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Pipes L.A. — Applied Mathemattics for Engineers and Physicists
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Название: Applied Mathemattics for Engineers and Physicists
Автор: Pipes L.A.
Аннотация: There has been a great impetus given during the last few years to the application of mathematical analysis for the solution of technical problems. This interest in the use of mathematics by the technologist is a result. of the remarkable developments that have appeared in the various branches of engineering and physics as a result of close collaboration of theory and experiment in the research laboratories of industrial plants and elsewhere. A half a century ago, engineers regarded the differential and integral’calculus as a mystery beyond the reach of the majority. However, at present, the engineering student takes the calculus in his stride. The use of complex quantities in the solution of electrical and mechanical problems has brought the engineer to at least a superficial study of the rudiments of the complex variable. Other studies of the
behavior of systems of technical importance have ushered in matrix algebra,. operational methods, the study of orthogonal functions, partial differential equations, and other mathematical techniques into the required mathematical equipment of a person who uses mathematics to solve-technical problems of various kinds, such as acoustical, electric矶,aeronautical, mechanical, thermal, etc.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
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Издание: 1st edition
Год издания: 1946
Количество страниц: 618
Добавлена в каталог: 26.09.2009
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Предметный указатель
Algebra, fundamental laws of 110
Algebra, fundamental laws of of operators 239
Algebra, fundamental laws of, fundamental theorem of 467
Algebra, fundamental laws of, matrix 191
Alternating currents 161
Analogues, table of 165
Beam, clamped, deflection of 218
Beam, clamped, deflection of, deflection of, by transverse forces 217
Beam, clamped, deflection of, on elastic foundation, deflection of 220
Beam, clamped, deflection of, vibration of 224
Beats 63 177
Ber and Bei functions 318
Bessel functions, expansion in series of 318
Bessel functions, expansion in series of for small values of argument 312
Bessel functions, expansion in series of of half an odd integer order 314
Bessel functions, expansion in series of of second kind 311
Bessel functions, expansion in series of of third kind 316
Bessel functions, expansion in series of, modified 317
Bessel functions, expansion in series of, recurrence formulas for 313
Bessel’s differential equation 307
Bessel’s differential equation, equivalent forms of 316
Bessel’s differential equation, solution of, by scries 308
beta function 302
Beta function, connection of, with gamma function 303
Calculus of variations 292
Cartesian coordinates 187
Cauchy — Riemann equations 448
Cauchy’s integral formula 455
Cauchy’s integral test 7
Cauchy’s integral theorem 452
Cauchy’s ratio test 8 12
Cauchy’s residue theorem 460
Channel, flow out of 508
Charged plate, field of 496
Chio, F. 74
Circuits, coupled by a condenser 154
Circuits, coupled by a condenser with mutual inductance 151
Circuits, coupled by a condenser, electrical 141
Circuits, coupled by a condenser, electrical forced oscillations of 146
Circuits, coupled by a condenser, filter 255
Coefficients, elastance 158
Coefficients, elastance, inductance 158
Coefficients, elastance, resistance 158
Collar, A. R. 191 197
Column, buckling of 223
Comparison Test 5
Complex conjugate 166
Complex numbers (see Numbers) Components, symmetrical 89
Composite functions, differentiation of 272
Condenser, charge on 488
Condenser, charge on, charging of 150
Condenser, charge on, circuits coupled by 154
Condenser, charge on, cylindrical 486
Condenser, charge on, elliptical 492
Condenser, charge on, parallel plate 508
Conductor, charge on 488
Conformal representation 480
Conjugate functions 479
Conjugate functions, application of, to hydrodynamics 515
Conjugate functions, solution of potential problems by method of 478
Conjugate imaginary 53
Conjugate, complex 166 205
Conservative systems 186 204
Conservative systems, small oscillations of 188
Contour, indentation of 472
Convergence, absolute 10
Convergence, absolute of Fourier series 58
Convergence, absolute, interval of 12
Convergence, absolute, uniform 18
Coordinates, Cartesian 187
Coordinates, Cartesian, curvilinear 353—355
Coordinates, Cartesian, cylindrical 357
Coordinates, normal 176 180 195
Coordinates, normal, polar 187
Coordinates, normal, spherical 357
Cord, deflection of 209
Cord, deflection of, elastic 214
Cord, deflection of, infinite 215
Cord, deflection of, stretched with elastic support 214
Cramer’s Rule 86 152
Curl of a vector field 349
Currents, alternating 161
Curvilinear coordinates, curl in 355
Curvilinear coordinates, curl in, divergence in 354
Curvilinear coordinates, curl in, gradient in 354
Curvilinear coordinates, curl in, Laplacian in 355
Curvilinear coordinates, curl in, orthogonal 353
Cylinder, eccentric, capacitance of 498
Cylinder, eccentric, capacitance of, in uniform field 409
Cylindrical coordinates 356
Cylindrical harmonics, general 411
Cylindrical harmonics, general, d’Alembert’s principle 141
Cylindrical harmonics, general, d’Alembert’s solution of wave equation 372
Damping matrix 203
Dandelin 98
Dandelin, de Moivre’s theorem 42
Del operator, V, successive applications of 352
Derivative of tabulated function 242
Descartes’ Rule of Signs 98
Determinants 69
Determinants, cofactors 71
Determinants, evaluation of 73
Determinants, minors 70
Determinants, properties of 72
Determinants, rank of 87
Diagram, vector 51
Difference equations 245
Difference tables 241
Differential 275
Differential equations with variable coefficients, operational solution of 557
Differentiation, of composite functions 272
Differentiation, of composite functions of a definite integral 284
Differentiation, of composite functions of implicit functions 277
Differentiation, of composite functions, partial 270
Diffusion 425
Diffusion equation 367
Dirichlet conditions 52 59
Distortion 171
Divergence, test for 6
Divergence, test for of a vector field 343
Duncan, W. J. 191 197
Dynamical matrix 189 192 196—201
Dynamical system 188
Electrical circuit 141
Electrical circuit forced oscillations of 146
Electrical circuit, energy of 143
Electrical circuit, free oscillations of 145
Electrical circuit, nonlinear 594
Electrical line with leaks 253
Electrostatics, basic principles of 483
Electrostatics, basic principles of and magnetostatics 365
Elliptic integral 27
Encke roots 98—104
Equations, Bessel 307—318
Equations, Bessel, cubic 95
Equations, Bessel, difference 245
Equations, Bessel, diffusion 367
Equations, Bessel, frequency 191
Equations, Bessel, homogeneous 70 87 173 189 204
Equations, Bessel, integral 555
Equations, Bessel, Lagrange 177 187 188 204
Equations, Bessel, Legendre 322—331
Equations, Bessel, linear algebraic 69
Equations, Bessel, linear differential 106 205
Equations, Bessel, Maxwell 364
Equations, Bessel, Poisson 362
Equations, Bessel, proof of 183
Equations, Bessel, quadratic 166
Equations, Bessel, satisfied by operators 240
Equations, Bessel, telegraphist’s 390
Equations, Bessel, transcendental 92
Equations, Bessel, transmission fine 390 393 395 543
Equations, Bessel, wave 63 366 370
Error function 305
Euler formula 40 50 54 167
Expansion, Fourier 55 57
Expansion, Heaviside, extension of 537 538
Expansion, Laplace 71
Expansion, Taylor’s 24 26 31
Factorial 301
Faltung theorem 213 525
Filter circuits 255
Finite difference operators 238
Flexibility matrix 197
Force, high-frequency effect of 171
Force, periodic external 169
Force, static 197
Forced oscillations 168
Four terminal networks 261
Fourier integral 65
Fourier series, convergence of 58
Fourier series, expansion 55 57
Fourier — Mellin theorem 521
Frequency equation 191
Frequency, angular 194 200
Frequency, high 171
Functions, analytic derivatives of 456
Functions, analytic singular points of 461
Functions, average value of a product of 62
Functions, Ber and Bei 318
Functions, Bessel 307—318
Functions, beta 303
Functions, complex 447
Functions, complex derivative of 449
Functions, complex line integrals of 451
Functions, composite differentiation of 272
Functions, effective values of 60
Functions, error 305
Functions, evaluation of indeterminate form 31
Functions, gamma 301
Functions, Hankel 316
Functions, harmonic general properties of 418
Functions, hyperbolic 44
Functions, impulse 125 534
Functions, inverse hyperbolic 46
Functions, inverse trigonometric 46
Functions, Legendre 322
Functions, logarithmic 45
Functions, meromorphic 463
Functions, stream 516
Gamma function 300
Gamma function, graph of 301
Gauss’s law of gravitation 364
Gauss’s theorem 343
Gradient 342
Graeffe’s root-squaring method 97 155 161 206
Gravitational field 363
Green’s Theorem 346
Hankel functions 316
Harmonic cylindrical 406
Harmonic functions, general properties of 418
Harmonic oscillations 167 175 180 190
Harmonic vibrations 49
Harmonic, general properties of surface 414
Harmonic, general properties of surface, spherical 412
Heat conduction 425
Heat conduction, general theorems of 443
Heat conduction, in circular plate 436
Heat conduction, in infinite bar 435
Heat conduction, two-dimensional 432
Heat flow, electrical analogy of 429
Heat flow, in semi-infinite solid 430
Heat flow, in solids 358
Heat flow, operational treatment of 547
Heat flow, two-dimensional 402
Heat flow, variable linear 426
Heaviside’s expansion theorem 537
Heaviside’s rules 537
Homogeneous equations 70 87 173 189 204
Hydrodynamics 357
Hyperbolic functions 44
Hyperbolic pole pieces 493
Implicit function, differentiation of 277
Impulsive functions 534
Indeterminate forms in functions 31 35
infinity 463
Integral equations 555
Integral, differentiation of 284
Integral, elliptic 27
Integral, evaluation of 26 288 467 552
Integral, Fourier 49 65
Integral, involving multiple functions 473
Integral, line 347
Integral, of complex functions 451
Integral, probability 305
Integral, surface 345
Integral, surface of tabulated function 243
Integration under the integral sign 286
Integra] test, Cauchy’s 7
Inverse hyperbolic and trigonometric functions 46
Jordan’s lemma 470
Joukoweki transformation 517
kinetic energy 177 185
Kirchhoff Laws 141 149 151 164 172
Lagrange 177 183
Lagrangian form 23
Laplace transformation 119 128 144 210
Laplace transforms, table of 130 567
Laplace transforms, use of, in nonlinear systems 600
Laplace’s differential equation 401
Laplace’s differential equation, in Cartesian, cylindrical, and spherical coordinate 401
Laplacian transformation 563
Laurent’s series 458
Legendre coefficients 328
Legendre polynomials 323
Legendre polynomials, as generating function 326
Legendre polynomials, associated 331
Legendre polynomials, expansion in series of 330
Legendre polynomials, orthogonality of 329
Legendre polynomials, Rodriguez’ formula for 324
Legrendre’s differential equation 322
Legrendre’s function of the second kind 325
Line integral 347
Linear algebraic equations 69
Linear differential equations 106
Linear differential equations, method of undetermined coefficients in 115
Linear transformations 88
Liouville’s theorem 466
Load, arbitrary 213
Load, arbitrary, concentrated 212
Load, arbitrary, uniform 210
Logarithmic decrement 167
Logarithmic function 45
Logarithmic transformation 496
Logarithms, computation of 29
L’Hospital’s Rule 31
Maclaurin see Series
Magnetostatics and electrostatics 365
Matrix 159
Matrix algebra 76 191
Matrix, column 160
Matrix, damping 203
Matrix, dynamical 189 197 199 201
Matrix, flexibility 197
Matrix, inverse 80
Matrix, modal 194
Matrix, special 77 84
Matrix, submatrices 83
Matrix, transposition of 77
Maxima and minima 279
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