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| Ïîèñê ïî óêàçàòåëÿì |
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| Hanna J.R., Rowland J.H. — Fourier Series, Transforms, and Boundary Value Problems |
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| Ïðåäìåòíûé óêàçàòåëü |
Long elastic string 307 314
M-test, Weierstrass, uniform convergence of integrals 102—103
M-test, Weierstrass, uniform convergence of series 91—92
Mean convergence 66
Mean, approximation in 64 66
Mellin transforms 215
Membrane, vibrating 273—276
Membrane, vibrating, BVP for 276
Membrane, vibrating, PDE for 276
Method of Frobenius 13—18
Modified Bessel functions 121
Modulus of elasticity 230
Neumann problem 248
Newton’s Second Law 220 270
Nonhomogeneous ODE 6
Normalized functions 43
Normalized vectors 42
Norms of Bessel functions 135—137
Norms of functions 43
Norms of Legendre polynomials 153 163
Norms of vectors 40
Numerical differentiation formulas, centered difference approximations 22
Numerical differentiation formulas, forward difference approximations 22
Numerical differentiation formulas, forward difference operator 200
Numerical solutions of differential equations 19—20 241—242
Odd functions 77
One sided, derivatives 69—70
One sided, limits 68
Operators 1—2
Operators, adjoint 58
Operators, Euler (Cauchy) 7—8
Operators, linear 1—2
Operators, product of 2
Operators, self-adjoint 58
Operators, sum of 1
Ordinary differential equations (odes) 2
Ordinary differential equations (ODEs), homogeneous 2
Ordinary differential equations (ODEs), linear 1
Ordinary differential equations (ODEs), nonhomogeneous 6
Ordinary point 10
orthogonal series 61—62
Orthogonal sets of Bessel functions 134—137
Orthogonal sets of functions 43
Orthogonal sets of Legendre polynomials 152—153
Orthogonal sets, complete 65—66
Orthogonal sets, Gram — Schmidt process 45
Orthogonality 40 43
Orthogonality of eigenfunctions 50
Orthogonality of functions 43
Orthogonality of vectors 40—42
Orthogonality, Hermitian 47—48
Orthogonality, relative to weight functions 48—49
Oscillations, electrical 271
Oscillations, mechanical 270
Parabolic type PDEs 23—24
Parseval’s identity 66
Partial differential equations (PDEs) 1 23—24
Partial differential equations (PDEs) for elastic bar 231
Partial differential equations (PDEs) for membrane 276
Partial differential equations (PDEs) for vibrating string 221—222
Partial differential equations (PDEs) of diffusion 238
Partial differential equations (PDEs), definition 23
Partial differential equations (PDEs), general linear, of second order 23
Partial differential equations (PDEs), general solutions 23 29—35
Partial differential equations (PDEs), linear types 23—24
Partial fractions 174—175
Partial fractions, Heaviside expansion formula 175—176
Periodic boundary conditions 53
periodic extension 74 78
Periodic functions 53 179 200
Piecewise continuous (PWC) functions 68
Piecewise smooth (PWS) functions 70
Plucked string problem 234
Pointwise convergence 59
Polynomial, associated 162—163
Polynomial, Hermite 49
Polynomial, Lauguerre 49
Polynomial, Legendre 143—144
Potential for a sphere 267
Potential, electric 247
Potential, gravitational 246—247
Potential, magnetic 247
Principal value, of improper integrals 113—114
Principle of superposition of solutions 4 224
Pseudo-norm 198
Recursion formula 10
Regular Sturm — Liouville problem 50
Right hand, derivative 69
Right hand, limit 68
Rodrigues’ formula 146—148
Root of unity 203
Runge — Kutta formula 19—20
Sawtooth function 88
Schwarz inequality 46
Self-adjoint operator 58
Semi-infinite bar, temperature in 295—296
Semi-infinite string 307
Separation of variables, method of 35—36 219
Series of Bessel functions 138—139
Series of Legendre polynomials 154—155
Series solutions 8—13
Series solutions, Frobenius 13—18
| Series solutions, Power 8—9 18
Series solutions, Taylor 18
Series, differentiation 9 92—94
Series, Fourier — Bessel 137—139
Series, Fourier, basic 72—73
Series, Fourier, generalized 107—108
Series, Frobenius 13—18
Series, integration of 94—96
Series, orthogonal 61—62
Series, orthonormal 62
Series, power 8—9 18
Series, Sturm — Liouville 62
Series, superposition of solutions by 4
Series, Taylor 18
Series, trigonometric 74
Singular points 10 14 54
Singular points, regular and irregular 14
Singular SLPs 54
Specific heat 236
Spherical coordinates 142 158
Spherical coordinates, Laplacian in 160—161
Spherical regions, potential in 267
Spherical regions, steady state temperature in 238
Spring problem 270
Square integrable (SI) 64
Square wave function 86
Stability 25
Steady state temperatures 238 248 253 256 263—264 268—269
Steady state temperatures in hemisphere 268
Steady state temperatures in semicircular cylinder 256—257
Steady state temperatures in sphere 264
Steady state temperatures in square plate 248
Step-size 241
String, vibrating 219—222
Struck string problem 234
Sturm — Liouville differential equations (SLDEs) 50
Sturm — Liouville differential equations (SLDEs), regular 50
Sturm — Liouville differential equations (SLDEs), singular 54
Sturm — Liouville problems (SLPs) 50
Sturm — Liouville problems (SLPs), periodic 53
Sturm — Liouville problems (SLPs), regular 50
Sturm — Liouville problems (SLPs), singular 54
Sturm — Liouville series 62
Sufficiency 169
Superposition of solutions by integrals 297
Superposition of solutions by series 4 224
Surface, insulated 238 245—246 248 252—254 256
Taylor series 18 61 65
Tchebysheff polynomials of first kind 48
Tchebysheff polynomials of second kind 49
Tchebysheff, first kind 48
Tchebysheff, second kind 49
Temperature in bar 238 245—246
Temperature in circular disk 254
Temperature in infinite bar 297 303—304
Temperature in semi-infinite bar 295—296 302 305
Temperature in semicircular cylinder 256—257
Temperature in sphere 264
Temperature in square plate 248 252—253
Tensile force, on string 219—221
Tension, in membrane 274—276
Termwise, differentiation 9 59 61 92—94
Termwise, integration 59 61 94—96
thermal conductivity 236
Total square error 64
transforms (see “Integral transforms”)
Trigonometric functions 46—47
Trivial solution 50 52
uniform convergence of Fourier series 89—92
Uniform convergence of improper integrals 102—103
Uniform convergence of series 58—60
Uniform convergence, Abel’s test for 243
Uniqueness of solutions of Cauchy problem 25
Uniqueness of solutions of heat problem 244—245
Uniqueness of solutions of IVPs 2—3
Uniqueness of solutions of vibrating string problem 227—228
Unit step function of Heaviside 175—176
Variation of parameters 14
Vectors, orthogonal 40
Vectors, orthonormal 42
Vectors, position 41
Vectors, rectangular 273—276
Vectors, reference set of 42
Vectors, unit 40
Vibrating membrane, circular 280
Vibrating rod 230—231
Vibrating string 219—222 283
Vibrating string, end conditions 228 283
Vibrating string, equation of 221—222
Vibrating string, initially displaced 221—222
Vibrating string, model for 219—222
Vibrating string, semi-infinite 307—310
Vibrating string, with external force 283
Volterra integral equation 184
Wave equation 221—222
Weierstrass M-test for 59—60 91 102—103
Weierstrass M-test for uniform convergence 58—60 102—103
Weierstrass M-test of integrals 102—103
Weierstrass M-test of series 58—60 242
Weight functions 48—49 53
Well posed problem 25
wronskian 3 56—57
Zeros of Bessel functions 134—137
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