Multivariable Calculus

by Stewart, James

• ISBN13: 9780495011637
• ISBN10: 0495011630
• Additional ISBN(s): 9780534393571, 9780538497879
• Edition: 6th
• Format: Hardcover
• Copyright: 2007-06-12
• Publisher: Brooks Cole
• More Book Details

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.