694 INDEX

rank, 419open set, 92, 318order, 20ordered fields, 20orientable, 616orientation, 527oriented curve, 527origin, 279orthogonal matrix, 432orthonormal, 433osculating plane, 354, 358outer measure

measurable, 652on R, 671

p series, 167parallelepiped

definition, 303volume, 303, 456

parameter, 284parametric curve, 339parametric equation, 284parametric function, 275parametrization, 74, 346

space curve, 339partial derivative, 463partial derivatives, 247partial fractions

expansion, 46rules, 215theory, 46

partial summation formula, 170Pascal

triangle, 30permutation, 444permutation matrices, 393permutation symbol, 309permutations, 25perpendicular, 296phase shift, 65pi systems, 664piecewise continuous, 184Piola Kirchhoff stress, 599pivot columns, 401planes, 311pointwise convergence, 113

series, 176polar coordinates, 490

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, 324position vector, 281postive number raised to real power, 73power series, 251

multiplication, 260of a quotient, 266raising to a power, 265

present value of an annuity, 30preservation of compactness, 108prime numbers less given number, 176principal normal, 354, 358product measure, 667product of Borel sets, 666product rule, 130

cross product, 343dot product, 343

projection, 416projection of a vector, 298Pythagorean theorem, 53

quotient rule, 130

radius of convergence, 252radius of curvature, 354, 358range, 47rank, 401, 414rank of a matrix, 451ratio test, 167rational function, 49rational function of cosines and sines, 217rational functions

sines and cosines, 217rational numbers, 15

dense, 28