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