Calculus Concepts and Contexts

ISBN-10: 0495557420
ISBN-13: 9780495557425
Edition: 4th 2010
Authors: James Stewart
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Book details

List price: $340.95
Edition: 4th
Copyright year: 2010
Publisher: Brooks/Cole
Publication date: 3/9/2009
Binding: Hardcover
Pages: 1152
Size: 9.00" wide x 10.00" long x 1.50" tall
Weight: 5.082
Language: English

Preface
To the Student
Diagnostic Tests
A Preview of Calculus
Functions and Models
Four Ways to Represent a Function
Mathematical Models: A Catalog of Essential Functions
New Functions from Old Functions
Graphing Calculators and Computers
Exponential Functions
Inverse Functions and Logarithms
Parametric Curves
Laboratory Project: Running Circles around Circles
Review
Principles of Problem Solving
Limits and Derivatives
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Laws
Continuity
Limits Involving Infinity
Derivatives and Rates of Change
Writing Project: Early Methods for Finding Tangents
The Derivative as a Function
What Does f?? Say about f? Review
Focus on Problem Solving
Differentiation Rules
Derivatives of Polynomials and Exponential Functions
Applied Project: Building a Better Roller Coaster
The Product and Quotient Rules
Derivatives of Trigonometric Functions
The Chain Rule
Laboratory Project: BTzier Curves
Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation
Inverse Trigonometric Functions and their Derivatives
Derivatives of Logarithmic Functions
Discovery Project: Hyperbolic Functions
Rates of Change in the Natural and Social Sciences
Linear Approximations and Differentials
Laboratory Project: Taylor Polynomials
Review
Focus on Problem Solving
Applications of Differentiation
Related Rates
Maximum and Minimum Values
Applied Project: The Calculus of Rainbows
Derivatives and the Shapes of Curves
Graphing with Calculus and Calculators
Indeterminate Forms and l'Hospital's Rule
Writing Project: The Origins of l'Hospital's Rule
Optimization Problems
Applied Project: The Shape of a Can
Newton's Method
Antiderivatives
Review
Focus on Problem Solving
Integrals
Areas and Distances
The Definite Integral
Evaluating Definite Integrals
Discovery Project: Area Functions
The Fundamental Theorem of Calculus
Writing Project: Newton, Leibniz, and the Invention of Calculus
The Substitution Rule
Integration by Parts
Additional Techniques of Integration
Integration Using Tables and Computer Algebra Systems
Discovery Project: Patterns in Integrals
Approximate Integration
Improper Integrals
Review
Focus on Problem Solving
Applications of Integration
More about Areas
Volumes
Discovery Project: Rotating on a Slant
Volumes by Cylindrical Shells
Arc Length
Discovery Project: Arc Length Contest
Average Value of a Function
Applied Project: Where To Sit at the Movies
Applications to Physics and Engineering
Discovery Project: Complementary Coffee Cups
Applications to Economics and Biology
Probability
Review
Focus on Problem Solving
Differential Equations
Modeling with Differential Equations
Direction Fields and Euler's Method
Separable Equations
Applied Project: How Fast Does a Tank Drain? Applied Project: Which Is Faster, Going Up or Coming Down? Exponential Growth and Decay
Applied Project: Calculus and Baseball
The Logistic Equation
Predator-Prey Systems
Review
Focus on Problem Solving
Infinte Sequences and Series
Sequences
Laboratory Project: Logistic Sequences
Series
The Integral and Comparison Tests
Estimating Sums
Other Convergence Tests
Power Series
Representations of Functions as Power Series
Taylor and Maclaurin Series
Laboratory Project: An Elusive Limit
Writing Project: How Newton Discovered the Binomial Series
Applications of Taylor Polynomials
Applied Project: Radiation from the Stars
Review
Focus on Problem Solving
Vectors and the Geometry of Space
Three-Dimensional Coordinate Systems
Vectors
The Dot Product
The Cross Product
Discovery Project: The Geometry of a Tetrahedron
Equations of Lines and Planes
Laboratory Project: Putting 3D in Perspective
Functions and Surfaces
Cylindrical and Spherical Coordinates
Laboratory Project: Families of Surfaces
Review
Focus on Problem Solving
Vector Functions
Vector Func

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