Page 897 - Advanced_Engineering_Mathematics o'neil
P. 897
Index 877
linear transformation function T , 241 tangent plane of, 359–361
mortality m(t),99 vector differential calculus analysis
odd, 436–438 and, 356–361
phase angle form of, 454–456 Gram-Schmidt orthogonalization
piecewise continuous, 81–82, process, 176
431–432 Graphs, 194–196, 236, 262–264,
piecewise smooth, 432 388–389, 456, 460, 462–463,
position y(x,t), 565–567 783–784
potential ϕ, 22–25, 380–381 amplitude spectrum, 456, 460
replacement r(t), 99–101 defined, 194, 262
shifting theorems for, 84–95 equipotential lines, 783–784
transfer, 487 filtering signals, 462–463
vectors of one variable, 345–349 Fourier series, 456, 460, 462–463
weight p, 511, 515 frequency spectrum, 460
window w(t), 483–485 labeled, 262–263
Fundamental matrix, 300–301 least squares line, 236
Fundamental period p, 452–454 matrix trees, 262–264
Fundamental set of solutions, regression line, 236
differential equations, 47 spanning tree, 263
streamlines, 783–784
G surfaces, 388–389
Gamma function (x), 533–534 walks of length, 195–196
Gauss filter, 463 Green’s first identity, 659
Gauss’s divergence theorem, 401–407 Green’s theorem, 374–379, 399–402
defined, 401–402 curve orientation and, 374–375
heat equation and, 405–407 extension of, 376–379
Stoke’s theorem and, 402, 408–413 three dimensions, 399–402
vector integral analysis using, two dimensions, 374–376
401–407 vector integral analysis using,
Gauss’s laws, 412 374–379, 399–402
General solutions, differential equations,
4, 47 H
Generating functions, 521–523, 548–549 Half-life (h) of an element, 10–11
Bessel functions, 548–549 Hamming filter, 463
Legendre polynomials, 521–523 Hankel’s integral, 561
Gershgorin method, 275–276 Harmonic conjugate, 683–684
Gibbs phenomenon, 438–440 Harmonic functions, 454–455, 641,
Gradient field ϕ, 356–361, 420 709–711
curvilinear coordinates and, 420 bounds on derivatives, 710–711
del operator ∇ for, 356–357 Cauchy’s theorem and, 709–711
directional derivative, 357–358 Fourier series and, 454–455
level surface of, 359–361 maximum principle, 710
normal vectors (lines) of, 359–361 mean value property, 709–710
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