Vector Calculus, 4th edition

  • Susan J. Colley

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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

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 1
Miscellaneous Exercises for 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 2
Miscellaneous Exercises for 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 3
Miscellaneous Exercises for 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 4
Miscellaneous Exercises for 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 5
Miscellaneous Exercises for 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 6
Miscellaneous Exercises for 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 7
Miscellaneous Exercises for 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 8
Miscellaneous Exercises for 8
Suggestions for Further Reading
Answers to Selected Exercises

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