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Johnson W.C. Ч Mathematical and physical principles of engineering analysis
Johnson W.C. Ч Mathematical and physical principles of engineering analysis

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Ќазвание: Mathematical and physical principles of engineering analysis

јвтор: Johnson W.C.


This book is the outgrowth of a course in engineering analysis which the author has developed over the past six years for students in the several branches of engineering at Princeton University. The purpose of the book is to present the essential physical and mathematical principles and methods of approach that underlie the analysis of many practical engineering problems. The point of view is primarily utilitarian in an engineering sense but is aimed at a sound understanding of basic principles and designed to form a firm foundation for more advanced work. The book emphasizes basic physical principles and physical reasoning, and devotes considerable attention to methods of attack, the use of assumptions, procedures in setting up equations, the use of mathematics as a tool in accurate and quantitative reasoning, and the physical interpretation of mathematical results. Graphical methods are used freely, and reasonable approximations arc encouraged provided that they lead to results within the required accuracy. Every effort is made to present the material from a broad and unspecialized point of view and to use material with which every graduate engineer should be familiar, whatever his field.

язык: en

–убрика: “ехнологи€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1944

 оличество страниц: 355

ƒобавлена в каталог: 20.12.2012

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
Absolute value, of complex number      184
Acceleration, of gravity      15
Action and reaction      13
Adequate physical equations      234
Admittance      191
Air resistance, on airplane wing      230Ч234
Air resistance, on falling body      156
Algebra, of complex numbers      182Ч186
Algebraic equations, roots of      109
Algebraic signs, in electrical equations      51Ч53
Algebraic signs, in mechanical equations      57Ч59
Algebraic signs, meaning of      48Ч50
Alternating currents      182Ч196
Alternating currents, combined with transient      194Ч196
Alternating currents, nonsinusoidal      239
Amplitude spectrum      267 274
Amplitude, of forced oscillation      190
Amplitude, of free oscillation      102
Analogies      28 67Ч70
Analogies, assumptions in      68
Analogies, duality in      69
Analogies, electric cable and heat flow      313
Analysis, harmonic      258Ч265
Angular velocity      21 57
Angular velocity, natural      102
Antinode      293
Assumptions, in electrical systems      51
Assumptions, in lumped-constant systems      280
Assumptions, in mechanical systems      56
Assumptions, use of      3Ч5
Ber and Bei functions      176
Bessel functions      168Ч179
Bessel functions of fractional order      174
Bessel functions of imaginary argument      175
Bessel functions of negative integral order      175
Bessel functions of positive integral order      172
Bessel functions of zero order      169
Bessel functions, derivatives of      173
Bessel functions, modified      175
Bessel functions, zeros of      170
Bessel's equation      169
boundary conditions      287
Boundary conditions for quenched slab      303
Boundary conditions for vibrating string      291
Boundary conditions in field plotting      323Ч325
Boundary conditions, applied by Fourier series      296
Branch currents      47
Buckingham $\pi$ theorem      219
Cable, electric      313
Capacitance, from field plot      329
Cauchy Ч Riemann equations      321
Cauchy's equation      167
Change, of dependent variable      134Ч137
Change, of units      218Ч219
Characteristic dimension      231
Characteristic equation      97 109
Characteristic impedance      316
Characteristic modes      294
Charge resonance      200
Checking, dimensional      207Ч213
Checking, limiting case      214Ч215
Circuits with distributed constants      280 311Ч317
Circuits with time-varying parameter      162
Circuits, alternating-current      182Ч196
Circuits, analogies to      67Ч70
Circuits, coupled      25 31 55
Circuits, dimensional analysis of      208 229
Circuits, duals of      63Ч67
Circuits, Fourier-integral analysis of      266Ч275
Circuits, mesh currents in      47
Circuits, nonlinear, methods for      75Ч89 155 229
Circuits, setting up equations for      50Ч56
Circuits, voltages in      23Ч26 51
Circuits, with nonsinusoidal voltage      239 251 257
Coefficient of restitution      34
Coefficients of inductance      24Ч25
Coefficients, Fourier      241Ч243
Complementary function      118
Complete physical equations      234
Complex Fourier series      254Ч258
complex numbers      182Ч186
Complex numbers, absolute value of      184
Complex numbers, algebraic operations on      183Ч186
Complex numbers, vector representation of      183
Complex roots, in characteristic equation      101 109Ч110
Condenser, capacitance, by field plot      329
Condenser, energy stored in      12
Condenser, reactance of      194
Condenser, voltage across      51
Conduction, of electricity, by field plot      328
Conduction, of heat, analogy to cable      313
Conduction, of heat, by field plot      317Ч328
Conduction, of heat, equation for rate of      301
Conduction, of heat, in cylinder      176Ч179
Conduction, of heat, in quenched slab      300Ч305
Conduction, of heat, steady      307 309Ч311
Conduction, of heat, variable      300Ч308
Conformal mapping      328
Conjugate functions      321
Conservation of angular momentum      20Ч22
Conservation of energy      11Ч13
Conservation of momentum      19Ч20
Constant flux linkages, principle of      26Ч30 163
Constant, dimensional      234
Constant, propagation      317
Constant, time      99
Constant-current network      72
Convergence of Fourier series      249
Coordinates, choice of      45Ч48
Correlation of data by dimensional analysis      226Ч229
Cosine, hyperbolic      145
Coupled circuits, energy stored in      31
Coupled circuits, flux linkages in      25Ч26
Coupled circuits, force between      32
Coupled circuits, setting up equations for      51 55
Coupled circuits, voltage induced in      25Ч26 51 55
Coupling of rotating systems      22
Critical damping      103Ч104 108
Cubic equation, roots of      109Ч110
Current, alternating      182Ч196 239
Current, induced      29
Current, mesh      47
Current, nonsinusoidal      239 251 257
Current, transient      40
Curvilinear squares      320
D'Alembert's principle      18 56
Damped oscillations      102 106 122
Damped oscillations of elastic string      333
Damping constant, as system parameter      57
Damping constant, in oscillatory solution      102
Damping factor      102
Damping, critical      103 108
Damping, effect of, on resonance      197Ч201
Damping, force of      56Ч57
Damping, solid and viscous      56
De Moivre's theorem      186
Degree, of differential equation      95
Degree, of freedom      46Ч47
Dependent variable, change of      134Ч137
Dependent variable, in electrical systems      47
Dependent variable, in mechanical systems      45 58
Derivatives, initial      113Ч114 132
Derivatives, initial, operator method      137Ч145
Derivatives, of Bessel functions      173
Derivatives, of Fourier series      250
Derivatives, of hyperbolic functions      148
Derivatives, of rotating vectors      187Ч188
Derivatives, partial      282Ч285
Differential equation with constant coefficients      97Ч149
Differential equation with nonsinusoidal driving forces      251Ч254 257
Differential equation, Bessel's      169
Differential equation, Cauchy Ч Riemann      321
Differential equation, Cauchy's      167
Differential equation, degree of      95
Differential equation, Euler's      167
Differential equation, exact      159
Differential equation, general solution, defined      96
Differential equation, graphical solution of      86Ч89
Differential equation, homogeneous linear      96Ч117 167
Differential equation, homogeneous linear, of first order      97Ч100
Differential equation, homogeneous linear, of general order      109Ч110
Differential equation, homogeneous linear, of second order      100Ч109
Differential equation, homogeneous linear, systems of      110Ч117
Differential equation, homogeneous, of first order      157
Differential equation, initial conditions for      43 96 113 132
Differential equation, initial conditions for, operator method      137Ч145
Differential equation, linear      see also "Differential equation nonhomogeneous
Differential equation, linear, defined      96
Differential equation, linear, general first-order      161
Differential equation, linear, homogeneous      96Ч117
Differential equation, linear, nonhomogeneous      96 117Ч134 161
Differential equation, linear, systems of      110Ч117 130Ч134
Differential equation, linear, with constant coefficients      97Ч149
Differential equation, nonhomogeneous linear      96 117Ч134 161
Differential equation, nonhomogeneous linear, general method      127Ч130
Differential equation, nonhomogeneous linear, reduction to homogeneous      119Ч127
Differential equation, nonhomogeneous linear, systems of      130Ч134
Differential equation, nonhomogeneous linear, with several driving forces      130
Differential equation, normal form of      84
Differential equation, numerical solution of      82Ч86
Differential equation, order of      44 95
Differential equation, ordinary      95Ч179
Differential equations with sinusoidal driving forces      124 188Ч193
Differential equations with variable coefficients      161 167Ч179
Differential equations with variables missing      164Ч166
Differential equations with variables separable      155
Differential equations, oscillatory solutions of      101 106 122
Differential equations, particular integral of      117
Differential equations, particular solution defined      96
Differential equations, setting up      45Ч70
Differential equations, simultaneous      110Ч117 130Ч134
Differential operator in partial differential equations      298
Differential operator in systems of equations      112 131
Differential operator in writing equations      54
Differential operator, algebraic properties of      111
Differential, exact      159
Differential, total      283Ч284
Differentiation, of Fourier series      250
Differentiation, partial      282Ч285
Dimension, characteristic      231
Dimension, fundamental      207 211
Dimensional analysis      218Ч235
Dimensional analysis in changing units      218
Dimensional analysis in model theory      230Ч234
Dimensional analysis in plotting analytical results      222
Dimensional analysis of force on airplane wing      230
Dimensional analysis of heat transfer      226
Dimensional analysis of nonlinear transient      229
Dimensional analysis of velocity of sound in gas      224
Dimensional analysis, correlation of data      226Ч229
Dimensional analysis, derivation of formulas      219Ч224
Dimensional checking      207Ч213
Dimensional constants      234
Dimensional formulas, table of      212
Discontinuity, convergence at      249
Displacement impedance      192
Distributed constants      280Ч331
Driving force      118
Driving force, constant      121
Driving force, nonsinusoidal      239Ч275
Driving force, sinusoidal      124 182Ч201
Driving force, two or more present      130
Driving-point impedance      191
Dual equations      63
Dual systems      63Ч67
Dual systems in analogies      69
Elastic mounting, of machines      204
Electric fields, plotting of      317Ч331
Electrical energy      12
Electrical energy, stored in inductive circuits      30
Electrical momentum      27
Electrical systems with distributed constants      280 311Ч317
Electrical systems with nonsinusoidal voltage      239 251 257
Electrical systems with time-varying parameter      162
Electrical systems, analogies for      67Ч70
Electrical systems, choice of variables in      47
Electrical systems, dimensional analysis of      208 229
Electrical systems, duals of      63Ч67
Electrical systems, Fourier-integral analysis of      266Ч275
Electrical systems, nonlinear, methods for      75Ч89 155 229
Electrical systems, on a-c voltage      182Ч196
Electrical systems, setting up equations for      50Ч56
Electrical systems, voltages in      23Ч26 51
Electrical transmission lines      311Ч317
Electromechanical system      73
Energy, calculation of forces from      31Ч34
Energy, kinetic      11 21
Energy, law of conservation of      11Ч13
Energy, stored, in condenser      12
Energy, stored, in coupled circuits      31
Energy, stored, in linear inductance      31
Energy, stored, in nonlinear inductance      30
Energy, stored, in rotating systems      21
Energy, stored, in spring      11Ч12
Equations, adequate      234
Equations, Bessel's      169
Equations, Cauchy Ч Riemann      321
Equations, Cauchy's      167
Equations, characteristic      97 109
Equations, checking of      206Ч215
Equations, cubic      109Ч110
Equations, dual      63
Equations, Euler's      167
Equations, gravity forces in      58
Equations, Laplace's      307 309 321
Equations, ordinary differential      95Ч179 see
Equations, partial differential      280Ч331
Equations, roots of algebraic      109Ч110
Equipotential lines      318
Error function      164
Euler's equation      167
Euler's formula      102
Even function      245
Even harmonics, effect of      244
exact differential equations      159
Expansion, in Fourier series      239Ч275
Expansion, in interval      249
Factor, damping      102
Factor, integrating      161
Factorial      174
Field plotting      317Ч331
Field plotting, boundary conditions in      323Ч325
Field plotting, calculations in      327Ч331
Field plotting, method of      321Ч325
Field plotting, superposition in      325
Field plotting, three-dimensional      331
Field, near slot      324
Field, of charged rings      331
Field, of conductor near iron surface      326
Field, of poles of machine      324
Filter      74 278
Fischer Ч Hinnen harmonic analysis      258Ч263
Flux function      318
Flux linkages      23
Flux linkages in coupled circuits      26
Flux linkages in linear inductance      24
Flux linkages in nonlinear inductance      29
Flux linkages, analogy to momentum      28
Flux linkages, principle of constant      26Ч30 163
Flux plotting      317Ч331
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