Page 890 - Advanced_Engineering_Mathematics o'neil
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870 Index
Constants (Continued) residue theorem and, 742–745
heat equation and, 611–612, 622–624 wave equation solution using,
separation λ, 568 586–587
spring k,61 Cramer’s rule, 260–262
temperature distribution and, 622–624 Critical damping, 63–64, 67
wave equation and, 568, 573–575 Critical length of a rod, Bessel function
Continuous complex function, 678–679 application, 542–543
Convection, 612 Cross product, 159–161
Convergence, 432–435, 442–445, collinear points for, 161
466–467, 469–470, 512–513, defined, 159
716–718 MAPLE computation of, 160
absolute, 716 orthogonal vectors, 160–161
cosine integral, 469–470 Cubes, Dirichlet problem for, 654–655
cosine series, 442–443 Curl, 362–363, 365, 421–423
eigenfunction expansion, 512–513 curvilinear coordinates, 421–423
Fourier integral, 466–467, 469–470 defined, 362
Fourier series, 432–435 del operator ∇ for, 362–363
power series, 716–718 differential calculus and 362–363, 365
radius of, 717–718 integral calculus and, 421–423
sine integral, 469–470 physical interpretation of, 365
sine series, 444–445 vector analysis and 362–363, 365,
Convolution, 96–101, 479–481 421–423
commutivity of, 480 Curvature κ(s), 349–354
defined, 96 defined, 350
Fourier transforms, 479–481 unit normal vector and, 352–353
frequency, 480 unit tangent vector and, 350–352
Laplace transforms, 96–101 vector differential calculus analysis
linearity of, 480 and, 349–354
replacement scheduling problem velocity v and, 349–354
using, 99–101 Curves, 349–354, 367–372, 380–387,
theorem, 96–101, 480 392–393, 408–410, 695–714
time, 480 boundary of a surface, 408–409
Coordinate functions, 367 Cauchy’s theorem and, 700–714
Coordinate surfaces, 415–416 coherent orientation of, 408–409
Cosine function, 441–442, 468–470, complex function integrals, 695–714
490–491, 586–587, 742–745 connected, 701
convergence of, 442–443, 469–470 coordinate functions, 367
Fourier integral, 468–470 curvature κ(s), 349–354
Fourier series, 441–442 domain, 701
Fourier transform, 490–491, 586–587 exterior of, 374, 700–701
integral evaluation using, 742–745 Green’s theorem and, 374–375
rational functions of, 743–754 initial point, 367
rational functions times, 742–743 integral over, 696–700
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