Calculus with Differential Equations

ISBN-10: 0132306336
ISBN-13: 9780132306331
Edition: 9th 2007
List price: $193.80
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Description: This the shortest mainstream calculus book available. The authors make effective use of computing technology, graphics, and applications, and provide at least two technology projects per chapter. This popular book is correct without being  More...

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Book details

List price: $193.80
Edition: 9th
Copyright year: 2007
Publisher: Prentice Hall PTR
Publication date: 4/10/2006
Binding: Hardcover
Pages: 880
Size: 9.00" wide x 11.25" long x 1.50" tall
Weight: 5.170
Language: English

This the shortest mainstream calculus book available. The authors make effective use of computing technology, graphics, and applications, and provide at least two technology projects per chapter. This popular book is correct without being excessively rigorous, up-to-date without being faddish. Maintains a strong geometric and conceptual focus. Emphasizes explanation rather than detailed proofs. Presents definitions consistently throughout to maintain a clear conceptual framework. Provides hundreds of new problems, including problems on approximations, functions defined by tables, and conceptual questions. Ideal for readers preparing for the AP Calculus exam or who want to brush up on their calculus with a no-nonsense, concisely written book.

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
Trigonometric Functions
Chapter Review
Review and Preview Problems
Limits
Introduction to Limits
Rigorous Study of Limits
Limit Theorems
Limits Involving Trigonometric Functions
Limits at Infinity; Infinite Limits
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
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
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
Transcendental Functions
The Natural Logarithm Function
Inverse Functions and Their Derivatives
The Natural Exponential Function
General Exponential and Logarithmic Functions
Exponential Growth and Decay
First-Order Linear Differential Equations
Approximations for Differential Equations
The Inverse Trigonometric Functions and Their Derivatives
The Hyperbolic Functions and Their Inverses
Chapter Review
Review and Preview Problems
Techniques of Integration
Basic Integration Rules
Integration by Parts
Some Trigonometric Integrals
Rationalizing Substitutions
Integration of Rational Functions Using Partial Fractions
Strategies for Integration
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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