678 INDEX

rank, 407open set, 90, 310order, 20ordered fields, 20orientable, 602orientation, 515oriented curve, 515origin, 271orthogonal matrix, 420orthonormal, 421osculating plane, 346, 349outer measure

measurable, 638on R, 657

p series, 159parallelepiped

definition, 296volume, 296, 444

parameter, 276parametric curve, 331parametric equation, 276parametric function, 267parametrization, 73, 338

space curve, 331partial derivative, 451partial derivatives, 239partial fractions

expansion, 46rules, 207theory, 46

partial summation formula, 162Pascal

triangle, 30permutation, 432permutation matrices, 381permutation symbol, 302permutations, 25perpendicular, 288phase shift, 65pi systems, 650piecewise continuous, 176Piola Kirchhoff stress, 585pivot columns, 389planes, 303pointwise convergence, 108

series, 168polar coordinates, 478

polar form complex number, 40polynomial, 35, 49

addition, 35degree, 35division, 36equality, 35monic, 36multiplication, 35

polynomialleading term, 35monic, 35

polynomialsfactoring, 42greatest common divisor, 36

polynomials in n variables, 316position vector, 273postive number raised to real power, 73power series, 243

multiplication, 252of a quotient, 258raising to a power, 257

present value of an annuity, 30preservation of compactness, 103prime numbers less given number, 168principal normal, 346, 349product measure, 653product of Borel sets, 652product rule, 124

cross product, 335dot product, 335

projection, 404projection of a vector, 290Pythagorean theorem, 53

quotient rule, 124

radius of convergence, 244radius of curvature, 346, 349range, 47rank, 389, 402rank of a matrix, 439ratio test, 159rational function, 49rational function of cosines and sines, 209rational functions

sines and cosines, 209rational numbers, 15

dense, 28