Instructor's Solutions Manual for Thomas' Calculus, Multivariable, Twelfth Edition vol 2

Title: INSTRUCTOR’S SOLUTIONS  MANUAL MULTIVARIABLE......Page 1
ISBN-10: 0-321-60072-X......Page 2
PREFACE TO THE INSTRUCTOR......Page 3
TABLE OF CONTENTS......Page 5
10.1 SEQUENCES......Page 7
10.2 INFINITE SERIES......Page 15
10.3 THE INTEGRAL TEST......Page 21
10.4 COMPARISON TESTS......Page 28
10.5 THE RATIO AND ROOT TESTS......Page 35
10.6 ALTERNATING SERIES, ABSOLUTE AND CONDITIONAL CONVERGENCE......Page 40
10.7 POWER SERIES......Page 46
10.8 TAYLOR AND MACLAURIN SERIES......Page 55
10.9 CONVERGENCE OF TAYLOR SERIES......Page 59
10.10 THE BINOMIAL SERIES......Page 65
CHAPTER 10 PRACTICE EXERCISES......Page 72
CHAPTER 10 ADDITIONAL AND ADVANCED EXERCISES......Page 80
11.1 PARAMETRIZATIONS OF PLANE CURVES......Page 85
11.2 CALCULUS WITH PARAMETRIC CURVES......Page 92
11.3 POLAR COORDINATES......Page 100
11.4 GRAPHING IN POLAR COORDINATES......Page 105
11.5 AREA AND LENGTHS IN POLAR COORDINATES......Page 112
11.6 CONIC SECTIONS......Page 117
11.7 CONICS IN POLAR COORDINATES......Page 127
CHAPTER 11 PRACTICE EXERCISES......Page 137
CHAPTER 11 ADDITIONAL AND ADVANCED EXERCISES......Page 147
12.1 THREE-DIMENSIONAL COORDINATE SYSTEMS......Page 153
12.2 VECTORS......Page 156
12.3 THE DOT PRODUCT......Page 161
12.4 THE CROSS PRODUCT......Page 166
12.5 LINES AND PLANES IN SPACE......Page 172
12.6 CYLINDERS AND QUADRIC SURFACES......Page 179
CHAPTER 12 PRACTICE EXERCISES......Page 184
CHAPTER 12 ADDITIONAL AND ADVANCED EXERCISES......Page 192
13.1 CURVES IN SPACE AND THEIR TANGENTS......Page 197
13.2 INTEGRALS OF VECTOR FUNCTIONS; PROJECTILE MOTION......Page 202
13.3 ARC LENGTH IN SPACE......Page 208
13.4 CURVATURE AND NORMAL VECTORS OF A CURVE......Page 211
13.5 TANGENTIAL AND NORMAL COMPONENTS OF ACCELERATION......Page 216
13.6 VELOCITY AND ACCELERATION IN POLAR COORDINATES......Page 222
CHAPTER 13 PRACTICE EXERCISES......Page 223
CHAPTER 13 ADDITIONAL AND ADVANCED EXERCISES......Page 229
14.1 FUNCTIONS OF SEVERAL VARIABLES......Page 233
14.2 LIMITS AND CONTINUITY IN HIGHER DIMENSIONS......Page 242
14.3 PARTIAL DERIVATIVES......Page 248
14.4 THE CHAIN RULE......Page 254
14.5 DIRECTIONAL DERIVATIVES AND GRADIENT VECTORS......Page 262
14.6 TANGENT PLANES AND DIFFERENTIALS......Page 267
14.7 EXTREME VALUES AND SADDLE POINTS......Page 274
14.8 LAGRANGE MULTIPLIERS......Page 287
14.9 TAYLOR'S FORMULA FOR TWO VARIABLES......Page 295
14.10 PARTIAL DERIVATIVES WITH CONSTRAINED VARIABLES......Page 297
CHAPTER 14 PRACTICE EXERCISES......Page 300
CHAPTER 14 ADDITIONAL AND ADVANCED EXERCISES......Page 314
15.1 DOUBLE AND ITERATED INTEGRALS OVER RECTANGLES......Page 319
15.2 DOUBLE INTEGRALS OVER GENERAL REGIONS......Page 320
15.3 AREA BY DOUBLE INTEGRATION......Page 334
15.4 DOUBLE INTEGRALS IN POLAR FORM......Page 338
15.5 TRIPLE INTEGRALS IN RECTANGULAR COORDINATES......Page 342
15.6 MOMENTS AND CENTERS OF MASS......Page 347
15.7 TRIPLE INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES......Page 352
15.8 SUBSTITUTIONS IN MULTIPLE INTEGRALS......Page 360
CHAPTER 15 PRACTICE EXERCISES......Page 365
CHAPTER 15 ADDITIONAL AND ADVANCED EXERCISES......Page 371
16.1 LINE INTEGRALS......Page 377
16.2 VECTOR FIELDS, WORK, CIRCULATION, AND FLUX......Page 382
16.3 PATH INDEPENDENCE, POTENTIAL FUNCTIONS, AND CONSERVATIVE FIELDS......Page 390
16.4 GREEN'S THEOREM IN THE PLANE......Page 395
16.5 SURFACES AND AREA......Page 401
16.6 SURFACE INTEGRALS......Page 410
16.7 STOKES' THEOREM......Page 418
CHAPTER 16 PRACTICE EXERCISES......Page 427
CHAPTER 16 ADDITIONAL AND ADVANCED EXERCISES......Page 435