Calculus : A Modern Approach, Premiere Edition

by Smith, Robert T.; Minton, Roland B.

• ISBN13: 9780072304749
• ISBN10: 007230474X
• Format: Paperback
• Copyright: 1999-11-01
• Publisher: McGraw-Hill College

Table of Contents

Preface	viii
Preliminaries	1	(73)
The Real Numbers and the Cartesian Plane	2	(8)
Lines and Functions	10	(12)
Graphing Calculators and Computer Algebra Systems	22	(9)
Solving Equations	31	(6)
Trigonometric Functions	37	(8)
Exponential and Logarithmic Functions	45	(12)
Transformations of Functions	57	(8)
Preview of Calculus	65	(9)
Limits and Continuity	74	(62)
The Concept of Limit	74	(9)
Computation of Limits	83	(10)
Continuity and Its Consequences	93	(12)
Limits Involving Infinity	105	(9)
Formal Definition of the Limit (Optional)	114	(13)
Limits and Loss-of-Significance Errors (Optional)	127	(9)
Differentiation	136	(79)
Tangent Lines and Velocity	136	(13)
The Derivative	149	(10)
Computation of Derivatives: The Power Rule	159	(9)
The Product and Quotient Rules	168	(8)
Derivatives of Trigonometric Functions	176	(7)
Derivatives of Exponential and Logarithmic Functions	183	(7)
The Chain Rule	190	(6)
Implicit Differentiation and Related Rates	196	(8)
The Mean Value Theorem	204	(11)
Applications of Differentiation	215	(71)
Linear Approximations and Newton's Method	216	(10)
Maximum and Minimum Values	226	(10)
Increasing and Decreasing Functions	236	(8)
Concavity	244	(8)
Overview of Curve Sketching	252	(11)
Optimization	263	(12)
Rates of Change in Applications (Optional)	275	(11)
Integration	286	(68)
Antiderivatives	287	(11)
Sums and Sigma Notation	298	(7)
Area	305	(8)
The Definite Integral	313	(11)
The Fundamental Theorem of Calculus	324	(10)
Integration by Substitution	334	(8)
Numerical Integration	342	(12)
Applications of the Definite Integral	354	(64)
Area Between Curves	354	(7)
Volume	361	(13)
Volumes by Cylindrical Shells	374	(6)
Arc Length and Surface Area	380	(7)
Projectile Motion	387	(9)
Work, Moments and Hydrostatic Force	396	(11)
Probability (Optional)	407	(11)
Exponentials, Logarithms and Other Transcendental Functions	418	(63)
The Natural Logarithm	419	(6)
Inverse Functions	425	(6)
The Exponential Function	431	(7)
Growth and Decay Problems	438	(9)
Separable Differential Equations	447	(7)
Euler's Method	454	(7)
The Inverse Trigonometric Functions	461	(5)
The Calculus of the Inverse Trigonometric Functions	466	(6)
The Hyperbolic Functions	472	(9)
Integration Techniques	481	(59)
Review of Formulas and Techniques	481	(5)
Integration by Parts	486	(6)
Trigonometric Techniques of Integration	492	(9)
Integration of Rational Functions Using Partial Fractions	501	(7)
Integration Tables and Computer Algebra Systems	508	(8)
Indeterminate Forms and L'Hopital's Rule	516	(9)
Improper Integrals	525	(15)
Infinite Series	540	(86)
Sequences of Real Numbers	540	(13)
Infinite Series	553	(10)
The Integral Test and Comparison Tests	563	(9)
Alternating Series	572	(8)
Absolute Convergence and the Ratio Test	580	(8)
Power Series	588	(8)
Taylor Series	596	(13)
Fourier Series	609	(17)
Parametric Equations and Polar Coordinates	626	(63)
Plane Curves and Parametric Equations	626	(11)
Calculus and Parametric Equations	637	(7)
Arc Length and Surface Area in Parametric Equations	644	(9)
Polar Coordinates	653	(12)
Calculus and Polar Coordinates	665	(8)
Conic Sections	673	(9)
Conic Sections in Polar Coordinates	682	(7)
Vectors and the Geometry of Space	689	(58)
Vectors in the Plane	689	(9)
Vectors in Space	698	(8)
The Dot Product	706	(8)
The Cross Product	714	(12)
Lines and Planes in Space	726	(9)
Surfaces in Space	735	(12)
Vector-Valued Functions	747	(51)
Vector-Valued Functions	747	(8)
The Calculus of Vector-Valued Functions	755	(11)
Motion in Space	766	(10)
Curvature	776	(7)
Tangent and Normal Vectors	783	(15)
Functions of Several Variables and Partial Differentiation	798	(83)
Functions of Several Variables	798	(11)
Limits and Continuity	809	(12)
Partial Derivatives	821	(10)
Tangent Planes and Linear Approximations	831	(10)
The Chain Rule	841	(6)
The Gradient and Directional Derivatives	847	(11)
Extrema of Functions of Several Variables	858	(12)
Constrained Optimization and Lagrange Multipliers	870	(11)
Multiple Integrals	881	(76)
Double Integrals	881	(17)
Area, Volume and Center of Mass	898	(8)
Double Integrals in Polar Coordinates	906	(7)
Surface Area	913	(5)
Triple Integrals	918	(11)
Cylindrical Coordinates	929	(6)
Spherical Coordinates	935	(8)
Change of Variables in Multiple Integrals	943	(14)
Vector Calculus	957	(86)
Vector Fields	958	(11)
Line Integrals	969	(15)
Independence of Path and Conservative Vector Fields	984	(9)
Green's Theorem	993	(9)
Curl and Divergence	1002	(10)
Surface Integrals	1012	(12)
The Divergence Theorem	1024	(7)
Stokes' Theorem	1031	(12)
Appendix A: Proofs of Selected Theorems	1043	(9)
Appendix B: Table of Integrals	1052	(8)
Appendix C: Answers to Select Exercises	1060	(38)
Bibliography	1098	(9)
Index	1107