Multivariable Calculus Concepts and Contexts

Stewart's CALCULUS: CONCEPTS AND CONTEXTS, FOURTH EDITION offers a streamlined approach to teaching calculus, focusing on major concepts and supporting those with precise definitions, patient explanations, and carefully graded problems. CALCULUS: CONCEPTS AND CONTEXTS is highly regarded because this text offers a balance of theory and conceptual work to satisfy more progressive programs as well as those who are more comfortable teaching in a more traditional fashion. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

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 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
Parametric Surfaces
Review
Focus on Problem Solving
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
Focus on Problem Solving
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
Focus on Problem Solving
Vector Calculus
Vector Fields
Line Integrals
The Fundamental Theorem for Line Integrals
Green's Theorem
Curl and Divergence
Surface Integrals
Stokes' Theorem
Writing Project: Three Men and Two Theorems
The Divergence Theorem
Summary
Review
Focus on Problem Solving
Appendixes
Intervals, Inequalities, and Absolute Values
Coordinate Geometry
Trigonometry
Precise Definitions of Limits
A Few Proofs
Sigma Notation
Integration of Rational Functions by Partial Fractions
Polar Coordinates
Complex Numbers
Answers to Odd-Numbered Exercises
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Multivariable Calculus Concepts and Contexts

Summary

Table of Contents

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