690 INDEX

preservation, 108continuous function, 108

comparison test, 164, 165complement, 318complement of a set, 93completeness, 32

convergence of Cauchy sequence, 97completeness axiom, 32completing the square, 34complex conjugate, 38complex numbers, 38

roots, 41complex numbers

arithmetic, 38triangle inequality, 39

component, 299component of a force, 297conditional convergence, 164conjugate

of a product, 45conservation of mass, 594conservative, 619

path independent line integral, 530vector field, 530

constitutive laws, 599continuity

equivalent formulations, 104inverse function, 110limits of sequences, 104litany of properties, 104on a compact set, 112one to one, 109preservation of inequality, 104uniform, 112

continuousat one point, 103

continuous and one to onemonotone, 109

continuous function, 102only at irrationals, 106

continuous functionscombinations, 104supremum and infimum, 118

continuous image of compact set, 108contitional convergence, 171contour graph, 461convergence

pointwise, 331

uniform, 331Coordinates, 279Coriolis acceleration

earth, 376Coriolis force, 274countable, 644Cramer’s rule, 455critical point, 499critical points, 139cross product, 301

area of parallelogram, 301coordinate description, 302geometric description, 301

curl, 581curvature, 354, 358

independence, 355cycloid, 623

D’Alembert, 469Darboux integral, 188De Moivre theorem, 44De Moivre’s theorem, 41deformation gradient, 595degree, 52DeMorgan’s laws, 19dense, 28density and mass, 537density of rationals, 28dependent, 412derivative, 473, 474

chain rule, 130equals zero, then function is constant,

145equivalent difference quotient, 130higher order derivatives, 131intermediate value property, 146inverse function, 131mean value theorem, 144product rule, 130quotient rule, 130sum, product, quotient, chain rule, 130

derivative of a function, 339derived series, 253determinant, 445

alternating property, 447cofactor, 422cofactor expansion, 450expanding along row or column, 423