Calculus Early Transcendentals

ISBN-10: 0131875337

ISBN-13: 9780131875333

Edition: 2007

List price: $193.80 Buy it from $37.45 Rent it from $17.08
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Description: Clear and Concise. Varberg focuses on the most critical concepts. This popular calculus text remains the shortest mainstream calculus book available -- yet covers "all" relevant material needed by, and appropriate to, the study of calculus at this level. It' s conciseness and clarity helps you focus on, and understand, critical concepts in calculus without them getting bogged down and lost in excessive and unnecessary detail. It is accurate, without being excessively rigorous, up-to-date without being faddish.

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Book details

List price: $193.80
Copyright year: 2007
Publisher: Prentice Hall PTR
Publication date: 5/15/2006
Binding: Hardcover
Pages: 880
Size: 8.70" wide x 10.90" long x 1.40" tall
Weight: 4.686
Language: English

Preface
Preliminaries
Real Numbers, Estimation, and Logic
Inequalities and Absolute Values
The Rectangular Coordinate System
Graphs of Equations
Functions and Their Graphs
Operations on Functions
Exponential and Logarithmic Functions
The Trigonometric Functions
The Inverse Trigonometric Functions
Chapter Review
Review and Preview Problems
Limits
Introduction to Limits
Rigorous Study of Limits
Limit Theorems
Limits at Infinity; Infinite Limits
Limits Involving Trigonometric Functions
Natural Exponential, Natural Log, and Hyperbolic Functions
Continuity of Functions
Chapter Review
Review and Preview Problems
The Derivative
Two Problems with One Theme
The Derivative
Rules for Finding Derivatives
Derivatives of Trigonometric Functions
The Chain Rule
Higher-Order Derivatives
Implicit Differentiation
Related Rates
Derivatives of Exponential and Logarithmic Functions
Derivatives of Hyperbolic and Inverse Trigonometric Functions
Differentials and Approximations
Chapter Review
Review and Preview Problems
Applications of the Derivative
Maxima and Minima
Monotonicity and Concavity
Local Extrema and Extrema on Open Intervals
Practical Problems
Graphing Functions Using Calculus
The Mean Value Theorem for Derivatives
Solving Equations Numerically
Antiderivatives
Introduction to Differential Equations
Exponential Growth and Decay
Chapter Review
Review and Preview Problems
The Definite Integral
Introduction to Area
The Definite Integral
The First Fundamental Theorem of Calculus
The Second Fundamental Theorem of Calculus and the Method of Substitution
The Mean Value Theorem for Integrals and the Use of Symmetry
Numerical Integration
Chapter Review
Review and Preview Problems
Applications of the Integral
The Area of a Plane Region
Volumes of Solids: Slabs, Disks, Washers
Volumes of Solids of Revolution: Shells
Length of a Plane Curve
Work and Fluid Force
Moments and Center of Mass
Probability and Random Variables
Chapter Review
Review and Preview Problems
Techniques of Integration and Differential Equations
Basic Integration Rules
Integration by Parts
Some Trigonometric Integrals
Rationalizing Substitutions
Integration of Rational Functions Using Partial Fractions
Strategies for Integration
First-Order Linear Differential Equations
Approximations for Differential Equations
Chapter Review
Review and Preview Problems
Indeterminate Forms and Improper Integrals
Indeterminate Forms of Type 0/0
Other Indeterminate Forms
Improper Integrals: Infinite Limits of Integration
Improper Integrals: Infinite Integrands
Chapter Review
Review and Preview Problems
Infinite Series
Infinite Sequences
Infinite Series
Positive Series: The Integral Test
Positive Series: Other Tests
Alternating Series, Absolute Convergence, and Conditional Convergence
Power Series
Operations on Power Series
Taylor and Maclaurin Series
The Taylor Approximation to a Function
Chapter Review
Review and Preview Problems
Conics and Polar Coordinates
The Parabola
Ellipses and Hyperbolas
Translation and Rotation of Axes
Parametric Representation of Curves in the Plane
The Polar Coordinate System
Graphs of Polar Equations
Calculus in Polar Coordinates
Chapter Review
Review and Preview Problems
Geometry in Space and Vectors
Cartesian Coordinates in Three-Space
Vectors
The Dot Product
The Cross Product
Vector-Valued Functions and Curvilinear Motion
Lines and Tangent Lines in Three-Space
Curvature and Components of Acceleration
Surfaces in Three-Space
Cylindrical and Spherical Coordinates
Chapter Review
Review and Preview Problems
Derivatives for Functions of Two or More Variables
Functions of Two or More Variables
Partial Derivatives
Limits and Continuity
Differentiability
Directional Derivatives and Gradients
The Chain Rule
Tangent Planes and Approximations
Maxima and Minima
The Method of Lagrange Multipliers
Chapter Review
Review and Preview Problems
Multiple Integrals
Double Integrals over Rectangles
Iterated Integrals
Double Integrals over Nonrectangular Regions
Double Integrals in Polar Coordinates
Applications of Double Integrals
Surface Area
Triple Integrals in Cartesian Coordinates
Triple Integrals in Cylindrical and Spherical Coordinates
Change of Variables in Multiple Integrals
Chapter Review
Review and Preview Problems
Vector Calculus
Vector Fields
Line Integrals
Independence of Path
Green's Theorem in the Plane
Surface Integrals
Gauss's Divergence Theorem
Stokes's Theorem
Chapter Review
Differential Equations
Linear Homogeneous Equations
Nonhomogeneous Equations
Applications of Second-Order Equations
Chapter Review
Appendix
Mathematical Induction
Proofs of Several Theorems
Answers to Odd-Numbered Problems
Index
Photo Credits
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