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Hanna J.R., Rowland J.H. Ч Fourier Series, Transforms, and Boundary Value Problems
Hanna J.R., Rowland J.H. Ч Fourier Series, Transforms, and Boundary Value Problems

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Ќазвание: Fourier Series, Transforms, and Boundary Value Problems

јвторы: Hanna J.R., Rowland J.H.

јннотаци€:

This volume introduces Fourier and transform methods for solutions to boundary value problems associated with natural phenomena. Unlike most treatments, it emphasizes basic concepts and techniques rather than theory. Many of the exercises include solutions, with detailed outlines that make it easy to follow the appropriate sequence of steps. 1990 edition.


язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

»здание: Second Edition

√од издани€: 1990

 оличество страниц: 354

ƒобавлена в каталог: 28.03.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Abbreviations, $N_{0}$ (set of natural numbers plus zero)      45
Abbreviations, AbelТs uniform convergence test      243
Abbreviations, AI (absolutely integrable)      107
Abbreviations, BVP* (boundary value problem)      1
Abbreviations, DFT* (discrete Fourier transform)      198
Abbreviations, FFT* (fast Fourier transform)      203
Abbreviations, IVP* (initial value problem)      2
Abbreviations, M (any set of n consecutive integers)      199
Abbreviations, N (set of natural numbers)      43
Abbreviations, ODE* (ordinary differential equation)      1
Abbreviations, PDE* (partial differential equation)      1
Abbreviations, PWC (piecewise continuous)      68
Abbreviations, PWS (piecewise smooth)      70
Abbreviations, SI (square integrable)      64
Abbreviations, SLDE* (Sturm Ч Liouville differential equation)      50
Abbreviations, SLP* (Sturm Ч Liouville problem)      50
Abbreviations, Z (set of all integers)      48
Absolutely integrable (AI)      107
Adjoint of operator      58
AiryТs equation      18
Approximation in mean      64 198Ч202
Arbitrary constants      1 6 11Ч12
Arbitrary functions      23 26 33
Associated Legendre differential equation      162
Associated Legendre functions      164
Associated Legendre polynomials      163
Auxiliary equation      5
Basic Fourier Series      72Ч74
bernoulli      68
Bessel equation      16 117
Bessel equation, modified type      121
Bessel equation, Sturm Ч Liouville type      134Ч135
Bessel functions      18 117 119
Bessel functions, boundedness of      132
Bessel functions, derivatives of      124Ч125
Bessel functions, first kind      18 119
Bessel functions, generating functions for      130
Bessel functions, graphs of      122
Bessel functions, integral form for      130Ч132
Bessel functions, integrals of      127Ч129
Bessel functions, modified      121
Bessel functions, norms      137
Bessel functions, orthogonal sets of      135 137
Bessel functions, second kind      121
Bessel functions, series of      137Ч139
Bessel functions, zeros of      134Ч137
Bessel transforms      210
BesselТs inequality      65
boundary conditions      2 24 219
Boundary conditions, Churchill type      248
Boundary conditions, Dirichlet type      247
Boundary conditions, linear homogeneous      219 222Ч225
Boundary conditions, Neumann type      248
Boundary conditions, nonhomogeneous      219 225
Boundary conditions, Robin type      248
Boundary value problems (BVPs)      1 24 219 270
Boundary value problems (BVPs), boundedness of solutions      36 222
Boundary value problems (BVPs), defined      24
Boundary value problems (BVPs), methods for solving      173 186 219 222Ч225 270Ч273 283Ч285 307-310
Boundary value problems (BVPs), solutions verified      225Ч228 242Ч245
Cauchy equation      7
Cauchy principal value      113Ч114
Cauchy Ч Kowalewsky theorem      25
Characteristic equations      5 8 27Ч31
Characteristic functions      50
Characteristic values      50
Classification, second order PDEs      23Ч24
Complete orthogonal sets      65Ч66
Complex conjugate      46Ч47 198
Complex-valued functions      46Ч47
Conduction of heat      236Ч238
Conductivity, thermal      236
Continuous functions      45 59
Continuous functions, piecewise (PWC)      68
Continuous functions, sectionally      68
Convergence in mean      64 66
Convergence of Fourier cosine series      78Ч79
Convergence of Fourier integrals      108
Convergence of Fourier series      75Ч76
Convergence of Fourier sine series      79
Convergence, point wise      66
Convergence, point wise, uniform, integrals      102Ч103
Convergence, point wise, uniform, series      58Ч59
Convolution      180Ч181
Convolution for Fourier exponential transforms      192Ч193
Convolution for Laplace transforms      180Ч181
Convolution for Mellin transforms      217
Cylindrical coordinates      140
Cylindrical coordinates, Laplacian in      141
Derivative, left hand      69
Derivative, right hand      69
Differential equations, Cauchy (Euler)      7
Differential equations, linear      2
Differential equations, linear homogeneous      2
Differential equations, nonhomogeneous      6
Differential equations, ODEs      1
Differential equations, PDEs      1
Differential equations, systems of      185
Differential operator      2
Differentiation of series      9 92Ч94
Diffusion, coefficient of      238
Diffusion, equation      238
Dirac delta function      177Ч179
Dirichlet problem      247Ч248
Discrete Fourier Transform      197Ч203
Discrete inner product      198
Discrete least squares approximation      198
Discrete norm      198
DТAlembert      68
dТAlembert solution of      28 34
dТAlembertТs solution      28 34
Eigenfunctions      50
Eigenfunctions, linear independence of      57
Eigenfunctions, series of      61 62
Eigenvalues      50
Elasticity, modulus      230
electrical circuits      271 273
Elliptic type, PDEs of      23Ч24
Error function      183 301Ч305
Euler      7 68
Euler, constant      120Ч121
Euler, differential equation      7
Euler, formulas      74
Euler, identity (relation)      32 112
Even function      76Ч77
Existence      2 25 169Ч170
Exponential, Fourier integrals      112Ч114
Exponential, Fourier series      80Ч82
Exponential, Fourier transforms      190 192
Exponential, function      5Ч6 30Ч31 46-48
Exponential, order      169
Exponential, solutions      5Ч6 30Ч31
Extension, nonperiodic      111
Extension, periodic      74 78
Fast Fourier Transform      203Ч205
Finite difference formulas      200
Finite difference method      241Ч242
Forward difference method      242
FOURIER      68
Fourier method of solution      222Ч225
Fourier method of solution, two dimensional      276Ч280
Fourier series      72Ч74
Fourier series in two variables      97Ч99
Fourier series, convergence      75Ч79
Fourier series, cosine      78
Fourier series, differentiation      92Ч94
Fourier series, exponential form      80Ч81
Fourier series, generalized      62
Fourier series, integration      94Ч96
Fourier series, sine      78Ч79
Fourier series, uniform convergence of      89Ч92
Fourier sine integral formula      110
Fourier sine integral formula, theorem      75Ч76
Fourier sine integral formula, transforms of two variables      208Ч209
Fourier sine integral formula, transforms, cosine kernel      191
Fourier sine integral formula, transforms, exponential kernel      192
Fourier sine integral formula, transforms, sine kernel      191
Fourier Ч Bessel series      137Ч139
Fourier, constants (coefficients)      62Ч65 73Ч74 78Ч79 81
Fourier, cosine form      109Ч110
Fourier, cosine kernel for      189
Fourier, exponential form      112Ч113
Fourier, exponential kernel for      190
Fourier, finite transforms      189Ч190
Fourier, integral formula      107Ч108
Fourier, integral theorem      108 110Ч111
Fourier, method      219 270
Fourier, sine form      110
Fourier, sine kernel for      189
Functions, analytic      10 25
Functions, associated      164
Functions, Bessel      18 119Ч121
Functions, characteristic      50
Functions, complex-valued      46Ч47
Functions, continuous      45Ч46 59
Functions, error      183 301Ч305
Functions, even      76Ч77
Functions, exponential      5Ч6 30Ч31 46-48
Functions, gamma      117Ч119 170
Functions, generating for Bessel functions      130Ч132
Functions, generating for Legendre polynomials      149Ч151
Functions, harmonic      161 248
Functions, hyperbolic      47
Functions, inner product of      43 198
Functions, Legendre      144
Functions, normalized      43
Functions, norms of      43 198
Functions, odd      76Ч77
Functions, orthogonal      43
Functions, orthonormal      43
Functions, piecewise continuous      68Ч70
Functions, piecewise smooth      70
Fundamental interval      74
Fundamental set      4
Gamma function      117Ч119 170
Gauss Ч Seidel method      251Ч252
General solution      4 6 28Ч33
Generalized Fourier series      62
Generalized functions (or distributions)      179
Geometric series (progressions)      180 199
Gibbs phenomenon      86Ч88
Gram Ч Schmidt orthogonalization      44Ч45
Hadamard example      25Ч26
Hankel transforms      209Ч212
Harmonic analysis      82Ч84 198Ч202
Harmonic functions      161 248
Harmonic functions in cylindrical regions      260Ч263
Harmonic functions in half-plane      312
Harmonic functions in rectangular regions      248Ч251
Harmonic functions in spherical regions      267Ч268
Harmonic functions in strip      313Ч314
Heat conduction, equation      238
Heat conduction, experimental observations      236
Heat conduction, flow      236
Heat conduction, problem      236Ч238
Heat conduction, problem, solution      238Ч241
Heat conduction, problem, uniqueness      244Ч245
Heat conduction, problem, verification      242Ч244
Hermite polynomials      49
Hermitian orthogonality      47Ч49
Homogeneous equations      2 5Ч7 23
HookeТs law      270
Hyperbolic functions      47
Hyperbolic type, PDEs of      23Ч24
Improper integral, principal value of      113Ч114
Improper integral, uniform convergence of      102Ч103
Indicial equation      14
Indicial equation, roots of      14
Inequality, BesselТs      65
Inequality, Schwarz      46
Initial value problems (IVPs)      2Ч3 24
Inner product      40 43 198
inner product of functions      43
Inner product of vectors      40
Insulated surface      238 245 254 291
Integral equation      184
Integral form, BesselТs function      130Ч132
Integral theorem, Fourier      108
Integral transforms      168 189 191 208Ч210 214Ч215
Integral transforms, Fourier      191
Integral transforms, Fourier, cosine      191
Integral transforms, Fourier, exponential      192
Integral transforms, Fourier, finite      189Ч190
Integral transforms, Fourier, finite, cosine      189
Integral transforms, Fourier, finite, exponential      190
Integral transforms, Fourier, finite, sine      189
Integral transforms, Fourier, sine      191
Integral transforms, Fourier, two variables      208
Integral transforms, Hankel      209Ч210
Integral transforms, Hankel, finite      210
Integral transforms, kernels of      210
Integral transforms, Laplace      168
Integral transforms, Legendre      214
Integral transforms, Mellin      215
Integrating factor      50
Integration of series      94Ч96
Integro-differential equations      184
Interpolation      202
Inverse transforms      173 189Ч192 198 208Ч211 214 217
Jump discontinuity      69
Kernel      168
Kirchhoff s Law      271
LagrangeТs relation      58
Laguerre polynomials      49
Laplace transforms      168
LaplaceТs equation      247
Laplacian in cylindrical coordinates      141
Laplacian in rectangular coordinates      247
Laplacian in spherical coordinates      160Ч161 164
Least squares approximation      64Ч66
Left hand, derivative      69Ч70
Left hand, limit      68Ч69
Legendre, equation      12 142
Legendre, functions of second kind      164
Legendre, functions, associated      164
Legendre, polynomials      142 144
Legendre, polynomials, associated      162Ч163
Legendre, polynomials, derivatives of      148 151
Legendre, polynomials, generating functions      149
Legendre, polynomials, norms      153Ч154
Legendre, polynomials, orthogonal sets of      152Ч153
Legendre, polynomials, RodriguesТ formula      146Ч148
Legendre, polynomials, series of      154Ч155
Legendre, transforms      214Ч215
Liebmann method      251Ч252
Limits in the mean      64 66
Limits, one sided      68
Linear combinations      2 4
Linear combinations, extensions of, by integrals      111 297
Linear combinations, extensions of, by series      74 78 224Ч225 229 240 250
Linear dependence (independence)      3
Linear dependence (independence) of eigenfunctions      57
Linear dependence (independence) of functions      3
Linear differential equations      2 4Ч6 23
Linear operators      1Ч2
Linear operators, adjoint of      58
Linear operators, product of      2
Linear operators, self-adjoint      58
Linear operators, sum of      1
Liouville (Sturm Ч Liouville problem)      50
1 2
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