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Laplace transformation theory and engineering applications
May, I95I.]
BOOK REVIEWS
555
~,¢fATHEMATICS,QUEEN AND SERVANT OF SCIENCE, by E. T, Bell. 437 pages, illustrations, 14 X 21 cm. New York, McGraw-Hill Book Co., 1951. Price, $5.00. This book is a revision and enlargement of two former publications, "The Queen of the Sciences," and "The Handmaiden of the Sciences," by the same author, who has also written "The Magic of Numbers" and "Men of Mathematics." Professor of Mathematics at California Institute of Technology, E. T. Bell is well qualified to interpret and popularize mathematics for the non-mathematician. This is exactly what is done in "Mathematics, Queen and Servant of Science," except that a lot of history of mathematics has been included. There is also much to be found in this book by the mathematician. There is a vast difference between the undergraduate problem-type of mathematics and the postgraduate pure mathematics. It is books such as this, which introduce the student to many of the concepts of pure mathematics while still not omitting the applied mathematics with which he may be familiar, that should be required reading for all those undergraduates majoring in mathematics. Familiarity with these concepts should enable the student to decide whether he wants to study pure mathematics and teach, or applied mathematics and perhaps be an industrial mathematician. It may seem surprising that certain topics in postgraduate pure mathematics can be presented understandably to one having no background in mathematics, yet this is done. DONALD B. HOUGHTON PRINCIPLES OF PHASE EQUILIBRIA, by F. E. W. Wetmore and D. J. LeRoy. 200 pages, diagrams, 16 X 24 cm. New York, McGraw-Hill Book Co., 1951. Price, $3.50. A clear understanding of the principles involved in phase equilibria is basic to the study of .many of the physical sciences. This is particularly true in the fields of mineralogy, metallurgy and physical chemistry. In writing this book the authors have drawn upon their teaching experience and have produced a text in which the subject is developed in terms of fundamental principles and laboratory criteria. Mathematical theory and formal thermodynamics have been avoided in the body of the text. The book consists of nine chapters and two appendices. The first chapter contains a general discussion of chemical equilibrium. Chapter 2 is devoted entirely to one-component systems. The next three chapters deal with systems consisting of two components. Chapters 7, 8 and 9 treat equilibria in three and four-component systems. The first appendix contains a thermodynamic derivation of the phase rule. The second appendi~ shows curves of free energy v s . composition for systems under various conditions. The book is printed on a good grade of paper and contains many diagrams, illustrating the material discussed in the text. There are exercises for the student at the end of each chapter which will give him an opportunity to apply his knowledge to the construction and analysis of phase diagrams. As a text for a short course in phase equilibria or as a supplementary text in a regular course in metallurgy or physical chemistry, the book is to be highly recommended. M. D. EARLE LAPLACE TRANSFORMATIONTHEORY AND ENGINEERING APPLICATIONS, by William Tyrrell. 230 pages, illustrations, 15 X 22 cm. New York, Prentice-Hall, 1950. Price, $3.75. In this book the author has presented the theory of the Laplace transformation in such a fo/-m as to be readily useful to the average engineer. At no time is the continuity of the development beclouded by excessively rigorous derivations, but at all times sufficient rigor is present so t[~at the reader may proceed with confidence and understanding. The presentation gains from the author's inclusion of many physical problems, the solutions to which are well known by other mathematical methods. The resultant comparisons serve well to illustrate the advantages of the Laplace transformation as well as to give a physical meaning to the solutions. In addition, the author has included many problems for the reader to work out on his own. The uses of the Laplace transformation which are covered in this text are dynamical applications, structural applications, partial differential equations, difference equations and closed loop systems. EZRA KRENDEL
BOOK REVIEWS
555
~,¢fATHEMATICS,QUEEN AND SERVANT OF SCIENCE, by E. T, Bell. 437 pages, illustrations, 14 X 21 cm. New York, McGraw-Hill Book Co., 1951. Price, $5.00. This book is a revision and enlargement of two former publications, "The Queen of the Sciences," and "The Handmaiden of the Sciences," by the same author, who has also written "The Magic of Numbers" and "Men of Mathematics." Professor of Mathematics at California Institute of Technology, E. T. Bell is well qualified to interpret and popularize mathematics for the non-mathematician. This is exactly what is done in "Mathematics, Queen and Servant of Science," except that a lot of history of mathematics has been included. There is also much to be found in this book by the mathematician. There is a vast difference between the undergraduate problem-type of mathematics and the postgraduate pure mathematics. It is books such as this, which introduce the student to many of the concepts of pure mathematics while still not omitting the applied mathematics with which he may be familiar, that should be required reading for all those undergraduates majoring in mathematics. Familiarity with these concepts should enable the student to decide whether he wants to study pure mathematics and teach, or applied mathematics and perhaps be an industrial mathematician. It may seem surprising that certain topics in postgraduate pure mathematics can be presented understandably to one having no background in mathematics, yet this is done. DONALD B. HOUGHTON PRINCIPLES OF PHASE EQUILIBRIA, by F. E. W. Wetmore and D. J. LeRoy. 200 pages, diagrams, 16 X 24 cm. New York, McGraw-Hill Book Co., 1951. Price, $3.50. A clear understanding of the principles involved in phase equilibria is basic to the study of .many of the physical sciences. This is particularly true in the fields of mineralogy, metallurgy and physical chemistry. In writing this book the authors have drawn upon their teaching experience and have produced a text in which the subject is developed in terms of fundamental principles and laboratory criteria. Mathematical theory and formal thermodynamics have been avoided in the body of the text. The book consists of nine chapters and two appendices. The first chapter contains a general discussion of chemical equilibrium. Chapter 2 is devoted entirely to one-component systems. The next three chapters deal with systems consisting of two components. Chapters 7, 8 and 9 treat equilibria in three and four-component systems. The first appendix contains a thermodynamic derivation of the phase rule. The second appendi~ shows curves of free energy v s . composition for systems under various conditions. The book is printed on a good grade of paper and contains many diagrams, illustrating the material discussed in the text. There are exercises for the student at the end of each chapter which will give him an opportunity to apply his knowledge to the construction and analysis of phase diagrams. As a text for a short course in phase equilibria or as a supplementary text in a regular course in metallurgy or physical chemistry, the book is to be highly recommended. M. D. EARLE LAPLACE TRANSFORMATIONTHEORY AND ENGINEERING APPLICATIONS, by William Tyrrell. 230 pages, illustrations, 15 X 22 cm. New York, Prentice-Hall, 1950. Price, $3.75. In this book the author has presented the theory of the Laplace transformation in such a fo/-m as to be readily useful to the average engineer. At no time is the continuity of the development beclouded by excessively rigorous derivations, but at all times sufficient rigor is present so t[~at the reader may proceed with confidence and understanding. The presentation gains from the author's inclusion of many physical problems, the solutions to which are well known by other mathematical methods. The resultant comparisons serve well to illustrate the advantages of the Laplace transformation as well as to give a physical meaning to the solutions. In addition, the author has included many problems for the reader to work out on his own. The uses of the Laplace transformation which are covered in this text are dynamical applications, structural applications, partial differential equations, difference equations and closed loop systems. EZRA KRENDEL