Page 889 - Advanced_Engineering_Mathematics o'neil
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Index 869
defined, 676 homogeneous linear system solutions
differentiable, 679–680 and, 306–308
exponential, 684–688 linear second-order equations for,
integrals of, 695–700 52–54
inverse Laplace transform for, Conformal mappings, 751–787, 800
746–750 angles preserved by, 754–755
limits L, 677–678 bilinear transformations, 758–763
MAPLE commands for, 799–800 construction of, 765–775
real integrals, evaluation of, 740–745 defined, 755
residues (Res), 733–738, 746–750, Dirichlet problem solutions using,
799–800 776–779
series representations of, 715–728 infinity, point at, 762–763
singularities, 729–733 inversion, 759–760
trigonometric, 684–688 magnification, 759
Complex numbers, 669–693, 715–716 MAPLE commands for, 800
argument, 672–673 mapping defined, 751
arithmetic of, 669–670 one-to-one, 757–758
bounded, 678 orientation preserved by, 754–755
Cauchy-Riemann equations, 680–684 plane fluid flow models, application
complex functions and, 669–693 of, 779–786
complex logarithms, 689 properties of, 754–755
complex plane, 670 Riemann mapping theorem, 765–773
conjugate, 671, 683–684 rotation, 759
continuous complex functions, Schwarz-Christoffel transformation,
678–679 773–775
defined, 669 stereographic projection, 762–763
differentiable complex functions, theorem for, 755–757
679–680 three point theorem for, 762–763
exponential functions and, 684–688 translation, 758
imaginary part, 669 Conjugate, complex numbers, 671,
inequality, 672 683–684
magnitude, 670–671 Conservative vector fields, 380–387
ordering, 673–675 Consistent system, 220–221
polar form, 672–673 Constant coefficient case, 50–54
power series and, 715–716 characteristic equations for, 51–54
powers of, 690–692 complex roots, 52–54
pure, imaginary, 670 real, distinct roots, 51
real part, 669 repeated roots, 51–52
trigonometric functions and, 684–688 Constants, 61, 568, 573–575, 611–612,
Complex roots, 52–54, 271–272, 615, 622–624
306–308 damping c, 61, 573–574
defined, 52 diffusivity k, 623–624
eigenvalues (λ), 271–272, 306–308 Euler γ , 538
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