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Pipes L.A. — Applied Mathemattics for Engineers and Physicists
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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1946

Количество страниц: 618

Добавлена в каталог: 26.09.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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