INDEX 679

density, 28real numbers, 15rearranged series

convergence, 156recurrence relation, 79recursively defined sequence, 79regular Sturm Liouville problem, 225related rates, 131relations

graph, 50removable discontinuity, 97Rieman integrable

functions of, 183Riemann integrable, 523, 527Riemann integral, 523, 527Riemann integral, Lebesgue integral, 659Riemann sum, 184Riemann sums, 522right handed system, 292Rolle’s theorem, 138root

polynomial, 35root test, 160roots

existence, 33rot, 567rotation matrix, 408row operations, 380, 413row reduced echelon form, 387

existence, 387unique, 389

saddle point, 490scalar field, 567scalar multiplication, 272scalar potential, 605scalar product, 285scalars, 272second derivative test, 141, 505sequence of partial sums, 153sequences, 79sequentially compact

closed and bounded, 92series

absolute convergence, 156conditional convergence, 156convergence criterion, 155double sum, 164

meaning of convergence, 153multiplication of series, 165nonnegative terms, 153p series test, 158ratio test, 159root test, 160

series of functionsuniform convergence, 168

setcomplement, 90

sgn, 431uniqueness, 432

sigma algebra, 633sigma finite, 652sign of a permutation, 432singular point, 487skew symmetric, 379, 394smooth and not analytic, 152smooth curve, 337smoothness more general than analytic, 152spacial coordinates, 580span, 398, 436speed, 139spherical coordinates, 618squeezing theorem, 84step function, 177Stirling’s formula, 230, 670Stoke’s theorem, 599Stokes, 593subspace, 398subtend, 51summation notation, 17sup

increasing sequence, 153interchange of order, 164

symmetric, 379, 394symmetric form of a line, 277symmetric matrices

diagonalization, 423

tangent plane, 484Taylor polynomial

sine, 144Taylor series, 243

coefficients, 247convergence and divergence, 243differentiation, 245multiplication, 252