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l.c.m. (least common multiple), 324 Lagrange function, 403 identity, vectors, 185 interpolation formula, 918 method of multiplier, 403 theorem, 301 Lagrangian, 403, 862 Laguerre differential equation, linear, second order, 513 polynomial, 513 Lanczos method, 283 Landau, order symbol, 56 Laplace differential equation, partial, 538, 669 expansion, 259 wave equation, 536 Laplace operator different coordinates, 657 polar coordinates, 401 vector components. 659 Laplace transformation, 710 addition law, 711 comparing to Fourier transformation, 730 convergence, 710 convolution, 713 one-sided, 713 convolution, complex, 714 definition, 710 differential equation, ordinary linear, constant coefficients, 721 linear, variable coefficients, 722 differential equation, partial, 723 differential equations, 721 differentiation, image space, 712 differentiation, original space, 712 discrete, 736 division law, 713 frequency-shift theorem, 711 image space, 710 integration, image space, 712 integration, original space, 712 inverse, 710, 718 inverse integral, 720 linearity law, 711 original function, 710 original space, 710 partial fraction decomposition, 718 piecewise differentiable function, 715 series expansion, 719 similarity law, 711 step function, 714 survey, 707 table, 1067 transform, 710 translation law, 711 largest area method, 374 lateral area cone, 156 cylinder, 154 polyhedron, 151 lateral face, 151 latitude, geographical, 160, 244 lattice, 342 Banach, 614 Bravais, 310 crystallography, 310 distributive, 342 vector, 614 Laurent expansion, 692 series, 692, 736 law cosine, 164 spherical triangle, 164 large numbers, 764 Bernoulli, 764 limit theorem, Lindeberg-Levy, 765 sine-cosine, 164 polar, 164 layer, spherical, 157 least common multiple (l.c.m.), integer numbers, 324 least squares method, 107, 277, 890, 909, 913, 919 calculus of observations. 787 Gauss, 403 regression analysis, 780 least squares problem, linear, 894 Lebesgue integral, 454, 637 comparison with Riemann integral, 453 measure, 636, 816 left singular vector, 285 left-hand coordinate system, 207 leg or side of an angle, 128 Legendre differential equation, 511 polynomial associated, 513 first kind, 511 second kind, 512 symbol, 329 Leibniz alternating series test, 410 formula, 385 lemma Jordan. 695 Schur, 306 lemniscate, 99, 234 length interval, 635 line integral, first type, 464 reduced, 174 vector, 189 length, arc space curve, 246 level curve, 117 line, 644 surface, 644 level set (fuzzy set), 364 library (numerical methods), 944 Aachen library, 946 IMSL library,945 NAG library, 944 limit cycle, 806, 833 stable, 806 unstable, 806 definite integral, 440 function complex variable, 671 one variable, 51 several variables, 122 theorems, 53 function series, 414 integration, depending on parameter, 459 partial sum, 414 sequence of numbers, 405 sequence, in metric space, 606 series, 406 superior, 416 line, 62 curvature, surface, 248 geodesic, 159 imaginary, 205 notion, 128 space, 150, 214 vector equation, 188 line element surface, 245 vector components, 660 line equation plane, 194 Hessian normal form. 195 intercept form. 195 polar coordinates, 195 through a point, 194 through two points, 194 slope, plane, 194 space, 217 line integral, 462 Cartesian coordinates, 661 first type, 463 applications, 464 general type, 467 second type, 464 vector field, 660 linear combination, vectors, 83, 181, 184 linear form, 600, 601 continuous. 623 linear programming assignment problem, 860 basic notions, 849 basic solution, 850 basis of the extreme point, 849 constraints, 846 degenerate extreme point, 849 distribution problem, 860 dual problem, 856 duality, 856 extreme point, 849 normal form, 849, 850 objective function, 846 primal problem, 856 round-tour problem, 861 surplus variable, 850 linearly dependent, 317 independent, 317 lines angle between, plane, 196 intersection point, plane, 195 orthogonal, 128, 197 parallel, 128, 150, 197 pencil, 196 perpendicular, 128, 197 skew, 150 Liouville approximation theorem, 4 formula, 501, 802 theorem, 801 Lipschitz condition higher-order differential equation, 498 ordinary differential equation, 488 locus, geometric, 194 logarithm binary, 10 Briggsian, 9 complex function, 678 decimal, 9 definition, 9 natural, 9, 698 Neperian, 9 principal value, 698 table, 10 taking of an expression, 9 logarithmic decrement, 83 logarithmic integral, 431, 460 logarithmic normal distribution, 759 logic, 286 fuzzy, 360 predicate, 289 propositional, 286 longitude, geographical, 160, 244 loop function, 1007 loop, graph, 348 Lorentz curve, 731 Lorenz system, 798, 801, 839 loxodrome, 177 arclength, 177 course angle, 178 intersection point, 178 intersection point of two loxodromes, 179 p space, 639 LU factorization (lower and upper triangular matrix). 891 Lyapunov exponent, 820 function, 803