iv
Chapter 27 INVERSE TRIGONOMETRIC FUNCTIONS
Chapter 28 INTEGRATION BY PARTS
Chapter 29 TRIGONOMETRIC INTEGRANDS AND SUBSTITUTIONS
Chapter 30 INTEGRATION OF RATIONAL FUNCTIONS: THE METHOD
OF PARTIAL FRACTIONS
Chapter 31 INTEGRALS FOR SURFACE AREA, WORK, CENTROIDS
Surface Area of a Solid of Revolution / Work / Centroid of a Planar Region /
Chapter 32 IMPROPER INTEGRALS
Chapter 33 PLANAR VECTORS
Chapter 34 PARAMETRIC EQUATIONS, VECTOR FUNCTIONS, CURVILINEAR
MOTION
Parametric Equations of Plane Curves / Vector-Valued Functions /
Chapter 35 POLAR COORDINATES
Chapter 36 INFINITE SEQUENCES
Chapter 37 INFINITE SERIES
Chapter 38 POWER SERIES
Chapter 39 TAYLOR AND MACLAURIN SERIES
Chapter 40 VECTORS IN SPACE. LINES AND PLANES
Chapter 41 FUNCTIONS OF SEVERAL VARIABLES
Multivariate Functions and Their Graphs / Cylindrical and Spherical Coordinates /
Chapter 42 PARTIAL DERIVATIVES
Chapter 43 DIRECTIONAL DERIVATIVES AND THE GRADIENT.
EXTREME VALUES
Chapter 44 MULTIPLE INTEGRALS AND THEIR APPLICATIONS
Chapter 45 VECTOR FUNCTIONS IN SPACE. DIVERGENCE AND CURL.
LINE INTEGRALS
Chapter 46 DIFFERENTIAL EQUATIONS
INDEX
220
232
238
245
253
260
268
274
289
305
312
326
340
347
361
376
392
405
425
431
443
CONTENTS