Applied vector analysis (Q2724081)

As vector analysis is fundamentally present in many domains of pure and applicative science, this book is a useful contribution that offers thorough descriptions of basic items, detailed derivations of related expressions and contains illustrative examples. Each of the seven chapters is followed by a set of problems with solutions to some of them given in the appendix. The book emerged from class notes the authors have been using for many years while lecturing at several universities including the Department of Engineering Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada where they currently teach. NEWLINENEWLINENEWLINEThe first chapter of the book is an interesting cross-section through the history of how vector analysis has been developing, starting from works by Gauss, Green and Hamilton till modern time. The subsequent two chapters introduce basic elements of vector algebra and vector functions of one variable in Cartesian coordinates. This includes properties of algebraic vector operations, vector differentiation, elements of analytical geometry and applications to kinematics of point motions on curves. NEWLINENEWLINENEWLINEChapter 4 is devoted to properties and physical significance of the del operator and related field operators of gradient, curl, divergence and Laplacian. Line, surface and volume integrals are introduced and discussed in Chapter 5. Derivations of integral theorems (Stokes, Green, etc.) are shown in details in Chapter 6 which ends the mostly mathematical treatment of the vector analysis. Its applications to some particular fields are found in the last, Chapter 7. This chapter has some drawbacks that make it less exact, even confusing at some places like the part applied to the fluid dynamics for example. The reason for this could also be typographical errors that can be found in the text. The book is concluded by a list of references and two appendices: Appendix A contains answers to odd numbered exercises while useful vector expressions and formulae are found in Appendix B. NEWLINENEWLINENEWLINEThe book can be a suitable literature for both the undergraduate and graduate engineering students.