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Pipes L.A. — Applied Mathemattics for Engineers and Physicists
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Название: Applied Mathemattics for Engineers and PhysicistsАвтор: 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
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 1st editionГод издания: 1946Количество страниц: 618Добавлена в каталог: 26.09.2009Операции: Положить на полку |
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Maxwell’s equations 364 Membrane, circular vibrations of 388 Membrane, circular vibrations of, rectangular vibrations of 384 Mermomorphic functions 463 Modal columns 190 192 201 Modes, normal 191 Networks, four terminal 261 Newton — Raphson method 54 Newton’s second law of motion 142 164 177 183 Nonconservative systems, forced oscil¬lations of 206 Nonconservative systems, forced oscil¬lations of, free oscillations of 203 Nonlinear dynamical systems, operational analysis of 587 Nonlinear electrical circuit, analysis of 594 Nonlinear oscillations 579 Nonlinear oscillatory system, restoring force, a general function of the displacement 585 Nonlinear systems, forced oscillations of 600 Normal coordinates 176 180 195 Normal modes 191 Numbers, complex 38 Numbers, complex, conjugate imaginary 39 Numbers, complex, exponential and trigonometric functions of 43 Numbers, multiplication and division of 41 Numbers, multiplication and division of, polar form of 40 148 168 170 Numbers, multiplication and division of, powers and roots of 42 Operational analysis of nonlinear dynamical systems 587 Operational calculus, basic theorems of 565 Operational calculus, basic theorems of, Faltung theorem of 213 525 Operational calculus, basic theorems of, fundamental rules of 523 Operational calculus, basic theorems of, historical introduction to 519 Operational evaluation of integrals 552 Operational solution, of differential equations with variable coefficients 557 Operational solution, of differential equations with variable coefficients of integral equations 555 Operators, algebra of 239 Operators, algebra of, equations satisfied by 240 Orthogonality 191 379 Oscillation chain of particles 249 Oscillation, of electrical systems 143 Oscillation, of electrical systems of mechanical systems 164 Oscillation, of electrical systems with one degree of freedom 164 Oscillation, of electrical systems, harmonic 175 190 Oscillation, of electrical systems, longitudinal, of bar 549 Oscillation, of electrical systems, principal 175 Oscillation, of electrical systems, principal orthogonality of 190 oscillations 188 Oscillations forced 168 Oscillations of hanging chain 380 Oscillations of triple pendulum 197 Oscillations with two degrees of freedom 172 Oscillations, damped 167 Oscillations, relaxation 605 Partial differential equations, operational solution of 542 Partial differentiation 270 Particles, oscillation of chain 249 Pendulum, oscillations of 581 Periodic functions 540 Pi function 301 Pivotal element 76 Plane wave 64 Plates, conducting 493 Poisson’s equation 362 Polar coordinates 187 Polar form 40 148 168 170 Polygon with one angle 505 Polynomials, summation formula for 244 Potential velocity 515 Potential, gravitational 360 Potential, gravitational of a ring 415 Potential, gravitational of spherical surface 417 Principal oscillations, orthogonality of 190 Probability integral 305 Ratio test, Cauchy 8 12 Rayleigh’s method of calculating natural frequencies 231 Reciprocity relations 159 Relaxation oscillations 605 Residues 460 Residues, evaluation of 464 Resonance phenomena 171 Ring, potential of 415 Rodrigues’ formula for Legendre’s polynomials 324 Schwarz’s transformation 502 Series of functions 18 Series, alternating 10 Series, binomial 24 Series, convergent 3 Series, divergent 3 Series, Fourier 49 51 170 Series, geometric 2 4 Series, infinite 1 Series, integration and differentiation of 20 Series, Maclaurin’s 23 29 43 Series, Maclaurin’s, approximate formulas derived from 28 Series, oscillating 3 Series, power 12 28 Series, Taylor’s 21 457 Series, theorems of 13 Series, use of, for computation of functions 29 Skin effect, in a circular wire 440 Skin effect, on a plane surface 438 Skin-effect or diffusion equation 367 Solid friction damping 579 Spherical coordinates 357 Steady state 147 161 169 170 206 395 Stoke’s Theorem 347 Stream function 516 String vibrating, in Fourier series, solution of 374 String vibrating, orthogonal functions of 378 String, waves on 372 Structures, theory of 209 Surface integral 345 Symmetrical components 89 Systems, conservative 186 204 Systems, dynamical 188 Systems, nonconservative 203 206 Table, of analogues 165 Table, of analogues, difference 241 Table, of analogues, Laplace transforms 130 Tabulated functions, derivatives of 242 Tabulated functions, derivatives of, integral of 243 Tangent, hyperbolic 47 Taylor’s expansion 24 26 31 210 272 Taylor’s Formula 23 Taylor’s series 21 457 Telegraphist’s equations 390 Theorem, binomial 24 Theorem, binomial of convergence of series 3 Theorem, binomial, de Moivre’s 42 Theorem, binomial, expansion 537 Theorem, binomial, expansion of 538 Theorem, Faltung 213 525 Theorem, Fourier — Mellin 521 Theorem, Gauss 343 Theorem, Green 346 Theorem, Stokes 347 Transcendental equations 92 Transform, direct, calculation of 528 Transform, inverse, calculation of 530 Transform, inverse, direct computation of 124 Transform, inverse, Laplace (see Laplace) the modified integral of 532 Transform, inverse, of periodic functions 540 Transform, inverse, of unit function 124 Transformation, boundaries expressible in parametric form 500 Transformation, logarithmic 496 Transformation, logarithmic, Schwarz’s 502 Transformation, of hyperbolic cosine 489 Transformations, successive 506 Transformations, successive, involving powers of 493 Transmission line equations 390 Transmission line equations, operational solution of 543 Transmission line, distortionless 393 Transmission line, distortionless and steady-state solution 395 Variable, change of 275 Variations, calculus of 292 Vector, addition and subtraction of, multiplication of, by scalars 333 Vector, concept of 333 Vector, diagram 51 Vector, of a matrix 76 Vectors, differentiation of 340 Vectors, multiple products of 338 Vectors, scalar product of 335 Vectors, vector product of 336 Velocity potential 515 Vibrations of beams 224 Vibrations of beams and beats 63 Vibrations of beams of a string 370 Vibrations of beams with one degree of freedom 164 Vibrations of beams with two degrees of freedom 172 Vibrations of beams, carrier wave of 62 Vibrations of beams, circular 388 Vibrations of beams, dynamical system of 188 Vibrations of beams, elastic 164 Vibrations of beams, free 165 Vibrations of beams, harmonic 49 Vibrations of beams, mechanical effect of periodic force on 169 Vibrations of beams, modulated 62 Vibrations of beams, nonlinear systems of, forced 600 Vibrations of beams, rectangular 384 Vibrations of beams, trains, of 265 Wall in a uniform field 513 Wallis’ formula 27 Wave equations 63 366 370 Wave harmonic 373 Waves on transmission lines 545 Wedge, field inside of 494 Weierstrass 19 27
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