With its important applications in a broad range of real-world problems, building a strong foundation in vector analysis is an essential part of the future engineer's education. Too often, however, the subject is treated only briefly in general calculus or engineering mathematics courses, and those treatments tend to be focused on theory rather than practical applications.

Applied Vector Analysis richly illustrates the application of vector calculus to physical problems. The authors clearly explain the theory, but focus on its application with an abundance of worked practical examples and exercises drawn from fluid mechanics, electromagnetic theory, and Maxwell's wave and heat equations.

Developed from class notes used over many years of teaching vector analysis, this book is an ideal text for a one-semester course for senior undergraduate or graduate engineering students. With its bibliography and convenient appendix of vector formula, Applied Vector Analysis will also provide a valuable reference for graduate students and professional engineers.

Table of Contents:
HISTORICAL BACKGROUND
Introduction
Hamilton's Quaternions
Grassmann's Calculus of Extension
The Work of Maxwell
Modern Vector Analysis
Other Contributions
ALGEBRA
Addition and Subtraction of Vectors
Scalar and Vector Products
Scalar and Vector Projections
Cartesian Frame of Reference
Vector Algebra Using Coordinates
Mixed Product in Coordinate Form
Vector Representation Using Coordinates
Lines and Planes Using Vector Algebra
The Equation of a Plane
Partial Derivatives
Iterated Partial Derivatives
Exercises
VECTOR FUNCTIONS
Vector Differentiation
Geometric Interpretation of R'
Higher-Order Derivatives
Curves, Length and Arc Length
Motion on a Curve, Velocity and Acceleration
Curvature, Components of Acceleration
Curvature, Tangential and Normal Components of Acceleration
Exercises
THE DEL OPERATOR
Gradient Characterizes Maximum Increase
Tangent Planes and Normal Lines
Tangent Planes
Normal Lines
Divergence and Curl of a Vector Field
Physical Interpretation of Divergence
Physical Interpretation of the Curl
The Laplacian Operator
Vector Identities
Exercises
INTEGRALS
Introduction
Line Integrals and Vector Functions
Work
Line Integrals Independent of Path
Conservative Vector Fields
Surface Integrals
Orientation of a Surface
Volume Integration
Triple Integrals in cylindrical Coordinates
Triple Integrals in Spherical Coordinates
Exercises
INTEGRAL THEOREMS
Green's Theorem
Region with Holes
Integrals Over Vector Fields
Stokes Theorem
Green's Theorrem in 3-D
The Divergence Theorem
Exercises
APPLICATIONS
Introduction
Accerleration Vector
Continuity Equation of Fluid Flow
Continuity Equation and Heat Conduction
Poisson's Equation
Vectors in Electromagnetic Theory
The Continuity Equation Again
Maxwell's Equations for Electromagnetic Fields
Waves Solutions of Maxwell's Equations
Ocean Wave Interactions
Solution Techniques for Snl
Graphical Simulation of a Vector Field
Exercises
BIBLIOGRAPHY
APPENDICES
Answers to Odd-Numbered Exercises
Vector Formulae at a Glance