452
Dirac delta function, Fourier transform of 451
Dirac delta function, Laplace transform of 497
Dirac delta function, translate of 117 497
Dirac delta function, two dimensional 635
Direction field 6
Directional derivative 5
Dirichlet - Neumann problem 141
Dirichlet condition 180
Dirichlet kernel 78
Dirichlet kernel, complex form of 84
Dirichlet kernel, Fourier coefficient of 84
Dirichlet kernel, properties of 83
Dirichlet kernel, representation of Fourier series using 78
Dirichlet problem 164 216
Dirichlet problem in a ball 275 286
Dirichlet problem in a box 169
Dirichlet problem in a cylinder 228
Dirichlet problem in a disk 216 373
Dirichlet problem in a disk, solution 218
Dirichlet problem in a horizontal strip 666
Dirichlet problem in a quadrant 665
Dirichlet problem in a rectangle 164 533
Dirichlet problem in a semi-infinite vertical strip 667
Dirichlet problem in a sphere 275 286
Dirichlet problem in a sphere with symmetry 274 290
Dirichlet problem in a wedge 222
Dirichlet problem in a wedge, Fourier series solution 168
Dirichlet problem in annular region 226
Dirichlet problem in circular regions 669
Dirichlet problem in cylindrical coordinates Dirichlet problem in cylindrical coordinates, solution 228 229
Dirichlet problem in the upper half-plane 429 643
Dirichlet problem, between two concentric spheres 280 291
Dirichlet problem, decomposition into subproblems 167
Dirichlet problem, outside a disk 225
Dirichlet problem, outside a sphere 280
Dirichlet problem, product solution in a rectangle 180 184
Dirichlet problem, solution by conformal mapping 663 664
Dirichlet problem, solution by the eigenfunction expansions method 177
Dirichlet problem, solution of biliarmonic equation 373
Dirichlet problem, solution using Green’s function 630
Dirichlet problem, solution with spherical harmonics 286
Dirichlet problem, uniqueness of solution 192 618 626
Dirichlet test 95
Dirichlet test and uniform convergence 95
Dirichlet test for complex series 100
Dirichlet test, applied to Fourier series 97
Dirichlet test, applied to Legendre series 318
Dirichlet, Peter Gustave Lejeune, (1805-1859) 392
Dirichlet’s principle 622
Discrete Fourier Transform 559
Discrete Fourier transform and Fourier series 572
|
|
|
| Реклама |
|
|
|
|
|
О проекте