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Asmar N.H. — Partial Differential Equations with fourier series and boundary value problems
Asmar N.H. — Partial Differential Equations with fourier series and boundary value problems



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Название: Partial Differential Equations with fourier series and boundary value problems

Автор: Asmar N.H.

Аннотация:

This example-rich reference fosters a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material accessible even to readers with limited exposure to topics beyond calculus. Encourages computer for illustrating results and applications, but is also suitable for use without computer access. Contains more engineering and physics applications, and more mathematical proofs and theory of partial differential equations, than the first edition. Offers a large number of exercises per section. Provides marginal comments and remarks throughout with insightful remarks, keys to following the material, and formulas recalled for the reader's convenience. Offers Mathematica files available for download from the author's website. A useful reference for engineers or anyone who needs to brush up on partial differential equations


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second edition

Год издания: 2005

Количество страниц: 814

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$p$-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 $z$      646
Argument, function, constant on rays      653
Argument, function, translate      654
Argument, principal value of arg $z$      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 $\geq$0      209 239
Bessel function of order 0      200
Bessel function of the second kind      241 246
Bessel function, $J_{p}$, $p = \pm\frac{1}{2}$      120
Bessel function, $J_{p}$, $p$ 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$\acute{e}$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
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