Calculus

ISBN-10: 0470183497

ISBN-13: 9780470183496

Edition: 9th 2009

List price: $276.95
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Description: Countless people have relied on Anton to learn the difficult concepts of calculus. The new ninth edition continues the tradition of providing an accessible introduction to the field. It improves on the carefully worked and special problems to increase comprehension. New applied exercises demonstrate the usefulness of mathematics. More summary tables and step-by-step summaries are included to offer additional support when learning the concepts. And Quick Check exercises have been revised to more precisely focus on the most important ideas. This book will help anyone who needs to learn calculus and build a strong mathematical foundation.

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Book details

List price: $276.95
Edition: 9th
Copyright year: 2009
Publisher: John Wiley & Sons, Incorporated
Publication date: 3/9/2009
Binding: Hardcover
Pages: 1312
Size: 8.75" wide x 10.25" long x 1.75" tall
Weight: 5.434
Language: English

Stephen Davis is the author of numerous books, including "The New York Times" bestsellers "Hammer of the Gods: The Led Zeppelin Saga" & "Walk This Way: The Autobiography of Aerosmith", & coauthor of "Fleetwood", the memoirs of Fleetwood Mac drummer Mick Fleetwood. His journalism has appeared in "Rolling Stone", "The New York Times", "The Boston Globe", & many other publications. He lives in New England.

Before Calculus
Functions
New Functions from Old
Families of Functions
Inverse Functions
Limits and Continuity
Limits
Computing Limits
Limits at Infinity; End Behavior of a Function
Limits
Continuity
Continuity of Trigonometric Functions
The Derivative
Tangent Lines and Rates of Change
The Derivative Function
Introduction to Techniques of Differentiation
The Product and Quotient Rules
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Related Rates
Local Linear Approximation; Differentials
The Derivative in Graphing and Applications
Analysis of Functions I: Increase, Decrease, and Concavity
Analysis of Functions II: Relative Extrema; Graphing Polynomials
Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents
Absolute Maxima and Minima
Applied Maximum and Minimum Problems
Rectilinear Motion
Newton's Method
Rolle's Theorem; Mean-Value Theorem
Integration
An Overview of the Area Problem
The Indefinite Integral
Integration by Substitution
The Definition of Area as a Limit; Sigma Notation
The Definite Integral
The Fundamental Theorem of Calculus
Rectilinear Motion Revisited: Using Integration
Average Value of a Function and Its Applications
Evaluating Definite Integrals by Substitution
Applications of the Definite Integral in Geometry, Science and Engineering
Area Between Two Curves
Volumes by Slicing; Disks and Washers
Volumes by Cylindrical Shells
Length of a Plane Curve
Area of a Surface Revolution
Work
Moments, Centers of Gravity, and Centroids
Fluid Pressure and Force
Exponential, Logarithmic, and Inverse Trigonometric Functions
Exponential and Logarithmic Functions
Derivatives and Integrals Involving Logarithmic Functions
Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions
Graphs and Applications Involving Logarithmic and Exponential Functions
L'H�opital's Rule; Indeterminate Forms
Logarithmic and Other Functions Defined by Integrals
Derivatives and Integrals Involving Inverse Trigonometric Functions
Hyperbolic Functions and Hanging Cubes
Principles of Integral Evaluation
An Overview of Integration Methods
Integration by Parts
Integrating Trigonometric Functions
Trigonometric Substitutions
Integrating Rational Functions by Partial Fractions
Using Computer Algebra Systems and Tables of Integrals
Numerical Integration; Simpson's Rule
Improper Integrals
Mathematical Modeling with Differential Equations
Modeling with Differential Equations
Separation of Variables
Slope Fields; Euler's Method
First-Order Differential Equations and Applications
Infinite Series
Sequences
Monotone Sequences
Infinite Series
Convergence Tests
The Comparison, Ratio, and Root Tests
Alternating Series; Absolute and Conditional Convergence
Maclaurin and Taylor Polynomials
Maclaurin and Taylor Series; Power Series
Convergence of Taylor Series
Differentiating and Integrating Power Series; Modeling with Taylor Series
Parametric and Polar Curves; Conic Sections
Parametric Equations; Tangent Lines and Arc Length for Parametric Curves
Polar Coordinates
Tangent Lines, Arc Length, and Area for Polar Curves
Conic Sections
Rotation of Axes; Second-Degree Equations
Conic Sections in Polar Coordinates
Three-Dimensional Space; Vectors
Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces
Vectors
Dot Product; Projections
Cross Product
Parametric Equations of Lines
Planes in 3-Space
Quadric Surfaces
Cylindrical and Spherical Coordinates
Vector-Valued Functions
Introduction to Vector-Valued Functions
Calculus of Vector-Valued Functions
Change of Parameter; Arc Length
Unit Tangent, Normal, and Binormal Vectors
Curvature
Motion Along a Curve
Kepler's Laws of Planetary Motion
Partial Derivatives
Functions of Two or More Variables
Limits and Continuity
Partial Derivatives
Differentiability, Differentials, and Local Linearity
The Chain Rule
Directional Derivatives and Gradients
Tangent Planes and Normal Vectors
Maxima and Minima of Functions of Two Variables
Lagrange Multipliers
Multiple Integrals
Double Integrals
Double Integrals over Nonrectangular Regions
Double Integrals in Polar Coordinates
Surface Area; Parametric Surfaces}
Triple Integrals
Triple Integrals in Cylindrical and Spherical Coordinates
Change of Variable in Multiple Integrals; Jacobians
Centers of Gravity Using Multiple Integrals
Topics in Vector Calculus
Vector Fields
Line Integrals
Independence of Path; Conservative Vector Fields
Green's Theorem
Surface Integrals
Applications of Surface Integrals; Flux
The Divergence Theorem
Stokes' Theorem
Appendix [order of sections TBD]
Graphing Functions Using Calculators and Computer Algebra Systems
Trigonometry Review
Solving Polynomial Equations
Mathematical Models
Selected Proofs
Web Appendices
Real Numbers, Intervals, and Inequalities
Absolute Value
Coordinate Planes, Lines, and Linear Functions
Distance, Circles, and Quadratic Functions
Second-Order Linear Homogeneous Differential Equations; The Vibrating String
The Discriminant
Answers
Photocredits
Index
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