# Vector Calculus, 5th edition

- Susan J. Colley
- , Santiago Cañez

**Find it fast**Quickly navigate your eTextbook with search

**Stay organized**Access all your eTextbooks in one place

**Easily continue access**Keep learning with auto-renew

**Vector Calculus** uses the language and notation of vectors and matrices to help you start the transition from first-year calculus to more advanced technical math. Its readable narrative, numerous figures, strong examples and exercise sets help foster a solid grasp of the concepts. An appropriate level of rigor collects most of the technical derivations at the ends of sections; many proofs are available for reference but are positioned in a way that does not disrupt the flow of main ideas. The **5th Edition** offers clarifications, new examples and new exercises throughout. For the first time, this book is now available as a Pearson eText that includes interactive GeoGebra applets. Background in single-variable calculus is assumed.

Published by Pearson (August 15th 2022) - Copyright © 2022

ISBN-13: 9780136800101

Subject: Calculus

Category: Vector Calculus

### 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