680 INDEX

of quotient, 258raising to a power, 257uniqueness, 247

Taylor’s formula, 143, 213, 503torque vector, 298torsion, 350torus, 560trace, 430traces, 306transformation rules, 622transpose of a matrix, 379triangle inequality, 22, 280, 286

complex numbers, 39trichotomy, 21trigonometric functions, 54trigonometric substitutions, 199

uniform continuity, 323uniform convergence, 109

series, 168uniform norm, 323uniformly Cauchy

sequence of functions, 110uniformly continuous, 107, 237, 327, 328unit tangent vector, 346, 349upper semicontinuous, 113upper sums, 68, 178Urysohn’s lemma, 329

vectorscalar multiplication, 272vector addition, 272

vectorcontravariant components, 615covariant components, 615

vector field, 515, 567vector fields, 320vector identities, 301vector potential, 569vector space axioms, 377vector valued function

continuity, 316derivative, 332integral, 332limit theorems, 318

vector valued functions, 314vectors, 271velocity, 139, 193

volumeparallelepiped, 444

volume element, 550volume increment, 550volume of parallelepiped, 548volume of unit ball in n dimensions, 589volumes

cross section, 172

Wallis formula, 229wave equation, 456Weierstrass approximation

estimate, 111Weierstrass approximation theorem, 112Weierstrass Bolzano theorem, 324Weierstrass M test, 168well ordered, 26work, 222, 516

zeropolynomial, 35