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