E
eccentricity, numerical curve second order, 207 ellipse, 198 hyperbola, 200 parabola, 203 edge angle, 150 figure, 150 graph, 348 length, 350 valuation, 350 multiple, 348 sequence, 351 cycle, 351 directed circuit, 351 isolated edge, 351 open, 351 path, 351 effective rate, 22 eigenfunction, 541 differential equation, 515 integral equation, 565, 570 normalized, 516 eigenvalue, 278, 541 differential equation, 515 integral equation, 565, 570 operator, 622 eigenvalue problem general, 278 matrices, 278 special, 278 eigenvector, 264, 278, 622 Einstein's summation convention, 262 element, 290 finite, 914 generic, 814 linearly independent, 598 neutral, 298 positive, 601 element of area, plane, table, 474 element of surface, curved, table, 482 element of volume, table, 479 elementary cell crystal lattice, 310 non-primitive, 310 primitive, 310 elementary formula, predicate logic, 289 elementary surface, parametric form, 482 elementary volume arbitrary coordinates, 479 Cartesian coordinates, 476 cylindrical coordinates, 477 spherical coordinates, 478 elimination method, Gauss, 276 elimination step, 891 ellipse, 198 arc, 200 area, 199 diameter, 198 equation, 198 focal properties, 198 focus, 198 perimeter, 200 radius of curvature, 199 semifocal chord, 198 tangent, 199 transformation, 205 vertex, 198 ellipsoid, 220 central surface, 224 cigar form, 220 imaginary, 224 lens form, 220 of revolution, 220 surface second order, 224 embedding, canonical, 626 encoding method, RSA, 331 encyphering, 334 endomorphism, linear operators, 601 endpoint, 348 energy particle, 539 spectrum, 540 system, 538 zero-point translational energy, 541 zero-point vibration energy, 546 entropy generalized, 825 metric, 819 topological, 819, 829 envelope, 236, 237 epicycloid, 101 curtate, 102 prolate, 102 epitrochoid, 102 equality asymptotic, 419 complex numbers, 34 matrices, 254 equality relation identity, 10 equation, 10 algebraic, 38, 43 biquadratic, 42 characteristic, 278, 494, 503, 505 cubic, 40, 63 curve plane, 194, 225 second degree, 205 second order, 205 defining, 508 degree, 38 Diophantine, 325 linear, 325 ellipse, 198 exponential, solution, 45 first degree, 39 fourth degree, 42 homogeneous, 629 hyperbola, 200 hyperbolic functions, solution, 46 inhomogeneous, 629 irrational, 39 Korteweg de Vries, 548 line plane, 194 space, 217 linear, 39 logarithmic, solution, 46 logistic, 798, 837 non-linear fixed point, 884 numerical solution, 884 normal form, 38 n-th degree, 43 operator equation, 629 parabola, 203 Parseval, 422, 516, 579, 618 pendulum, 841 plane, 214 general, 214 Hessian normal form, 214 intercept form, 215 plane curve, 194 polynomial numerical solution, 887 quadratic, 39, 62 root, definition, 38 Schrodinger linear, 538 non-linear, 547 second degree, 39 sine-Gordon, 549 solution, general, 38 space curve, 214, 238 vector form, 238 sphere, 243 surface normal form, 220 second order, 223 space, 213, 243 system of, 38 term algebra, 341 third degree, 40 transcendent, 38 trigonometric, solution, 46 vector, 187 equation system linear^ 271, 890 overdetermined, 893 non-linear, 890, 896 numerical method, iteration, 890 numerical solution, 890 direct method, 890 overdetermined, 277, 890 row echelon form, 890 underdetermined, 890 equations Delambre, 166 L'Huilier. 167 Mollweide, 142 Neper, 167 equilibrium point, 797 hyperbolic, 804 equivalence, 286 class, 297 logic, 287 proof, 5 relation, 296 Eratosthenes sieve, 320 error absolute, 792, 939 absolute maximum error, 792 apparent, 790 average, 789, 791 computer calculation, 941 defined, 792 density function, 788 discretization, 942 equation, 893 estimation, iteration method, 897 input error, 941 least mean squares, 421 mean, 789 square, 790, 791 normally distributed, 788 percentage, 792 probable, 789, 791 relations between error types, 789 relative, 792, 939 relative maximum error, 792 round-off, 942 single measurement, 790 standard, 790 true, 790 truncation error, 942 type 1 error rate, 753 error (continued) type, measurement errors. 788 error analysis, 796 error calculus direct problem, 941 inverse problem, 941 error curve, 72 error estimation, mean value theorem, 389 error function, 461 Gauss, 759 error integral, Gauss, 461 error orthogonality, 909 error propagation. 794 law, 795 error types, computer calculation, 941 ess. sup (essential supremum), 639 Euclidean algorithm, 3, 14 polynomial rings, 315 norm, 318 vector norm, 258 vector space, 318 Euler angle, 211 broken line method, 904 circuit, 352 constant, 460 differential equation n-th order, 504 variational calculus. 554 formula, 247, 420 formulas, 421,424 function, 331 graph, 352 integral of the second kind, 459 integral, first kind, 1056 integral, second kind, 1056 numbers, 412 polygonal method, 904 relation (complex numbers), 35, 698 theorem, 154 trail, 352 open, 352 Euler-Hierholzer theorem, 352 event, 747 certain, 747 complete system of, 748, 750 elementary, 747 impossible, 747 independent, 750 random, 747 set of events, 747 simple, 747 evolute, 236 evolution equation, 547 function, 547 evolution strategies, 870 evolvent, 236, 237 of circle, 104 excess, spherical triangle, 163 exchange theorem, 395 exchange, cyclic, sides and angles, 141 excluded middle, 287 existential quantifier, 289 expansion Fourier, forms, 423 Laplace, 259 Laurent, 692 Maclaurin, 418 Taylor, 389, 417, 691 expectation, 753 expected value, 753 bivariate distribution, 779 two-dimensional distribution, 779 exponent, 7 exponential distribution, 760 exponential function, 71 complex, 679 general, 699 natural, 698 exponential integral, 461 exponential sum, 72 expression algebraic, 10 manipulation, 979 analytic, 48 domain, 48 explicit form, 48 implicit form, 48 parametric form, 49 Boolean, 344 concurrent, 345 explicit form, 48 finite, 908 partial differential equations, 911 implicit form, 48 integral rational, 11 irrational, 11, 17 non-polynomial, manipulation, 981 parametric form, 49 propositional logic, 286 rational, 11, 14 semantically equivalent, 345 tautology, 288 transcendent, 11 vector analysis, 659 extension principle, 368 extension theorem of Hahn, 625 extension, linear functional, 624 extraction of the root complex numbers, 38 real numbers, 8 extrapolation principle, 902 extremal, radius of curvature, 558 extreme value, 390 absolute, 390 determination, 391 higher derivatives, 391 side conditions, 403 sign change, 390 function, 401 relative, 390