# 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.

ISBN-13: 9780137549276

Subject: Calculus

Category: Vector Calculus

1. Vectors
• 1.1 Vectors in Two and Three Dimensions
• 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

#### Index

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