11R9. Engineering Analysis in Applied Mechanics. - JW Brewer (Univ of California, Davis CA). Taylor & Francis Publ, New York NY. 2002. 472 pp. ISBN 1-56032-932-7. $75.00.
Reviewed by T Krzyzynski (Dept of Mech Eng, Koszalin Univ of Tech, Raclawicka 15-17, Koszalin, 75-620, Poland).
This is a book which constitutes a comprehensive course of application of mathematical methods in engineering analysis in solid mechanics, dynamics, and thermodynamics. The author, who deals with mathematics as a language of technology, addresses his book to students of mechanical engineering.
This book consists of six chapters, two appendices, answers to selected exercises, and a subject index. Each chapter ends with review questions, exercises, and references to the subject considered, and is illustrated by good-quality figures. Four chapters and one appendix contain a section called Computer Assignments, which presents an illustration on how to solve problems by means of computer programs like MATLAB.
In Chapter 1 (Theory of Equations), fundamentals of equations derived and solved in mechanical sciences are briefly discussed. The emphasis of this chapter is on the existence and uniqueness of the solutions of algebraic equations.
Chapter 2 (Theory of the Extreme Values of Functions) deals with mathematical theory of maxima and minima of algebraic functions. The attention is focused on mathematical and engineering significance of the terms: necessary and sufficient conditions of existence of function extrema.
Chapter 3 (Calculus of Variations), stating a natural extension of Chapter 2, is devoted to fundamentals of the subject in its title and presents applications in engineering economics, mechanical design, and automatic control.
Chapter 4 (Extremum Principles of Thermodynamics) covers applications of extremum principles in thermodynamics. A mental model of thermodynamics is introduced to illustrate concepts presented. In this chapter, besides the physics of thermodynamics and the mathematical structure of thermodynamics, one can study problems like Legendre transforms, thermodynamics of engines and thermodynamic stability.
Chapter 5 (Stationarity and Extremum Principles of Solid Mechanics) is dedicated to applications of extremum principles in problems encountered in solid mechanics. A reader becomes familiar with the principle of virtual work of rigid and deformable bodies, and questions like stability of static equilibrium, complementary energy, and energy methods.
Chapter 6 (Equations of Motion and the Stationarity Principles of Lagrange and Hamilton) is focused on deriving the differential equations of motion of by using either Lagrange’s or Hamilton’s equations. The attention is restricted to the idealization of modeling dynamical systems as rigid bodies. This completes the considerations presented in Chapter 5, where the system internal energy is taken into account as an elastic strain.
Appendix A (Matrix Algebra and the Linear Independence of Vectors) and Appendix B (Review of Elementary Real Analysis) provide a quick reference and background material for problems discussed in the text.
The structure of each of the parts of the book makes it possible to study the problems considered not only in an effective, but also pleasurable way. In the opinion of this reviewer Engineering Analysis in Applied Mechanics is a very useful book for both students and lecturers. It can serve as resource for engineers and scientists and is also recommended for their libraries.