- Email: [email protected]
Radio communication at ultra high frequency
Feb., i95i. ]
Book
REVIEWS
303
ORDINARY NoN-LINEAR DIFFERENTIAL EQUATIONSIN ENGINEERINGAND PHYSICAL SCIENCES, by N. W. McLachlan. 201 pages, diagrams, 16 )< 24 cm. Oxford, Clarendon Press, 1950. Price, $4.25. Since the purpose of this texi is to provide an introduction to the subject, it is appropriate to define the "ordinary, non-linear" part of the title for the beginner. By an ordinary differential equation is meant one in which there is a single independent variable, so that the derivatives are ordinary derivatives (as distinct from partial derivatives). A differential equation is called non-linear in the dependent variable when the degree of the dependent variable and/or its derivatives differs from unity, or if they occur as products. The author limits the text to ordinary non-linear differential equations except for an appendix on sound waves in a loudspeaker horn, in which a partial non-linear differential equation is considered. The author points out correctly that the literature contains many articles on application but neglects the theoretical side of the subject. Nevertheless, he goes on to state: " . . . the text is confined chiefly to the presentation of various analytical methods employed in the solution of important technical problems Accordingly the book is not an analytical treatise with technical applications. It aims to show how certain types of non-linear problems may be solved, and how experimental results may be interpreted by aid of non-llnear analysis." The contents of the book include: General Introduction, Equations Readily Integrable, Equations Integrable by Elliptic Integrals and Functions, Equations Having Periodic Solutions, Method of Slowly Varying Amplitude and Phase, The Equivalent Linear Equation, Equations Having Periodic Coefficients, and Graphical and Numerical Solutions. In addition to the previously mentioned appendix, another treats a method of using Mathleu's equation as a stability criterion of the solutions of non-linear equations. Exercises appear only as part of the body of the text, but in that capacity comprise much of the book. The references and cross references number over three hundred. The graphical solution presented is the familiar method of isoclines accompanied by the usual figures. Indeed, the main contribution of the book is not that it offers anything fundamentally new, but that it gathers under one cover a considerable amount of work done in a field that is rapidly expanding. Its publication at this time when the pure mathematician is showing interest in the subject and the government is sponsoring research in non-linear problems should result in a circulation reflecting the need for such books. D. B. HOUGHTON RADIO COMMUNICATIONAT ULTRA HIGH FREQUENCY, by J. Thomson. 203 pages, 14 X 22 cm. London, Methuen & Co.; distributed by John Wiley & Sons, Inc., 1950. Price, $4.50. * Professor Thomson has performed a distinct service for the electronic engineer who is interested in the implications and applications of the techniques of ultra high frequency electronics developed in the past decade. Both the specialist who perhaps has difficulty in seeing the forest for the trees and the engineer who is interested in a concise survey, will find this volume stimulating and informative. With a mifiimum'amount of engineering details and with strong emphasis on physical principles, the author surveys the problems involved: circuits, tubes, frequency control, modulation techniques, and communications systems. Especially noteworthy are his discussions of the unsolved problems, a feature far too often completely neglected in engineering texts and reference books. For these reasons, this volume, while topical, will not soon be relegated to that section of the bookshelf reserved for books read but never reread. FRANK T. INNES NUMERICAS MATHEMATICALANALYSIS,by James B. Scarborough. Second edition, 511 pages, diagrams, 16 X 24 cm. Baltimore, The Johns Hopkins Press, 1950. Price, $6.00. The first edition of this well known work has long been a helpful tool for those scientists and engineers who had need for a source of information on interpolation and accuracy of interpolation, numerical differentiation, integration, and the solution of equations as well as
Book
REVIEWS
303
ORDINARY NoN-LINEAR DIFFERENTIAL EQUATIONSIN ENGINEERINGAND PHYSICAL SCIENCES, by N. W. McLachlan. 201 pages, diagrams, 16 )< 24 cm. Oxford, Clarendon Press, 1950. Price, $4.25. Since the purpose of this texi is to provide an introduction to the subject, it is appropriate to define the "ordinary, non-linear" part of the title for the beginner. By an ordinary differential equation is meant one in which there is a single independent variable, so that the derivatives are ordinary derivatives (as distinct from partial derivatives). A differential equation is called non-linear in the dependent variable when the degree of the dependent variable and/or its derivatives differs from unity, or if they occur as products. The author limits the text to ordinary non-linear differential equations except for an appendix on sound waves in a loudspeaker horn, in which a partial non-linear differential equation is considered. The author points out correctly that the literature contains many articles on application but neglects the theoretical side of the subject. Nevertheless, he goes on to state: " . . . the text is confined chiefly to the presentation of various analytical methods employed in the solution of important technical problems Accordingly the book is not an analytical treatise with technical applications. It aims to show how certain types of non-linear problems may be solved, and how experimental results may be interpreted by aid of non-llnear analysis." The contents of the book include: General Introduction, Equations Readily Integrable, Equations Integrable by Elliptic Integrals and Functions, Equations Having Periodic Solutions, Method of Slowly Varying Amplitude and Phase, The Equivalent Linear Equation, Equations Having Periodic Coefficients, and Graphical and Numerical Solutions. In addition to the previously mentioned appendix, another treats a method of using Mathleu's equation as a stability criterion of the solutions of non-linear equations. Exercises appear only as part of the body of the text, but in that capacity comprise much of the book. The references and cross references number over three hundred. The graphical solution presented is the familiar method of isoclines accompanied by the usual figures. Indeed, the main contribution of the book is not that it offers anything fundamentally new, but that it gathers under one cover a considerable amount of work done in a field that is rapidly expanding. Its publication at this time when the pure mathematician is showing interest in the subject and the government is sponsoring research in non-linear problems should result in a circulation reflecting the need for such books. D. B. HOUGHTON RADIO COMMUNICATIONAT ULTRA HIGH FREQUENCY, by J. Thomson. 203 pages, 14 X 22 cm. London, Methuen & Co.; distributed by John Wiley & Sons, Inc., 1950. Price, $4.50. * Professor Thomson has performed a distinct service for the electronic engineer who is interested in the implications and applications of the techniques of ultra high frequency electronics developed in the past decade. Both the specialist who perhaps has difficulty in seeing the forest for the trees and the engineer who is interested in a concise survey, will find this volume stimulating and informative. With a mifiimum'amount of engineering details and with strong emphasis on physical principles, the author surveys the problems involved: circuits, tubes, frequency control, modulation techniques, and communications systems. Especially noteworthy are his discussions of the unsolved problems, a feature far too often completely neglected in engineering texts and reference books. For these reasons, this volume, while topical, will not soon be relegated to that section of the bookshelf reserved for books read but never reread. FRANK T. INNES NUMERICAS MATHEMATICALANALYSIS,by James B. Scarborough. Second edition, 511 pages, diagrams, 16 X 24 cm. Baltimore, The Johns Hopkins Press, 1950. Price, $6.00. The first edition of this well known work has long been a helpful tool for those scientists and engineers who had need for a source of information on interpolation and accuracy of interpolation, numerical differentiation, integration, and the solution of equations as well as