Page 900 - Advanced_Engineering_Mathematics o'neil

880 Index

Integration, 446–448, 695–714, 718 Laplace transform, 77–120, 317–318,
Cauchy’s theorem for, 700–714 587–593, 746–750
complex, 695–714 availability function f (t),99
Fourier series, 446–448 Bessel functions, 114–117
integrals of complex functions, convolution theorem, 96–101
695–700 defined, 77
Jordan curve theorem for, 700–701 derivatives, theorem of, 82
power series, 718 Dirac delta function δ(t),102–106
Interior point, 674 exponential matrix solutions using,
Interlacing lemma, 552 317–318
Intervals, 567–577, 612–624 forcing function ( f ), 77–79
heat equation on [0, L], 612–624 Heaviside function (H), 86–95
wave motion in, 567–577 higher derivatives, theorem of, 82
Inverses, 79, 95–97, 226–231, 259–260, impulses (δ),102–106
473–474, 494 initial value problem solutions using,
defined, 227–228 81–84
determinant for, 259–260 inverse, 79, 93–95, 746–750
discrete Fourier transform (DFT), 494 jump discontinuities, 81, 86–87
Fourier transform, 473–474 linearity of, 79
Laplace transform, 79, 95–97 MAPLE routines for, 78–79
linear systems and, 229–231 mortality function m(t),99
matrices, 226–231, 259–260 partial fractions decomposition and,
nonsingular matrix, 227–229 84, 118–120
singular matrix, 227, 229–230 piecewise continuity, 81–82
Inversion mapping, 759–762 polynomial coefficients and, 112–117
Irregular singular point, 126 replacement scheduling problem
Isolated singularities, 729 using, 99–101
Isolated zeros, 722–724 residue theorem integral evaluation
using, 746–750
selected functions, 78
J
shifting theorems, 84–95
Jordan curve theorem, 700–701
system solutions using, 106–110,
Joukowski transformation, 785–786
317–318
Jump discontinuities, 81, 86–87
wave (motion) equations, techniques
for, 587–593
K Laplace’s equation, 407, 421–423,
Kepler’s problem, Bessel integral 641–642
application, 556–560 curvilinear coordinates and, 421–423
Kirchhoff’s current and voltage laws, 33 del operator ∇ for, 641

harmonic functions of, 641
L heat transfer and, 407
Labeled graph, 262–263 potential equation, as, 641–642
Laplace integrals, 469–470 steady-state equation, as, 641

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October 15, 2010 16:21 THM/NEIL Page-880 27410_26_Ind_p867-898