Calculus: Analytic Geometry and Calculus, with Vectors

Index 737

Taylor formulas, 621, 632-640
with remainders, 632-640
Taylor series, 621, 633-634, 636
(See also Power series)
Tchebycheff polynomials, 465
Telescopic sum, 482, 594
Temperature of rod, 553-554
Terms, 335, 588

Termwise differentiation, 620, 632
Termwise integration, 620-621, 672
Tetrahedron, 54, 92, 105
Thread unwound from spool, 190
Topology, 66, 675-676
Torus, 65, 186, 247, 412, 575
Total variation, 352-353
Transcendental functions, 448
Transcendental numbers, 449
Transform, 34, 75, 122
Transformation, 122
of coordinates, 101
Transformers, 34, 75, 96, 112, 122
of vectors, 96, 97
Translation of axes, 392-393
Transpose of matrix, 109
Transversals of three skew lines,
108
Transverse acceleration, 437, 545
Trapezoidal formula, 278
Trends, 294-313
Triangle, area of, 92
Triangle inequality, 33
Triangular roller, 437
Triangulation of surfaces, 447
Trigonometric functions, 10, 38,
242, 43 8-4 79
definitions of, 10
derivatives of, 161, 165, 441-443
graphs of, 38, 442, 443, 450
integrals of, 205, 449-457
inverse, 461-464
table of values of, end papers
Trigonometric inequalities, 441
Trigonometric integrands, 449-457
Trigonometric series, 618-619

Triple integrals, 695-714

in cylindrical coordinates, 702-

707

in rectangular coordinates, 695-

702

in spherical coordinates, 707-714

Trisection of angles, 389, 536-538,

546

Trisectrix of Maclaurin, 546

Trochoids, 400

Uniform circular motion, 46, 182

Uniform continuity, 326

Uniform convergence, 342

Unilateral limits, 133-144

Uniqueness theorem, for power

series, 621

for trigonometric series, 619

Unit normal, 52

Unit vectors, 49, 52, 60, 68

Universal gravitational constant,

74

Upper bound, 212

Upper integral (Darboux), 346

Upper sum (Darboux), 344

V (for victory), 41

Vector(s), 41-47, 48-110

abstract, 586

algebra of, 48-110

components of, 61, 179

derivatives of, 178, 183, 540

independent, 58

integrals of, 210, 259

modern terminology, 177

series of, 597

span of, 57

Vector functions, 112, 150-151, 586

Vector (cross) products, 51, 97-107,

428, 541, 561

Velocities, 178, 190, 436-437, 540-

541