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| Greenberg M.D. — Advanced engineering mathematics |
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| Предметный указатель |
Euler constant 206
Euler formula 92 1117
Euler formulas 851 857
Euler method 293
Euler theorem 629
Euler, L. 23 33 1017
Even function 846
Exact differential 63 839
Exact differential equation 62
Existence and uniqueness for algebraic systems 502
Existence and uniqueness for first-order ODE 26 49 160
Existence and uniqueness for initial-value problems 83
Existence and uniqueness for linear algebraic systems 401
Existence and uniqueness in phase plane 348
Expansion of vector 449 454
Explicit numerical scheme 1006
Explosive growth 61
Exponential function 1116
Exponential growth 61
Exponential integral 206 731
Exponential matrix 586
Exponential solutions 95
Extended complex plane 1158
Extremum 656 665
Extremum local 656
Extrusion 975
Eyeglasses 124
Factorization of operator 109 126
Faraday's law 824
Fast Fourier transform (FFT) 931
Feigenbaum, M. 338
Fermat's principle 674
Fermat, P. de 674
Feshbach, H. 986
FFT 931
Field, irrotational 826
Finite complex plane 1158
Finite-difference method 999
Finite-difference method empirical estimate of the order 1104
Finite-difference method for Poisson equation 1092
Finite-difference method for wave equation 1054
Finite-difference method in nonreetangular domains 1097
Finite-difference method Neumann boundary conditions 1104
Finite-difference method Robin boundary conditions 1104
Finite-difference method with iterative solution 1100
Fixed point 33
Fixed point of mapping 1165
Fletcher, R. 670
Flow over plate 1136
Flux 762
Focus (spiral) 354
Forcing function 133
Formal solution 958
Fourier coefficients 851
Fourier convolution integral 923
Fourier cosine transform 935
Fourier cosine transform, table Appendix E
Fourier cosine transform, transform of derivative 936
Fourier integral 915
Fourier integral theorem 915
Fourier law of heat conduction 800
Fourier series 851 864
Fourier series, complex form 864
Fourier sine transform 935
Fourier sine transform, table Appendix E
Fourier sine transform, transform of derivative 936
Fourier transform 921
Fourier transform  -shift 924
Fourier transform application to ODE's 936
Fourier transform application to PDE's 981 1051 1088
Fourier transform convolution theorem 923
Fourier transform inversion formula 921
Fourier transform of nth derivative 923
Fourier transform table Appendix D
Fourier transform x-shift 924
Fourier — Bessel series 91
Fourier — Legendre series 911
Fourier, J. 844
Free fall 51
Free vibration 557
Free-body diagram 160
Frenet, F.J. 721
Frequency spectrum 914
Frobenius theorem 201
Function space 432 435 881
Fundamental period 286 848
Fundamental set of solutions 87
Fundamental theorem of the calculus 21 675 1195 1197
Gamma function 223
Gauss elimination 396 401
Gauss — Jordan reduction 404
Gauss — Seidel iteration 1008 1101
Gauss's law 805
Gauss, C.F. 1109
General solution of ODE 83 86 134
General solution of PDE 1045
Generalized eigenvalue problem 554 568
Generalized exponential function 1135
Generalized factorial function 225
Generating function for Bessel function 243
Generating function for Chebyshev polynomials 913
Generating function for Legendre polynomials 215
Generating set 439
Geometric series 191 1087 1213 1217
Gestalt psychology 377
Gibbs phenomenon 854
Gibbs, J.W. 854
Goursat, E. 1190
Gradient 767
Gram — Schmidt orthogonalization 455 456
Gravitation, law of 752
Green's functions 1207
Green's identities 801
Green's theorem 819
Green, G. 810
Greenberg, M.D. 1207
Grid points 999
Guinness I. Grattan- 845
Half-life 40
Half-range expansion 870
Hamilton, W.R. 765 810
Hanging chain 3 1021
Harmonic function 1145
harmonic oscillator 10
Harmonic oscillator, forced oscillation 149
Harmonic oscillator, free oscillation 110
Harmonic series 219 856 875
Hartman — Grobman theorem 362
Hartog, D. 517
Hastings, C.Jr. 983
Heal equation 943
Heat conduction 799
Heaviside step function 269
Heaviside, O. 269
Helix 719
Helmholtz equation 1040
Helmholtz, H. von 1040
Henon map 33
Henon, M. 33
Hermite, C. 604
Hermitian conjugate 604 900
Hermitian form 608
Hermitian matrix 604
High (frequency) mode 167 559
Higher-order ODE's 99
Hildebrand, F.B. 679
Hodgkin, A. 376
Holmes, P.J. 383
Homeomorphism 366
Homogeneous differential equation 117 393
| Homogeneous equation  61
Homogeneous function 60 629
homogeneous solution 28
Homogeneous system 502
Hooke's law 13 515
Hopf bifurcation 379
Hoppensteadl, F.C. 376
Horizontal inflection point 657
Horizontal p-integral 220
Hubel, D.H. 376
Huxley, A. 376
Hyperbolic cosine 1118
Hyperbolic functions 91 1118
Hyperbolic PDE 947
Hyperbolic sine 1118
Identity matrix 473
Ill-conditioned matrix 524
Ill-conditioned system 410
Im 1109
Image vector 53
Images, method of 992 1049
Imaginary axis 1111
Imaginary part (Im) 1111
Implicit finite-difference method 1005 1006
Implicit function 642
Implicit function theorem 642 647
Important little integral 1193 1206
Improper (singular) integral 218
Improved Euler method 304
Impulse 275 859
Inconsistent 393
Indicial equation 200
Induction method of proof 90
inductor 35
Infinite series 176
Infinity, point at 1158
Initial conditions 6
Initial-value problem 6
Inner product 433 882
Inner product axioms 434 436
Input 38
Integral curve 2
Integral equation 265
Integral representation of Bessel function 243
Integral representation of Legendre polynomial 217
Integral representations (general) 133
Integral transform 247
Integrating factor method 22 23 66
Integrodifferential equation 36
Interior point 616 1114
Inverse Fourier transform 1253
Inverse function 645
Inverse image 531
Inverse Laplace transform 1251
Inverse matrix 508 518
Inverse-square law 53
Invertible matrix 51
Involutory matrix 480
Irregular singular point 194
Irrotational field 826
Irrotational How 833
Iterated integral 725
Iterative algorithm 1007
J-integral 1249
Jacobi iteration 1008 1100
Jacobian 649
Jeffery, R.L. 845
Johnson, D.E. 216
Johnson, J.R. 216
Jordan curve theorem 1199
Jordan form 580 582
Jordan, D.W. 382 384
Jordan, Wilhelm 404
Joukowski transformation 1177 1179
Jump phenomenon 382
Kelvin, Lord (Sir William Thomson) 810
Kepler's laws 53
Kernel (nullspace) 531
Kernel of integral operator 247 930 984
Kirchhoff's laws 36
Kirchhoff, G.R. 36
Kline, M. 845
Knopp, K. 1190 1218
Kober, H. 1166
Korteweg — de Vries (KdV) equation 953
Kronecker delta 427 461 473
Kronecker, L. 461
kth-order zero 1236
Kutta — Joukowski lift formula 813 1086
L'Hopital's rule for f(z) 1146 1255
Lagrange identity 687 695 898
Lagrange multipliers 667
Lagrange, J.-L. 27 33 667 1017
Laplace convolution integral 259
Laplace equation 1058
Laplace transform 247
Laplace transform application to ODE's 261
Laplace transform application to PDE's 981 1051
Laplace transform convolution theorem 258
Laplace transform design of the transform 268
Laplace transform differentiation with respect to s 283
Laplace transform initial-value theorem 285
Laplace transform integration with respect to s 285
Laplace transform inversion formula 252
Laplace transform kernel 247
Laplace transform large s behavior of transform 285
Laplace transform multiplication by 1/s 282
Laplace transform of derivative 257
Laplace transform of periodic function 287
Laplace transform s-shift 281
Laplace transform t-shift 282
Laplace transform, derivation of 938
Laplace transform, existence of 249
Laplace transform, linearity of 255
Laplace transform, table Appendix C
Laplace transform, uniqueness of inverse transform 252
Laplacian 779
Laurent series 1225
LC circuit 159 271
LD (linearly dependent) 76
Leacock, S.I. 138
Leading 1404
Least squares 673
Least time, principle of 675
Least-square approximation 884
Left-hand limit 852
Legendre equation 125 212 910 1082
Legendre function of second kind 217
Legendre polynomial 213
Legendre, A.M. 125 212
Leibmann iteration 1101
Leibniz rule 676
Leibniz, G.W. 33
Leon, S.J. 498
Lerch's theorem 253
Level curve 758
Level set 759
Levinson, N. 373
LI (linearly independent) 76
Libby, W. 41
Light extinction 45
Limit concept 616
Limit cycle 374
Limit of f(z) 1136
Line 6
Line integral 718
Lineal element 21
Linear combination of a set 76
Linear dependence 444
Linear differential equation 7
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