674 INDEX

preservation, 103continuous function, 103

comparison test, 156, 157complement, 310complement of a set, 90completeness, 32

convergence of Cauchy sequence, 94completeness axiom, 32completing the square, 34complex conjugate, 39complex numbers, 38

roots, 41complex numbers

arithmetic, 38triangle inequality, 39

component, 291component of a force, 289conditional convergence, 156conjugate

of a product, 45conservation of mass, 579conservative, 605

path independent line integral, 518vector field, 518

constitutive laws, 585continuity

equivalent formulations, 100inverse function, 105limits of sequences, 100litany of properties, 99on a compact set, 107one to one, 104preservation of inequality, 100uniform, 107

continuousat one point, 99

continuous and one to onemonotone, 104

continuous function, 98only at irrationals, 102

continuous functionscombinations, 99supremum and infimum, 114

continuous image of compact set, 103contitional convergence, 163contour graph, 449convergence

pointwise, 323

uniform, 323Coordinates, 271Coriolis acceleration

earth, 365Coriolis force, 266countable, 630Cramer’s rule, 443critical point, 487critical points, 133cross product, 293

area of parallelogram, 293coordinate description, 294geometric description, 293

curl, 567curvature, 346, 349

independence, 347cycloid, 609

D’Alembert, 457Darboux integral, 180De Moivre theorem, 44De Moivre’s theorem, 41deformation gradient, 580degree, 52DeMorgan’s laws, 19dense, 28density and mass, 525density of rationals, 28dependent, 400derivative, 461, 462

chain rule, 124equals zero, then function is constant,

139equivalent difference quotient, 124higher order derivatives, 125intermediate value property, 140inverse function, 125mean value theorem, 138product rule, 124quotient rule, 124sum, product, quotient, chain rule, 124

derivative of a function, 331derived series, 245determinant, 433

alternating property, 435cofactor, 410cofactor expansion, 438expanding along row or column, 411