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868 Index
Bessel functions (Continued) defined, 701–703
MAPLE commands for, 555, 799 deformation theorem and, 704,
modified, 543–545 711–712
Neumann’s function (second kind) of harmonic functions and, 709–711
order zero, 538–540 independence of path and, 703–704
recurrence relations, 549–550 integral formula, 706–709, 713–714
second kind of order n, 538–540 Jordan curve theorem for, 700–701
zeros of, 550–552 maximum principle, 710
Bessel’s inequality, 175, 448–450, mean value property, 709–710
515–518 Center of system, 337
eigenfunction expansions and, Cesàro filter function Z(t), 461–463
515–518 Cesàro sum σ(t), 461–463
Fourier series and, 448–450 Characteristic function, 487
special functions and, 515–518 Characteristic polynomials, 269–271
vectors, 175 Characteristic triangle, 599–601
Bilinear transformation, 758–763 Circles, see Disks
Boundary conditions, 427–428, 506, Circuit law, Kirchhoff’s, 33
566–567, 611–612, 622–624 Circuits, see Electrical circuits
Fourier series, 427–428 Circular membranes, vibrations in,
heat equations, 611–612, 622–624 602–608
periodic, 506 Closed-form solutions, 121
Sturm-Liouville problems, 506 Coefficients of a system, 213
wave equations, 566–567 Cofactor expansion, 256–258
Boundary curve of a surface, 408–409 Collinear points, 161
Boundary data for D, 641–642 Column space (rank), matrices, 208–212
Boundary points, 674–675 Compact set, 678
Bounded complex functions and Competing species model, phase
numbers, 678 portraits applied to, 340–341
Bounds on derivatives, harmonic Complementary domains, 766–767, 780
functions, 710–711 Complementary error function (erfc),
631
C Complements, orthogonal vectors,
Carbon dating, 11 177–180
Cauchy problem, d’Alembert’s solution Complex Fourier series, 457–460
for, 594–601 Complex functions, 667–787, 799–800.
Cauchy-Riemann equations, 680–684 See also Integration
Cauchy-Schwartz inequality, 155, Cauchy-Riemann equations for,
163–164 680–684
Cauchy’s theorem, 700–714 complex integration, 695–714
bounds on derivatives, 710–711 complex logarithms, 689
complex function integration and, complex numbers and, 669–693
700–714 conformal mappings, 751–787, 800
consequences of, 703–714 continuous, 678–679
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