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Calculus : Early Transcendental Functions,9780072869538
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Calculus : Early Transcendental Functions

by
Edition:
3rd
ISBN13:

9780072869538

ISBN10:
0072869534
Format:
Hardcover
Pub. Date:
1/23/2006
Publisher(s):
McGraw-Hill Science/Engineering/Math
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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


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