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Franklin P. — Fourier Methods
Franklin P. — Fourier Methods

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Название: Fourier Methods

Автор: Franklin P.

Язык: en

Рубрика: Математика/Анализ/Дифференциальные уравнения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1949

Количество страниц: 289

Добавлена в каталог: 09.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute value      12
Algebra of complex numbers      1
Analytic functions      124
Analytic functions, derivatives of      4
Average power      50(30) 62 64(29—33) 80
Average value      48 55(27)
Average value of a periodic function      58
Average value of a trigonometric product      60
Average value, less than rins      50(31)
Average velocity      55(26)
Ber and bei      140(17)
Bessel’s equation      125(15)
Bessel’s functions      125(15—21) 143 17)
Boundary value problems      147
Cabin, electric      132 170 175(7—15)
Capacity      30
Catenary      27(29—33)
Characteristic impedance      130(7) 250
Characteristic output current      89(12 14)
Circuits, electric      29
Circuits, electric, fundamental      39
Circuits, electric, solved by transforms      232
Circuits, mechanical      30
Circuits, mechanical, solved by transforms      241(12—17)
CIS      17
Complementary function      34 40
Complex cmf      30 40
Complex current      30 40
Complex Fourier series      90
complex numbers      1 15
Complex numbers, powers of      16
Complex numbers, roots of      17 19(37) 27(27)
Complex plane      15
Convolution      98(15—17) 213 214(40)
Curl      137 139
Current, complex      36 40
Current, complex, steady-state      30 40 173
Current, complex, transient      30 40 173
Cutoff angular frequency      195(3)
Cylindrical coordinates      130
De Moivre’s Theorem      17
Dead systems      204 217 237 244
Delayed unit-step function      258
Derivatives, for complex values      4
Derivatives, for complex values, partial      102
Derivatives, for complex values, partial, transforms of      244 203(0 7)
Derivatives, for complex values, transforms of      202 203
Differential equations      31 37
Differential equations, partial      100 147 244
Differential equations, partial, solved by integrals      168(26—32)
Differential equations, partial, solved by series      147
Differential equations, partial, solved by transforms      244 249
Differential equations, solved by integrals      93
Differential equations, solved by transforms      208 217 220
Diffusion      102
Distortionless line      135(3—5)
Distributed constants      133 249
Divergence      137 139
Driving point impedance      238
e, $\epsilon$      32
Elect ostatic field      139
Electric cable      132 170 175(7—15)
Electric circuits      29
Electric circuits, fundamental      39
Electric circuits, solved by transforms      232
Electric network      37
Electric network, solved by transforms      237
Electric scalar potential      139
Electricity, flow of      132
Electromagnetic waves      141 144(8—13)
Electromotive force (cmf), complex      36 40
electromotive force (EMF)      29
emf      see “Electromotive force”
erf      169(30—32)
Error function      169(30—32)
Even function      51 80
Even-harmonic function      77 80
Exponential function      2 6
Faltung      98(15)
Final value theorem      216(55 59)
Finite transmission line      256 266(30—49)
Flow, of electricity      132
Flow, of electricity, of heat      100 149
Forced vibrations      31
Fourier coefficient formula      68 73 75 78
Fourier coefficient formula, complex      90
Fourier cosine series      74
Fourier integral      91 168(20—32)
Fourier integral theorem      92
Fourier series      68
Fourier series, complex      80
Fourier series, half-range      73
Fourier sine series      75
Fourier transform      93
Fourier’s theorem      69
Full-wave rectifier      55(22) 81(20)
Functions, analytic      4 124
Functions, analytic, Bessel’s      125(15—21) 143(3 17)
Functions, analytic, complementary      34 40
Functions, analytic, delayed unit-step      258
Functions, analytic, error      169(30—32)
Functions, analytic, even      51 80
Functions, analytic, even-harmonic      77 80
Functions, analytic, exponential      2 6
Functions, analytic, Gudermannian      11 (31—37)
Functions, analytic, hyperbolic      7 11
Functions, analytic, hyperbolic, inverse      25
Functions, analytic, logarithmic      12
Functions, analytic, odd      52 80 167(20)
Functions, analytic, odd-harmonic      70 80 107(20)
Functions, analytic, periodic      57
Functions, analytic, piecewise regular      87
Functions, analytic, rational      220
Functions, analytic, regular      87
Functions, analytic, theta      175(9 10 15)
Functions, analytic, trigonometric      2 7
Functions, analytic, trigonometric, inverse      19
Functions, analytic, unit-step      200 258
Fundamental electric circuits      39
Gibbs’s phenomenon      71
Gradient      139
Gudermannian      11(31—37)
Half-range Fourier series      73
Half-wave rectifier      55(23) 72(28) 82(27)
Hammered musical string      181(10 19)
Harmonic analysis      83
Heat flow      100 149
Heaviside expansion      231(33—38)
Heaviside’s operational calculus      108
Hollow wave guides      112 115(11 15) 190 104(1—11)
Hyperbolic functions      7 11
Hyperbolic functions, inverse      25
i      1 32
i. j, k      113(13) 138
Im      32
Imaginary part      32
Imaginary unit      1
Impedance      33 —11
Impedance, characteristic      130(7) 250
Impedance, driving point      238
Impedance, total      238
Impedance, transfer      235 237
Impedances in parallel      13(17) 238
Impulse      212(17)
Inductance      30
Inductance, mutual      44(20)
Initial value theorem      215(51 56 58)
Inlinite transmission line      251 200 (24—20)
Integrals, transforms of      203
Inverse hyperbolic functions      25
Inverse trigonometric functions      10
j      32
Jacobi’s theta function      175(9 10 15)
Kirchhoff’s laws      37 41
Laplace transforms      95 198
Laplace transforms, table of      210 (see also “Transform solution”)
Laplace’s equation      103 120 140 148
Laplace’s equation in cylindrical coordinates      130
Laplace’s equation in spherical coordinates      130
Light, velocity of      142
ln      12
Logarithmic function      12
Lossless transmission line      134 183 240
Lumped constants      20 238 249 252
MaeLaurin’s series      2 124
MaeLaurin’s series, expansion by      257 207(31)
MaeLaurin’s series, summation by      153(12 14) 100(12)
Magnetic scalar potential      140
Maxwell’s equations      138 190
Mechanical system      30 —15(24—28)
Mechanical system, solved by transforms      211(12—17)
Mutual inductance      1—1(20)
Natural logarithm      12
Odd function      52 80 107(20)
Odd-harmonic function      70 80 107(20)
Operational calculus      108
Palse, rectangular      67 71(22)
Parallel impedances      43(17) 238
Partial derivatives      102
Partial derivatives, transforms of      244 263(6 7)
Partial differential equations      100 147 244
Partial differential equations, direct integration of      106 109(16—27)
Partial differential equations, formed by elimination      110
Partial differential equations, Laplace      see “Laplace’s equation”
Partial differential equations, linear      113(13 17) 115 118(11—13)
Partial differential equations, particular solution of      119
Partial differential equations, transform solution of      244 249
Partial fractions      220
Particular integral      32
Periodic functions      57
Piecewise regular function      67
Plucked musical string      180(5 15)
Poisson’s equation      140
Poisson’s integral      159(9)
Power transmission line      136(6—11)
Power, average      56(30) 62 64(29—33) 90
Powers of complex numbers      16
Radiation from an antenna      142
Radio equations      134 135(1 2) 183
Re      32
Reactance      33
Real part      32
Rectangular pulse      67 71
Rectifier, full-wave      55(22) 81(26)
Rectifier, full-wave, half-wave      55(23) 72(28) 82(27)
Regular function      67
Regular function, piecewise      67
Resistance      30
RMS      50
rms, exceeds average      56(31)
Root mean square      50
Roots of complex numbers      17 19(37) 27(27)
Rotating vectors      19(36)
Schedule of harmonic analysis      86
Skin effect      143 145(16 17)
Solution, steady-state      163 172
Solution, steady-state, transient      163 172
Spherical coordinates      130
Spherical waves      131(9—11)
Steady-state current      36 40 173
Steady-state solution      163 172
String      see “Vibrating string”
Substitution property      205 217(60 61)
Table, for harmonic analysis      86
Table, for harmonic analysis, of Laplace transforms      210
Telegraph equations      134 170
temperatures      100 148
Temperatures in a plate      149 155
Temperatures in a rod      160 167(16—32)
thermal conductivity      101
Theta function      175(9 10 15)
Total impedance      238
Transfer impedance      235 237
Transform solution      198
Transform solution of differential equations      208 217 220
Transform solution of differential equations, partial      244 249
Transform solution of electric circuits      232
Transform solution of electric networks      237
Transform solution of mechanical systems      241 (12—17)
Transform solution of transmission lines      249
Transform solution of transmission lines, finite      256 266(30—49)
Transform solution of transmission lines, infinite      251 266(24—29)
Transforms, Fourier      93
Transforms, Fourier, Laplace      95 198
Transforms, Fourier, Laplace, table of      210
Transient current      36 40 173
Transient response      237
Transient solution      163 172
Translation property      200
transmission line      133
Transmission line, distortionless      135(3—5)
Transmission line, long      170
Transmission line, lossless      134 183 249
Transmission line, power      136(6—11)
Transverse electric wave      194(1—3)
Transverse magnetic wave      195(4 5)
Traveling waves      128 253 259
Traveling waves, damped      135(4 5) 249
Trigonometric functions      2 7
Trigonometric functions, inverse      19
Trigonometric products      60
Trigonometric, identities      1
Unit impulse      242(17)
Unit vectors      113(13) 138
Unit, imaginary      1 32
Unit-step function      200 258
Unit-step function, delayed      258
Vector differential operators      137 139
Vectors, representing complex numbers      15
Vectors, representing complex numbers, rotating      19(36)
Vectors, representing complex numbers, unit      113(13) 138
Velocity, average      55(26)
Velocity, average, of light      142
Vibrating membrane      129 132(12)
Vibrating string      127 131(4 6) 176 181(12—19)
Vibrating string, hammered      181(10 19)
Vibrating string, plucked      180(5 15)
Vibrations, forced      31
Wave equation      129 142 176 181(12—19)
Wave guides      142 145(14 15) 190 194(1—11)
Waves, electromagnetic      141 144(8—13)
Waves, electromagnetic, dumped      135(4 5) 249
Waves, electromagnetic, spherical      131(9—11)
Waves, electromagnetic, transverse electric      194(1—3)
Waves, electromagnetic, transverse magnetic      195(4 5)
Waves, electromagnetic, traveling      128 253 259
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