Applied Vector Analysis, Second Edition: (Electrical Engineering Textbook Series)

In engineering and applied science, the practical problems that arise are often described using mathematical models. In order to interpret these figures and make a judicious decision relating to such problems, engineers and scientists need ample knowledge of vector analysis. Illustrating the application of vector analysis to physical problems, this new edition of Applied Vector Analysis expands its coverage of the field to encompass new concepts, such as the divergence theorem, position vectors, and Berouilli's equation. It provides the grounding in vector analysis engineers and scientists require with an emphasis on practical applications This user-friendly volume is divided into seven chapters, each providing a clear manifestation of theory and its application to real-life problems. Beginning with a brief historical background of vector calculus, the authors introduce the algebra of vectors using a single variable. Within this framework, the book goes on to discuss the Del operator, which plays a significant role in displaying physical problems in mathematical notation. Chapter 6 contains important integral theorems, such as Green's theorem, Stokes theorem, and divergence theorem. Specific applications of these theorems are described using selected examples in fluid flow, electromagnetic theory, and the Poynting vector in Chapter 7. The appendices supply important vector formulas at a glance and mathematical explanations to selected examples from within the text. One of the most valuable branches of mathematics, vector analysis is pertinent to the investigation of physical problems encountered in many disciplines. Using real-world applications, concise explanations of fundamental concepts, and extensive examples, Applied Vector Analysis, Second Edition provides a clear cut exposition of the fields' practical uses.

Table of Contents:
HISTORICAL BACKGROUND Introduction Hamilton's quaternions Grassmann's calculus of extension The work of Maxwell Modern vector analysis Other contributions THE ALGEBRA OF VECTORS Introduction Addition and subtraction of vectors Geometrical interpretation of addition and subtraction of vectors Multiplication by a number Centroid or centre of mean position 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 OF ONE VARIABLE Introduction Vector differentiation Geometric interpretation of dR/dt 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 Radial and transverse components of velocity and acceleration Exercises THE DEL OPERATOR Introduction Gradient characterizes maximum increase Tangent planes and normal lines Tangent plane Normal lines Divergence and curl of a vector field Physical interpretation of divergence Physical interpretation of the curl The Laplacian operator Vector identities Exercises LINE, SURFACE AND VOLUME 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 Introduction Green's theorem Region with holes Integrals over vector fields Green's theorem in vector form Stokes' theorem in 3-D The divergence theorem Orthogonal curvilinear coordinates Exercises APPLICATIONS Introduction Acceleration vector Continuity equation of fluid flow Euler's equation of motion Continuity equation and heat conduction Poisson's equation Vectors in electromagnetic theory The continuity equation revisited Maxwell's equations for electromagnetic fields Solutions of Maxwell's wave equations The Poynting vector Graphical simulation of a vector field APPENDICES: Answers to some selected exercises Vector formulae at a glance

About the Author :
Dalhousie University, Halifax, Nova Scotia, Canada Qatar University, Doha