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Sokolnikoff I.S. Mathematics of Physics and Modern Engineering
Sokolnikoff I.S.  Mathematics of Physics and Modern Engineering









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: Mathematics of Physics and Modern Engineering

: Sokolnikoff I.S.

: en

: /

:

ed2k: ed2k stats

: 2nd edition

: 1966

: 810

: 24.04.2008

: | | ID
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$e^X$      172 536 581
$e^{ix}$      173 536
$J_n (x)$      see Bessels functions
$K_n (x)$      see Bessels functions
$\Delta$      510 692
$\nabla$      370
$\nabla^2$      387 407
Abels theorem on differential equations      54p
Abels theorem on power series      142
Absolute convergence of integrals      755
Absolute convergence of series      127 170
Absolute value of complex numbers      168 528
Acceleration, normal      313
Acceleration, tangential      313
Acceleration, vector      302p 313
Acceleration, vector, in cylindrical coordinates      367p
Adams method      723 728
Addition of complex numbers      166 529
Addition of matrices      327
Addition of series      117
Addition of vectors      288 317
Addition, parallelogram law of      288 529
Adiabatic expansion      50p
Algebraic equations      677
Algebraic equations, solution of, by graphical methods      678
Algebraic equations, solution of, by iterative methods      679
Algebraic equations, systems of linear      350 687 689 719
Alternating series      128
Amplitude of simple harmonic motion      44
Amplitude of waves      428
Analytic functions      540
Analytic functions, branch points of      570
Analytic functions, Cauchys formula for      555
Analytic functions, Cauchys theorem for      547
Analytic functions, differentiation of      511 557
Analytic functions, essential singular points of      570 574
Analytic functions, geoimetric representation of      575
Analytic functions, integrals of      515 547 551
Analytic functions, Laurents expansion for      565
Analytic functions, mapping by      575591
Analytic functions, maximum modulus theorem for      558 561
Analytic functions, poles of      570
Analytic functions, residue theorem for      573
Analytic functions, residues of      570
Analytic functions, singular points of      543 569
Analytic functions, Taylors series for      561
Angle, phase      44 528
Angle, solid      399p
angular momentum      305
Angular velocity      302 399p
Antenna, radiation from      486
Arc length      301
Arc length in curvilinear coordinates      362
Arc length of an ellipse      147
Argands diagram      528
Argument of a complex number      528
Arithmetic means      667
Asymptotic equality      12 123
Atmospheric pressure      50 (see also Pressure)
Attraction of a cone      277p
Attraction of a cylinder      277p
Attraction of a sphere      47 277p 410
Attraction, Coulombs law of      408n
Attraction, Newtons law of      16
Augmented matrix      750
Average, arithmetic      667
Average-value theorem      498
Base or coordinate vectors      319
Base or coordinate vectors in curvilinear coordinates      363
Base or coordinate vectors in cylindrical coordinates      367p
Base or coordinate vectors in spherical coordinates      367p
Base or coordinate vectors, orthonormal      321
Base or coordinate vectors, transformation of      337 367p
Basis      319
Beams on elastic foundations      86p 94p
Beams, bending of      15
Beams, buckling of      95p
Beams, cantilever      16
Beams, vibration of      435p
Bending moment      16 435
Bernoulli Euler law      10
Bernoullis differential equation      27
Bessels differential equation      159
Bessels functions      162 198 480
Bessels functions, asymptotic formulas for      199p
Bessels functions, expansion in series of      481
Bessels functions, generating function for      166
Bessels functions, orthogonality of      198
Bessels functions, zeros of      198
Bessels inequality      202
beta function      149 765
Biharmonic equation      430p
Bilinear forms      349
Bilinear transformation      577p
Binomial distribution      639
Binomial distribution, generating function for      640p
Binomial frequency function      639
Binomial law of probability      639
Binomial law of probability, Laplaces approximation to      647
Binomial law of probability, normal approximation to      647
Binomial theorem      155
Binormal      312
Boltzmann constant      633
Boundary-value problems      91 442 730
Bounds for Fourier coefficients      211
Branch points      570
Buffons needle problem      637
Cable, flow of electricity in      514
Cable, hanging under gravity      40 454
Cable, oscillations of      445 454
Cable, supporting roadway      42p
Calculus of variations      264
Calculus of variations, isoperimetric problems      269
Calculus of variations, problems with constraints      269
Cantilever beam      16
Cartesian reference frames      321
Catenary      41
Cauchy Riemann equations      413
Cauchy Schwarz inequality      322
Cauchys convergence criterion      115
Cauchys differential equation      78
Cauchys inequality      322
Cauchys integral formula      555
Cauchys integral test      120
Cauchys integral theorem      547
Cauchys principal value of an integral      602
Center of gravity      275 281
Center of mass      44 303
Center of mass, motion of      44 304
Chain rule      228
Chain under gravity      40
Change of variables in functions      237
Change of variables in integrals      270
Channel, flow from      594
Chaplygins method      37
Characteristic equation      54 67 521 733
Characteristic equation for systems of linear differential equations      100 106p 733
Characteristic equation of a matrix      344
Characteristic frequencies      477 479p 481 482p
Characteristic functions      732
Characteristic values      344 507p 732
Characteristic vectors      344
Characteristics      440 508 517
Characteristics, discontinuities on      519
Chemical combinations      14
Chemical reactions      15
Circle of convergence      170 562
Circulation      397 591
Clairauts equation      27p
Cofactors      741
Column, axially loaded      86p 90
Column, Eulers critical load for      92
Combinations      611
Combinatory analysis      611
Comparison tests for inlegrals      755n
Comparison tests for series      122 125 131
Complementar function      59
Complex function      534
Complex function, continuitv of      510
Complex function, differentiation of      511
Complex function, integration of      543
complex numbers      166 527
Complex numbers, absolute value of      168 528
Complex numbers, addition of      166 529
Complex numbers, argument of, principal      528
Complex numbers, conjugate      529
Complex numbers, modulus of      528
Complex numbers, operations on      528
Complex numbers, phase angle of      528
Complex numbers, polar form of      528
Complex numbers, roots of      531
Complex potential      587
Complex roots of unity      532
Complex variable, elementary functions of      534
Complex-variable theory      523601
Components of a vector      291 317 321
Composite functions      230
Compound probability      617 635
Condenser discharge      81 84
Conductivity, thermal      115 455
Conformal mapping      583 598
Conformal mapping, examples of      575595
Conformal mapping, invariance of harmonic functions under      585
Conformal mapping, Riemanns theorem on      586
Conformal mapping, Schwarz Christoffel formula for      599
Conjugate complex numbers      529
Conjugate harmonic functions      560 588
Conjugate matrix      343
Conservation of energy      43
Conservation of matter      417
Conservation of momentum      44
Conservative force fields      108
Constraints in calculus of variations      269
Continuity      218
Continuity of complex functions      540
Continuity of scalar functions      368
Continuity of vector functions      299 368
Continuity, equation of      112 417
Continuity, piecewise      755
Contour integrals      see Line integrals
Convergence of series      see Series
Convergence, circle of      170 562
Convergence, interval of      139
Convergence, radius      139 170 562
Convergence, uniform      132
Convolution      188
Convolution theorem      188 762
Coordinate lines      272 359
Coordinate surfaces      359
Coordinate vectors      319
Coordinate, affine      366
Coordinate, curvilinear      357
Coordinate, cylindrical      see Cylindrical coordinates
Coordinate, divergence in      106
Coordinate, gradient in      107
Coordinate, orthogonal      363
Coordinate, parabolic      108p
Coordinate, spherical      360 367p
Coordinate, volume in      361
Correlation coefficient      666
Coulombs law      108n 167
Couple      305
Covariance      661
Cramers Rule      326 719
Cross product      291
Crouts reduction      687n
Curl      396
Curl in caitesian coordinates      398
Curl in curvilinear coordinates      406
Curl, relation to rotation      399p
Current flow      416
Current flow in cables      514
Current flow in electrical circuits      81 87 100 761p 768p
Curvature      150 311
Curve fitting by finite differences      694
Curve fitting by graphical means      701
Curve fitting by least squares      702
Curve fitting by trigonometric functions      711
Curve integral      7
Curve of minimum descent      269p 767
Curve on a surface      309
Curve, elastic      16 86p
Curve, Frenets formulas for      311
Curve, length of      301
Curve, minimizing      265
Curve, motion on      301 313
Curve, normal to      311
Curve, piecewise of sectionally smooth      372
Curve, pursuit      33
Curve, trihedral associated with      312
Curvilinear coordinates      see Coordinates
Cycloid, motion on      46p 269p 767
Cylindrical coordinates      359
Cylindrical coordinates, acceleration components in      367p
Cylindrical coordinates, base vectors in      367p
Cylindrical coordinates, velocity components in      367p
Cylindrical coordinates, volume element in      365
D      57
Damped oscillations      449
Damping, viscous      82 449
De Moivres Formula      530
Deformation of contours      549
Del, $\nabla$      see Gradient
Delmite integrals      see Integrals
Dependence, linear      52 70 317
Derivative, directional      243 253 369
Derivative, normal      244 253 369
Derivative, partial      219
Determinante      325 741753
Determinants, cofactors of      741
Determinants, differentiation of      743
Determinants, expansion of      326 741
Determinants, minors of      741
Determinants, multiplication of      325 745
Determinants, solution of equations by      326 748
Determinants, Wronskian      52 54p 71
Difference equations      510 734
Difference equations, Dirichlets problem for      511
Difference equations, elliptic      511 518
Difference equations, hyperbolic      513 518
Difference equations, parabolic      512 518
Difference operators      510 692
Differences, backward      692
Differences, finite, method of      734
Differences, forward      691
Differentiability      226
Differential      223 310
Differential equations, elliptic      505 511 518
Differential equations, Eulers      78 267
Differential equations, exact      20
Differential equations, hyperbolic      507
Differential equations, Lagranges      26
Differential equations, ordinary      see Ordinary differential equations
Differential equations, parabolic      506 512
Differential equations, partial      see Partial differential equations
Differential equations, systems of      95 733
Differential form, quadratic      362
Differential of arc length      362
Differential of volume      364
Differential operators      57 430p
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