9780534410025

Multivariable Calculus Concepts and Contexts

by
  • ISBN13:

    9780534410025

  • ISBN10:

    0534410022

  • Edition: 3rd
  • Format: Hardcover
  • Copyright: 11/5/2004
  • Publisher: Brooks Cole
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Summary

Stewart's MULTIVARIABLE CALCULUS: CONCEPTS AND CONTEXTS, Third Edition offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. MULTIVARIABLE CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because it has successfully brought peace to departments that were split between reform and traditional approaches to teaching calculus. Not only does the text help reconcile the two schools of thought by skillfully merging the best of traditional calculus with the best of the reform movement, it does so with innovation and meticulous accuracy.

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
Laboratory Project: An Ellusive Limit
The Binomial 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
Answers to Odd-Numbered Exercises
Index
Table of Contents provided by Publisher. All Rights Reserved.

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