Advanced Calculus fi..

738 Advanced Calculus, Fifth EditionLiouville, substitution, 144 (Prob. 13)theorem, 566 (Prob. 6)Lipschitz condition, 652Logarithmic derivative, 582function, 549-552potential, 252 (Prob. 2), 350,699residue, 582-584Lorentz condition, 341Lower limit of sequence, 379-381Maclaurin series, 428,561-565Magnitude of a vector, 2, 3,46,211 (Prob. 15)Mapping. See Conformal mapping;Transformation of coordinates; Function;Linear equations, mappingMass, 229,233, 313 (Prob. 3), 349Matrices, 18-71,436addition, 19augmented, 32characteristic equation, 35column vectors, 19determinant of, 26diagonal, 36eigenvalues, 35-38, 156,641eigenvectors, 35-38,61 (Prob. 12), 156,64 1entry, 18identity, 18inverse of, 26,33Jacobian, 91,207kernel of, 58,64of maximum rank, 65minor of, 65multiplication, 21nonsingular, 28nullity, 64order of, 18orthogonal, 41orthogonally congruent, 42permutation, 31 (Prob. 11)powers of, 24,28product of, 21rank of, 33,6347row echelon form, 33row vectors, 18scalar times, 19similar, 36singular, 28, 29square, 18subtraction. 20syrnmetric.40 'triangular, 32zero, 18Matrix function, 638-644Maxima and minima, 145-160,446,705,707Maxwell equations, 341Mean value. See Average valueMean value theorem, 217,230,233,445Mechanical system of N particles, 662,668Mesh, 215, 225Metric space, 81Minkowski inequality, 498Moment of inertia, 229,313 (Prob. 3)Monotone sequence, 167,378Morera's theorem, 554Multilinear, 372Multiple integrals, 232M-test for integrals, 454for series, 416Multiplication of matrices, 21of series, 407-409of vector by scalar, 2,46of vectors, 3-5,46Multiplicity of zero, 571,573,577, 581,582Multiply connected, 292,297-300,555, 558Nabla symbol, 125, 179Negative direction, 273-275triple, 5Neighborhood, 74-76,538Newtonian potential, 253 (Rob. 3), 361Newton's Second Law, 281Nonhomogeneous differential equations,631-646Nonorientable surface, 307Norm, 2-3,46,211 (Prob. 15), 497,517,672-673 (Prob. 8)Normal component of acceleration, 128(Prob. 7)to curves, surfaces, 8, 125, 128 (Probs. 6,7),245Normalized orthogonal systems, 497Normal modes, 645,6644565,670,677479,686,700,nth term test, 386Numerical evaluation of integrals, 218-219,221-223,279 (Prob. 6)methods for differential equations, 649,703'