5R1. Fields, Flows and Waves: An Introduction to Continuum Models.-(School of Math, Univ of Edinburgh, James Clerk Bldg, Kings bldg, Mayfield Road, Edinburgh, EH9 3JZ, United Kingdom).Springer-Verlag London Ltd, Surrey, UK. 2003. 270 pp. Softcover. ISBN 1-85233-708-7. $34.95.
(Dept of Civil and Architec Eng, Illinois Inst of Tech, 3201 S Dearborn St, Rm 213, Chicago IL 60616-3793).
This book is intended primarily as a textbook for second-year undergraduate students in mathematics, mathematical physics, and engineering. The book is designed as a first introduction to the use of mathematical techniques, within continuum theories. It is presumed that the readers have some knowledge of several variable calculus and partial derivatives. The author presents many physical problems to motivate the discussion of the conservation and balance laws derived in the text; however, the emphasis of the book is on the solution to the resulting ordinary and partial differential equations. The physical and practical aspects are used to aid in the formulation of the models and in interpreting the mathematical predictions. To this extent many simple examples that allow closed form solutions are included in the text, which help provide insight into the mathematical solutions presented. Each chapter also includes student exercises with solutions given in the end of the book. A sizeable number of figures are also included that illustrate details of the mathematical solutions.
Chapter 1 begins with a general discussion of conservation and balance laws along with their application to steady state heat flow. Chapter 2 introduces unsteady heat flow and Chapter 3 presents the concepts of fields and potentials with applications in electrostatics. Solutions to Laplace’s Equation and Poisson’s Equation are presented in Chapter 4. Chapter 5 introduces wave theory in the context of elastic strings. Chapters 6 and 7 give a basic introduction into fluid flow and elasticity, respectively, and provide further context for the mathematical formulations that were derived in previous chapters. Chapter 8 gives a more extensive treatment of plane waves. Wave refraction and reflection and guided waves with applications in acoustics and elasticity are also considered. Chapter 9 extends the topics of Chapter 8 to electromagnetic waves. Finally, the text ends with a presentation of how the previously developed mathematical techniques can be applied to describe the growth and spread of biological organisms.
It is clear from the presentation of the material that the author’s aim is to employ examples from physical phenomena to motivate the derivation of mathematical formulations and to gain insight into the resulting solutions. Several topics in engineering and physics are presented; however, the discussion of these topics is too brief for students to gain a deep understanding of the material. As such, Field, Flows, and Waves: An Introduction to Continuum Models is recommended to students in mathematics and mathematical physics that require only a quick introduction to the several physical topics covered in the text and would prefer to concentrate on the mathematical techniques required to solve such problems.