Vector Calculus, 4th edition

  • Susan J. Colley

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Overview

Vector Calculus uses the language and notation of vectors and matrices to teach multivariable calculus. This text is distinguished from others by its easy-to-understand narrative, numerous figures, thoughtfully selected examples, and carefully crafted exercise sets.

Published by Pearson (July 14th 2021) - Copyright © 2012

ISBN-13: 9780137549276

Subject: Calculus

Category: Vector Calculus

Table of contents

Table of Contents

  1. Vectors
    • 1.1 Vectors in Two and Three Dimensions
    • 1.2 More About Vectors
    • 1.3 The Dot Product
    • 1.4 The Cross Product
    • 1.5 Equations for Planes; Distance Problems
    • 1.6 Some n-dimensional Geometry
    • 1.7 New Coordinate Systems
    • True/False Exercises for Chapter 1
    • Miscellaneous Exercises for Chapter 1
  2. Differentiation in Several Variables
    • 2.1 Functions of Several Variables;Graphing Surfaces
    • 2.2 Limits
    • 2.3 The Derivative
    • 2.4 Properties; Higher-order Partial Derivatives
    • 2.5 The Chain Rule
    • 2.6 Directional Derivatives and the Gradient
    • 2.7 Newton's Method (optional)
    • True/False Exercises for Chapter 2
    • Miscellaneous Exercises for Chapter 2
  3. Vector-Valued Functions
    • 3.1 Parametrized Curves and Kepler's Laws
    • 3.2 Arclength and Differential Geometry
    • 3.3 Vector Fields: An Introduction
    • 3.4 Gradient, Divergence, Curl, and the Del Operator
    • True/False Exercises for Chapter 3
    • Miscellaneous Exercises for Chapter 3
  4. Maxima and Minima in Several Variables
    • 4.1 Differentials and Taylor's Theorem
    • 4.2 Extrema of Functions
    • 4.3 Lagrange Multipliers
    • 4.4 Some Applications of Extrema
    • True/False Exercises for Chapter 4
    • Miscellaneous Exercises for Chapter 4
  5. Multiple Integration
    • 5.1 Introduction: Areas and Volumes
    • 5.2 Double Integrals
    • 5.3 Changing the Order of Integration
    • 5.4 Triple Integrals
    • 5.5 Change of Variables
    • 5.6 Applications of Integration
    • 5.7 Numerical Approximations of Multiple Integrals (optional)
    • True/False Exercises for Chapter 5
    • Miscellaneous Exercises for Chapter 5
  6. Line Integrals
    • 6.1 Scalar and Vector Line Integrals
    • 6.2 Green's Theorem
    • 6.3 Conservative Vector Fields
    • True/False Exercises for Chapter 6
    • Miscellaneous Exercises for Chapter 6
  7. Surface Integrals and Vector Analysis
    • 7.1 Parametrized Surfaces
    • 7.2 Surface Integrals
    • 7.3 Stokes's and Gauss's Theorems
    • 7.4 Further Vector Analysis; Maxwell's Equations
    • True/False Exercises for Chapter 7
    • Miscellaneous Exercises for Chapter 7
  8. Vector Analysis in Higher Dimensions
    • 8.1 An Introduction to Differential Forms
    • 8.2 Manifolds and Integrals of k-forms
    • 8.3 The Generalized Stokes's Theorem
    • True/False Exercises for Chapter 8
    • Miscellaneous Exercises for Chapter 8

Suggestions for Further Reading

Answers to Selected Exercises

Index

Your questions answered

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