696 INDEX

of quotient, 266raising to a power, 265uniqueness, 255

Taylor’s formula, 149, 221, 515torque vector, 305torsion, 358, 359torus, 574trace, 442traces, 314transformation rules, 636transpose of a matrix, 391triangle inequality, 22, 288, 294

complex numbers, 39trichotomy, 21trigonometric functions, 54trigonometric substitutions, 207

uniform continuity, 331uniform convergence, 114

series, 176uniform norm, 331uniformly Cauchy

sequence of functions, 115uniformly continuous, 112, 245, 335, 336unit tangent vector, 354, 358upper semicontinuous, 118upper sums, 69, 186Urysohn’s lemma, 337

vectorscalar multiplication, 280vector addition, 280

vectorcontravariant components, 629covariant components, 629

vector field, 527, 581vector fields, 328vector identities, 309vector potential, 583vector space axioms, 389vector valued function

continuity, 324derivative, 340integral, 340limit theorems, 326

vector valued functions, 322vectors, 279velocity, 145, 201

volumeparallelepiped, 456

volume element, 564volume increment, 564volume of parallelepiped, 562volume of unit ball in n dimensions, 603volumes

cross section, 180

Wallis formula, 237wave equation, 468Weierstrass approximation

estimate, 115Weierstrass approximation theorem, 117Weierstrass Bolzano theorem, 332Weierstrass M test, 176well ordered, 26work, 230, 528

zeropolynomial, 35