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CHAPTER1 LINEAR COORDINATE SYSTEMS.ABSOLUTE VALUE.INEQUALITIES 1

CHAPTER2 RECTANGULAR COORDINATE SYSTEMS 9

CHAPTER3 LINES 18

CHAPTER4 CIRCLES 30

CHAPTER5 EQUATIONS AND THEIR GRAPHS 39

CHAPTER6 FUNCTIONS 53

CHAPTER7 LIMITS 61

CHAPTER8 CONTINUITY 71

CHAPTER9 THE DERIVATIVE 79

CHAPTER10 RULES FOR DIFFERENTIATING FUNCTIONS 86

CHAPTER11 IMPLICIT DIFFERENTIATION 98

CHAPTER12 TANGENT AND NORMAL LINES 102

CHAPTER13 LAW OF THE MEAN.INCREASING AND DECREASING FUNCTIONS 108

CHAPTER14 MAXIMUM AND MINIMUM VALUES 115

CHAPTER15 CURVE SKETCHING.CONCAVITY.SYMMETRY 129

CHAPTER16 REVIEW OF TRIGONOMETRY 141

CHAPTER17 DIFFERNTIATION OF TRIGONOMETRIC FUNCTIONS 152

CHAPTER18 INVERSE TRIGONOMETRIC FUNCTIONS 166

CHAPTER19 RECTILINEAR AND CIRCULAR MOTION 175

CHAPTER20 RELATED RATES 182

CHAPTER21 DIFFERENTIALS.NEWTON S METHOD 188

CHAPTER22 ANTIDERIVATIVES 196

CHAPTER23 THE DEFINITE INTEGRAL.AREA UNDER A CURVE 206

CHAPTER24 THE FUNDAMENTAL THEOREM OF CALCULUS 216

CHAPTER25 THE NATURAL LOGARITHM 225

CHAPTER26 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 234

CHAPTER27 L HOPITAL S RULE 243

CHAPTER28 EXPONENTIAL GROWTH AND DECAY 252

CHAPTER29 APPLICATIONS OF INTEGRATION I：AREA AND ARC LENGTH 257

CHAPTER30 APPLICATIONS OF INTEGRATION II:VOLUME 266

CHAPTER31 TECHNIQUES OF INTEGRATION I:INTEGRATION BY PARTS 281

CHAPTER32 TECHNIQUES OF INTEGRATION II：TRIGONOMETRIC INTEGRANDS AND TRIGONOMETRIC SUBSTITUTIONS 289

CHAPTER33 TECHNIQUES OF INTEGRATION III:INTEGRATION BY PARTIAL FRACTIONS 304

CHAPTER34 MISCELLANEOUS SUBSTITUTIONS 314

CHAPTER35 IMPROPER INTEGRALS 320

CHAPTER36 APPLICATIONS OF INTEGRATION II:APEA OF A SURFACE OF REVOLUTION 329

CHAPTER37 PARAMETRIC REPRESENTATION OF CURVES 336

CHAPTER38 CURVATURE 342

CHAPTER39 PLANE VECTORS 351

CHAPTER40 CURVILINEAR MOTION 363

CHAPTER41 POLAR COORDINATES 370

CHAPTER42 INFINITE SEQUENCES 385

CHAPTER43 INFINITE SERIES 394

CHAPTER44 SERIES WITH POSITIVE TERMS.THE INTEGRAL TEST.COMPARISON TESTS 400

CHAPTER45 ALTERNATING SERIES.ABSOLUTE AND CONDITIONAL CONVERGENCE.THE RATIO TEST 410

CHAPTER46 POWER SERIES 419

CHAPTER47 TAYLOR AND MACLAURIN SERIES.TAYLOR S FORMULA WITH REMAINDER 432

CHAPTER48 PARTIAL DERIVATIVES 442

CHAPTER49 TOTAL DIFFEREANTIAL.DIFFERENTIABILITY.CHAINRULES 452

CHAPTER50 SPACE VECTORS 464

CHAPTER51 SURFACE AND CURVES IN SPACE 478

CHAPTER52 DIRECIONAL DERIVATIVES.MAXIMUM AND MINIMUM VALUES 490

CHAPTER53 VECTOR DIFFERENTIATION AND INTEGRATION 498

CHAPTER54 DOUBLE AND ITERATED INTEGRALS 511

CHAPTER55 CENTROIDS AND MOMENTS OF INERTIA OF PLANE AREAS 520

CHAPTER56 DOUBLE INTEGRATION APPLIED TO VOLUME UNDER A SURFACE AND THE AREA OF A CURVED SURFACE 530

CHAPTER57 TRIPLE INTEGRALS 539

CHAPTER58 MASSES OF VARIABLE DENSITY 552

CHAPTER59 DIFFERNTIAL EQUATIONS OF FIRST AND SECOND ORDER 559

INDEX 573