Calculus : Early Transcendental Functions

by SMITH

• ISBN13: 9780072869538
• ISBN10: 0072869534
• Edition: 3rd
• Format: Hardcover
• Copyright: 2006-01-23
• Publisher: McGraw-Hill Science/Engineering/Math

Summary

Smith/Minton's Calculus: Early Transcendental Functions, 3/e focuses on student comprehension of calculus. The authors' writing style is clear and understandable, reminiscent of a classroom lecture, which enables students to better grasp techniques and acquire content mastery. Modern applications in examples and exercises connect the calculus with relevant and interesting topics and situations. Detailed examples provide students with helpful guidance that emphasizes what is important and where common pitfalls occur. The exercise sets are balanced with routine, medium, and challenging problems. Technology is integrated throughout the text, but only where it makes sense. These elements all combine to provide a superior text from which students can read, understand, and very effectively learn calculus.

Table of Contents

New Features	xiii
A Commitment to Accuracy	xiv
Preface	xv
Guided Tour	xxiv
Application Index	xxx
Preliminaries	1	(72)
Polynomials and Rational Functions	2	(18)
Graphing Calculators and Computer Algebra Systems	20	(9)
Inverse Functions	29	(7)
Trigonometric and Inverse Trigonometric Functions	36	(12)
Exponential and Logarithmic Functions	48	(13)
Hyperbolic Functions
Fitting a Curve to Data
Transformations of Functions	61	(12)
Limits and Continuity	73	(72)
A Brief Preview of Calculus: Tangent Lines and the Length of a Curve	74	(5)
The Concept of Limit	79	(8)
Computation of Limits	87	(10)
Continuity and Its Consequences	97	(13)
The Method of Bisections
Limits Involving Infinity	110	(11)
Asymptotes
Formal Definition of the Limit	121	(13)
Exploring the Definition of Limit Graphically
Limits and Loss-of-Significance Errors	134	(11)
Computer Representation of Real Numbers
Differentiation	145	(96)
Tangent Lines and Velocity	146	(13)
The Derivative	159	(11)
Numerical Differentiation
Computation of Derivatives: The Power Rule	170	(10)
Higher Order Derivatives
Acceleration
The Product and Quotient Rules	180	(9)
The Chain Rule	189	(7)
Derivatives of Trigonometric Functions	196	(10)
Derivatives of Exponential and Logarithmic Functions	206	(10)
Implicit Differentiation and Inverse Trigonometric Functions	216	(10)
The Mean Value Theorem	226	(15)
Applications of Differentiation	241	(102)
Linear Approximations and Newton's Method	242	(13)
Indeterminate Forms and L'Hopital's Rule	255	(10)
Maximum and Minimum Values	265	(12)
Increasing and Decreasing Functions	277	(9)
Concavity and the Second Derivative Test	286	(10)
Overview of Curve Sketching	296	(12)
Optimization	308	(13)
Related Rates	321	(6)
Rates of Change in Economics and the Sciences	327	(16)
Integration	343	(88)
Antiderivatives	344	(10)
Sums and Sigma Notation	354	(8)
Principle of Mathematical Induction
Area	362	(7)
The Definite Integral	369	(14)
Average Value of a Function
The Fundamental Theorem of Calculus	383	(10)
Integration by Substitution	393	(9)
Numerical Integration	402	(14)
Error Bounds for Numerical Integration
The Natural Logarithm as an Integral	416	(15)
The Exponential Function as the Inverse of the Natural Logarithm
Applications of the Definite Integral	431	(78)
Area Between Curves	432	(9)
Volume: Slicing, Disks, and Washers	441	(15)
Volumes by Cylindrical Shells	456	(8)
Arc Length and Surface Area	464	(8)
Projectile Motion	472	(12)
Applications of Integration to Physics and Engineering	484	(12)
Probability	496	(13)
Integration Techniques	509	(56)
Review of Formulas and Techniques	510	(4)
Integration by Parts	514	(7)
Trigonometric Techniques of Integration	521	(9)
Integrals Involving Powers of Trigonometric Functions
Trigonometric Substitution
Integration of Rational Functions Using Partial Fractions	530	(8)
Brief Summary of Integration Techniques
Integration Tables and Computer Algebra Systems	538	(8)
Improper Integrals	546	(19)
A Comparison Test
First-Order Differential Equations	565	(46)
Modeling with Differential Equations	566	(11)
Growth and Decay Problems
Compound Interest
Separable Differential Equations	577	(10)
Logistic Growth
Direction Fields and Euler's Method	587	(12)
Systems of First-Order Differential Equations	599	(12)
Predator-Prey Systems
Infinite Series	611	(104)
Sequences of Real Numbers	612	(14)
Infinite Series	626	(10)
The Integral Test and Comparison Tests	636	(12)
Alternating Series	648	(8)
Estimating the Sum of an Alternating Series
Absolute Convergence and the Ratio Test	656	(8)
The Root Test
Summary of Convergence Tests
Power Series	664	(8)
Taylor Series	672	(13)
Representation of Functions as Power Series
Proof of Taylor's Theorem
Applications of Taylor Series	685	(9)
The Binomial Series
Fourier Series	694	(21)
Parametric Equations and Polar Coordinates	715	(70)
Plane Curves and Parametric Equations	716	(10)
Calculus and Parametric Equations	726	(8)
Arc Length and Surface Area in Parametric Equations	734	(8)
Polar Coordinates	742	(13)
Calculus and Polar Coordinates	755	(9)
Conic Sections	764	(10)
Conic Sections in Polar Coordinates	774	(11)
Vectors and the Geometry of Space	785	(68)
Vectors in the Plane	786	(10)
Vectors in Space	796	(8)
The Dot Product	804	(11)
Components and Projections
The Cross Product	815	(13)
Lines and Planes in Space	828	(9)
Surfaces in Space	837	(16)
Vector-Valued Functions	853	(66)
Vector-Valued Functions	854	(10)
The Calculus of Vector-Valued Functions	864	(12)
Motion in Space	876	(11)
Curvature	887	(8)
Tangent and Normal Vectors	895	(13)
Tangential and Normal Components of Acceleratior
Kepler's Laws
Parametric Surfaces	908	(11)
Functions of Several Variables and Partial Differentiation	919	(110)
Functions of Several Variables	920	(16)
Limits and Continuity	936	(13)
Partial Derivatives	949	(13)
Tangent Planes and Linear Approximations	962	(11)
Increments and Differentials
The Chain Rule	973	(10)
The Gradient and Directional Derivatives	983	(13)
Extrema of Functions of Several Variables	996	(16)
Constrained Optimization and Lagrange Multipliers	1012	(17)
Multiple Integrals	1029	(86)
Double Integrals	1029	(17)
Area, Volume, and Center of Mass	1046	(12)
Double Integrals in Polar Coordinates	1058	(8)
Surface Area	1066	(6)
Triple Integrals	1072	(12)
Mass and Center of Mass
Cylindrical Coordinates	1084	(8)
Spherical Coordinates	1092	(8)
Change of Variables in Multiple Integrals	1100	(15)
Vector Calculus	1115	(106)
Vector Fields	1116	(14)
Line Integrals	1130	(15)
Independence of Path and Conservative Vector Fields	1145	(11)
Green's Theorem	1156	(9)
Curl and Divergence	1165	(11)
Surface Integrals	1176	(13)
The Divergence Theorem	1189	(10)
Stokes' Theorem	1199	(9)
Applications of Vector Calculus	1208	(13)
Second-Order Differential Equations	1221
Second-Order Equations with Constant Coefficients	1222	(9)
Nonhomogeneous Equations: Undetermined Coefficients	1231	(9)
Applications of Second-Order Equations	1240	(9)
Power Series Solutions of Differential Equations	1249
Appendix A: Proofs of Selected Theorems	1	(12)
Appendix B: Answers to Odd-Numbered Exercises	13
Credits	1	(1)
Index	1