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| Авторизация |
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| Franklin P. — Fourier Methods |
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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,  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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