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Multivariable Calculus,9780495011637
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Multivariable Calculus

by
Edition:
6th
ISBN13:

9780495011637

ISBN10:
0495011630
Format:
Hardcover
Pub. Date:
6/12/2007
Publisher(s):
Cengage Learning
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Summary

Success in your calculus course starts here! James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. With CALCULUS, Sixth Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. His patient examples and built-in learning aids will help you build your mathematical confidence and achieve your goals in the course!

Table of Contents

Parametric Equations and Polar Coordinates
Curves Defined by Parametric Equations
Laboratory Project: Families of Hypocycloids
Calculus with Parametric Curves
Laboratory Project: Bezier Curves
Polar Coordinates
Areas and Lengths in Polar Coordinates
Conic Sections
Conic Sections in Polar Coordinates
Review
Problems Plus
Infinite Sequences and Series
Sequences
Laboratory Project: Logistic Sequences
Series
The Integral Test and Estimates of Sums
The Comparison Tests
Alternating Series
Absolute Convergence and the Ratio and Root Tests
Strategy for Testing Series
Power Series
Representation of Functions as Power Series
Taylor and Maclaurin Series
Writing Project: How Newton Discovered the Binomial Series
Applications of Taylor Polynomials
Applied Project: Radiation from the Stars
Review
Problems Plus
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
Cylinders and Quadric Surfaces
Cylindrical and Spherical Coordinates
Laboratory Project: Families of Surfaces
Review
Problems Plus
Vector Functions
Vector Functions and Space Curves
Derivatives and Integrals of Vector Functions
Arc Length and Curvature
Motion in Space: Velocity and Acceleration
Applied Project: Kepler's Laws
Review
Problems Plus
Partial Derivatives
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Tangent Planes and Linear Approximations
The Chain Rule
Directional Derivatives and the Gradient Vector
Maximum and Minimum Values
Applied Project: Designing a Dumpster
Discovery Project: Quadratic Approximations and Critical Points
Lagrange Multipliers
Applied Project: Rocket Science
Applied Project: Hydro-Turbine Optimization
Review
Problems Plus
Multiple Integrals
Double Integrals over Rectangles
Iterated Integrals
Double Integrals over General Regions
Double Integrals in Polar Coordinates
Applications of Double Integrals
Surface Area
Triple Integrals
Discovery Project: Volumes of Hyperspheres
Triple Integrals in Cylindrical and Spherical Coordinates
Applied Project: Roller Derby
Discovery Project: The Intersection of Three Cylinders
Change of Variables in Multiple Integrals
Review
Problems Plus
Vector Calculus
Vector Fields
Line Integrals
The Fundamental Theorem for Line Integrals
Green's Theorem
Curl and Divergence
Parametric Surfaces and Their Areas
Surface Integrals
Stokes' Theorem
Writing Project: Three Men and Two Theorems
The Divergence Theorem
Summary
Review
Problems Plus
Second-Order Differential Equations
Second-Order Linear Equations
Nonhomogeneous Linear Equations
Applications of Second-Order Differential Equations
Series Solutions
Review
Problems Plus
Appendixes
Intervals, Inequalities, and Absolute Values
Coordinate Geometry and Lines
Graphs of Second-Degree Equations
Trigonometry
Sigma Notation
Proofs of Theorems
Complex Numbers
H
Table of Contents provided by Publisher. All Rights Reserved.


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