Table of contents for Calculus : early transcendental functions / Robert T. Smith, Roland B. Minton.

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TABLE OF CONTENTS
Preface xiii
	Chapter 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

Library of Congress Subject Headings for this publication:

Calculus -- Textbooks.