000			07334cam a2200361 i 4500
999			_c8759 _d8759
001			14144450
005			20170426133437.0
008			051017s2007 maua 001 0 eng
010			_a 2005030239
020			_a9780072869538 (acidfree paper)
020			_a0072869534 (acidfree paper)
040			_aDLC _cDLC _dDLC _erda
050	0	0	_aQA303.2 _b.S653 2007
082	0	0	_a515 _222 _bS.R.C
100	1		_aSmith, Robert T. _q(Robert Thomas), _d1955- _eauthor.
245	1	0	_aCalculus. _pEarly transcendental functions / _cRobert T. Smith, Roland B. Minton.
250			_athird edition.
264		1	_aBoston : _bMcGraw-Hill Higher Education, _c[2007]
264		4	_cc2007.
300			_a1 volume (various pagings) : _billustrations ; _c27 cm
336			_2rdacontent _atext
337			_2rdamedia _aunmediated
338			_2rdacarrier _avolume
500			_aIncludes indexes.
505	0		_aChapter 0 PRELIMINARIES 1 0.1 The Real Numbers and the Cartesian Plane 2 0.2 Lines and Functions 11 0.3 Graphing Calculators and Computer Algebra Systems 24 0.4 Solving Equations 34 0.5 Trigonometric Functions 40 0.6 Exponential and Logarithmic Functions 50 Fitting a Curve to Data 0.7 Transformations of Functions 63 0.8 Preview of Calculus 72 CHAPTER 1 LIMITS AND CONTINUITY 81 1.1 The Concept of Limit 82 1.2 Computation of Limits 91 1.3 Continuity and Its Consequences 102 The Method of Bisections 1.4 Limits Involving Infinity 114 1.5 Formal Definition of the Limit 124 Exploring the Definition of Limit Graphically 1.6 Limits and Loss-of-Significance Errors 137 Computer Representation of Real Numbers CHAPTER 2 DIFFERENTIATION: ALGEBRAIC, TRIGONOMETRIC, EXPONENTIAL AND LOGARITHMIC FUNCTIONS 149 2.1 Tangent Lines and Velocity 150 2.2 The Derivative 164 Numerical Differentiation 2.3 Computation of Derivatives: The Power Rule 176 General Derivative Rules Higher Order Derivatives - Acceleration 2.4 The Product and Quotient Rules 187 2.5 Derivatives of Trigonometric Functions 196 2.6 Derivatives of Exponential and Logarithmic Functions 205 2.7 The Chain Rule 213 2.8 Implicit Differentiation and Related Rates 220 2.9 The Mean Value Theorem 229 CHAPTER 3 APPLICATIONS OF DIFFERENTIATION 241 3.1 Linear Approximations and L'Hopital's Rule 242 3.2 Newton's Method 251 3.3 Maximum and Minimum Values 258 3.4 Increasing and Decreasing Functions 269 3.5 Concavity 278 3.6 Overview of Curve Sketching 286 3.7 Optimization 298 3.8 Rates of Change in Applications 310 CHAPTER 4 INTEGRATION 321 4.1 Antiderivatives 322 4.2 Sums and Sigma Notation 334 Principle of Mathematical Induction 4.3 Area 342 4.4 The Definite Integral 350 Average Value of a Function 4.5 The Fundamental Theorem of Calculus 364 4.6 Integration by Substitution 374 4.7 Numerical Integration 384 Error Bounds for Numerical Integration CHAPTER 5 APPLICATIONS OF THE DEFINITE INTEGRAL 401 5.1 Area between Curves 402 5.2 Volume 411 Volumes by Slicing The Method of Disks The Method of Washers 5.3 Volumes by Cylindrical Shells 425 5.4 Arc Length and Surface Area 434 5.5 Projectile Motion 442 5.6 Work, Moments and Hydrostatic Force 453 5.7 Probability 465 CHAPTER 6 EXPONENTIALS, LOGARITHMS AND OTHER TRANSCENDENTAL FUNCTIONS 479 6.1 The Natural Logarithm Revisited 480 6.2 Inverse Functions 487 6.3 The Exponential Function Revisited 495 6.4 Growth and Decay Problems 503 Compound Interest 6.5 Separable Differential Equations 512 Logistic Growth 6.6 Euler's Method 521 6.7 The Inverse Trigonometric Functions 530 6.8 The Calculus of the Inverse Trigonometric Functions 536 6.9 The Hyperbolic Functions 543 The Inverse Hyperbolic Functions Derivation of the Catenary CHAPTER 7 INTEGRATION TECHNIQUES 555 7.1 Review of Formulas and Techniques 556 7.2 Integration by Parts 560 7.3 Trigonometric Techniques of Integration 568 Integrals Involving Powers of Trigonometric Functions Trigonometric Substitution 7.4 Integration of Rational Functions Using Partial Fractions 578 7.5 Integration Tables and Computer Algebra Systems 586 7.6 Indeterminate Forms and L'Hopital's Rule 596 7.7 Improper Integrals 604 - A Comparison Test CHAPTER 8 INFINITE SERIES 621 8.1 Sequences of Real Numbers 622 8.2 Infinite Series 636 8.3 The Integral Test and Comparison Tests 647 8.4 Alternating Series 658 Estimating the Sum of an Alternating Series 8.5 Absolute Convergence and the Ratio Test 666 The Root Test 8.6 Power Series 674 8.7 Taylor Series 682 Proof of Taylor's Theorem 8.8 Applications of Taylor Series 695 8.9 Fourier Series 703 CHAPTER 9 PARAMETRIC EQUATIONS AND POLAR COORDINATES 721 9.1 Plane Curves and Parametric Equations 722 9.2 Calculus and Parametric Equations 732 9.3 Arc Length and Surface Area in Parametric Equations 739 9.4 Polar Coordinates 746 9.5 Calculus and Polar Coordinates 760 9.6 Conic Sections 769 9.7 Conic Sections in Polar Coordinates 779 CHAPTER 10 VECTORS AND THE GEOMETRY OF SPACE 787 10.1 Vectors in the Plane 788 10.2 Vectors in Space 798 10.3 The Dot Product 805 Components and Projections 10.4 The Cross Product 814 10.5 Lines and Planes in Space 827 10.6 Surfaces in Space 836 CHAPTER 11 VECTOR-VALUED FUNCTIONS 851 11.1 Vector-Valued Functions 852 11.2 The Calculus of Vector-Valued Functions 861 11.3 Motion in Space 872 11.4 Curvature 882 Tangential and Normal Components of Acceleration Kepler's Laws CHAPTER 12 FUNCTIONS OF SEVERAL VARIABLES AND PARTIAL DIFFERENTIATION 907 12.1 Functions of Several Variables 908 12.2 Limits and Continuity 924 12.3 Partial Derivatives 936 12.4 Tangent Planes and Linear Approximations 948 Increments and Differentials 12.5 The Chain Rule 960 12.6 The Gradient and Directional Derivatives 967 12.7 Extrema of Functions of Several Variables 979 12.8 Constrained Optimization and Lagrange Multipliers 994 CHAPTER 13 MULTIPLE INTEGRALS 1011 13.1 Double Integrals 1012 13.2 Area, Volume and Center of Mass 1028 13.3 Double Integrals in Polar Coordinates 1039 13.4 Surface Area 1046 13.5 Triple Integrals 1052 Mass and Center of Mass 13.6 Cylindrical Coordinates 1064 13.7 Spherical Coordinates 1071 13.8 Change of Variables in Multiple Integrals 1079 CHAPTER 14 VECTOR CALCULUS 1095 14.1 Vector Fields 1096 14.2 Line Integrals 1108 14.3 Independence of Path and Conservative Vector Fields 1123 14.4 Green's Theorem 1134 14.5 Curl and Divergence 1143 14.6 Surface Integrals 1153 Parametric Representation of Surfaces 14.7 The Divergence Theorem 1167 14.8 Stokes' Theorem 1175 APPENDIX A PROOFS OF SELECT THEOREMS 1188 APPENDIX B ANSWERS TO ODD-NUMBERED EXERCISES 1199 BIBLIOGRAPHY 1251 CREDITS 1261 INDEX 1262
650		0	_aCalculus _vTextbooks.
700	1		_aMinton, Roland B., _d1956- _eauthor.
856	4	1	_3Table of contents only _uhttp://www.loc.gov/catdir/toc/ecip062/2005030239.html
856	4	2	_3Publisher description _uhttp://www.loc.gov/catdir/enhancements/fy0702/2005030239-d.html
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
942			_2ddc _cBK