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Index 887
Rectangular membranes, vibrations in, S
608–610 Saddle point, 333
Recurrence relations, 123–126, Scalar field, 356
523–524, 549–550 Scalar triple product, 162
Bessel functions, 549–550 Scalars, 147–149, 188. See also
Legendre polynomials, 523–524 Determinants
power series solutions, 123–126 defined, 147
Reduction of order method, 51–52 matrix algebra operations by, 188
Regression line, 236 vector algebra operations by, 147–149
Removable singularities, 729 Scale factors, 417
Repeated roots, 51–52, 273
Scaling, Fourier transforms, 476
Replacement function r(t), 99–101
Schwarz-Christoffel transformation,
Replacement scheduling problem,
773–775
99–101
Second-order differential equations,
Residue (Res), 729–750, 799–800
43–75
defined, 734
constant coefficient case, 50–54
diffusion in a cylinder, application of,
Euler’s equation, 72–74
748–750
forcing function ( f ),43
inverse Laplace transform and,
homogeneous equations, 45–48
746–750
initial value problem for, 45–47
MAPLE commands for, 799–800
integral curves for, 44–45
pole of order m, at, 736–738
nonhomogeneous equations, 48–49,
rational functions and, 740–745
55–60
real integral evaluation using,
reduction of order method for, 51–52
740–750
spring motion, applications for, 61–71
simple pole, at, 734–736
Wronskian W of, 46–47
singularities and, 729–733
theorems, 733–738 Semi-infinite mediums, 585–587,
Resonance, 67–69 633–635
discontinuous temperature in,
Riccati equation, 28–29
634–635
Riemann mapping theorem, 765–773
RMS bandwidth, 485 Fourier transforms for solutions of,
586–587
Rodrigues’s formula, 532
Rotation mapping, 759 heat equations for, 633–635
Row equivalence, 202 Laplace transform used for, 633–635
Row operations, 198–208 temperature distribution in, 633–634
augmented matrix, 206–207 wave (motion) equations for, 585–587
elementary matrix, 198–202 Separable equations, 3–13
leading entry, 203, 207–208 applications of, 8–13
MAPLE commands for, 202, 207–208 defined, 3
reduced (row echelon) form, 203–208 first-order differential equations, 3–13
pivot position, 207–208 Separation constant λ, 568
Row space (rank), matrices, 208–212 Sequences, see Series representation
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