INDEX 695

density, 28real numbers, 15rearranged series

convergence, 164recurrence relation, 81recursively defined sequence, 81regular Sturm Liouville problem, 234related rates, 137relations

graph, 50removable discontinuity, 101Rieman integrable

functions of, 191Riemann integrable, 535, 540Riemann integral, 535, 540Riemann integral, Lebesgue integral, 673Riemann sum, 193Riemann sums, 534right handed system, 300Rolle’s theorem, 144root

polynomial, 35root test, 168roots

existence, 33rot, 581rotation matrix, 420row operations, 392, 425row reduced echelon form, 399

existence, 399unique, 401

saddle point, 502scalar field, 581scalar multiplication, 280scalar potential, 619scalar product, 293scalars, 280second derivative test, 148, 517sequence of partial sums, 161sequences, 81sequentially compact

closed and bounded, 95series

absolute convergence, 164conditional convergence, 164convergence criterion, 163double sum, 172

meaning of convergence, 161multiplication of series, 173nonnegative terms, 161p series test, 166ratio test, 167root test, 168

series of functionsuniform convergence, 176

setcomplement, 93

sgn, 443uniqueness, 444

sigma algebra, 647sigma finite, 666sign of a permutation, 444singular point, 499skew symmetric, 391, 406smooth and not analytic, 159smooth curve, 345smoothness more general than analytic, 159spacial coordinates, 595span, 410, 448speed, 145spherical coordinates, 632squeezing theorem, 86step function, 185Stirling’s formula, 238, 684Stoke’s theorem, 613Stokes, 607subspace, 410subtend, 51summation notation, 17sup

increasing sequence, 161interchange of order, 172

symmetric, 391, 406symmetric form of a line, 285symmetric matrices

diagonalization, 435

tangent plane, 495Taylor polynomial

sine, 151Taylor series, 251

coefficients, 255convergence and divergence, 251differentiation, 253multiplication, 260