Ordinary Differential Equations (Classics in Applied Mathematics, Series Number 6) by George F. Carrier (PDF)

Description

Offers an alternative to the ‘rote’ approach of presenting standard categories of differential equations accompanied by routine problem sets. The exercises presented amplify and provide perspective for the material, often giving readers opportunity for ingenuity. Little or no previous acquaintance with the subject is required to learn usage of techniques for constructing solutions of differential equations in this reprint volume.

User’s Reviews

Editorial Reviews: Review ‘This volume is a new edition of the original text, published in 1968. In these days of drearily identical textbooks, it is good to see one that is unique; its reappearance is welcome … The range of topics considered is extensive. In just over 200 pages, you will meet first- and second-order differential and difference equations, power and asymptotic series, eigenvalue expansions, special functions, (error, gamma, Bessel, Airy, and Legendre), the Laplace transform, variational calculus, solution of partial differential equations using separation of variables, nonlinear differential equations, numerical methods, and singular perturbation methods … In summary, this is a nice book, moderately priced and well worth owning …The publishers have done us a service in reissuing it.’ J. M. Anthony Danby, SIAM Review’A refreshing change from the omnipresent ‘cookbook’ approach; heuristic arguments and beautiful, open-ended problems drive the discussion. Most problems end with a question forcing the solver to think about what he or she just did. Covers all the usual topics; great source of challenging problems for standard course.’ American Mathematical Monthly Book Description Teaches techniques for constructing solutions of differential equations in a novel way, often giving readers opportunity for ingenuity. About the Author George F. Carrier is T. Jefferson Coolidge Professor of Applied Mathematics, Emeritus, at Harvard University. He was recently awarded the National Medal of Science by President George Bush. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Carrier and Pearson is a very interesting book. It is quite concise, and it severely restricts its scope in order to achieve depth – it covers little besides exact, approximate, and (some) numerical solution techniques for first-order and second-order linear ODEs. Its main property is that it takes a simple, highly heuristic approach to these ODEs and is full of rather tough problems, which take up about as much space in the text as the exposition. (Indeed, the authors claim that 78% of the value of the book lies in doing the problems.) It is moderately difficult; I would not recommend C&P to most students as a first text.The most attractive feature of C&P is indeed its problems, which make vigorous use of the solution techniques presented, introduce the reader to new techniques at times, and give some insight into exactly when those techniques are applicable. If one were to do all of the problems (something I certainly have not done), he or she would really know this subject! C&P’s exposition is high in quality, too; when working on a problem set in my second course on ODEs, I would often turn to C&P and find a clean, short, understandable explanation of the tool I needed.Its drawbacks largely stem from the same philosophy that makes it such a nice book about low-order linear ODEs. Its treatment makes heavy use of basic algebraic manipulation, and it avoids theory almost entirely. C&P eschews the vector-space ideas that clarify topics like the solution of nonhomogeneous linear equations. The simplifying emphasis on basic algebra also obscures the generalization of things like the Wronskian to higher-order systems, and it certainly prevents an even remotely rigorous treatment of Sturm-Liouville systems or eigenfunction expansions. The lack of a modern, geometric view of ODEs (cf. Arnol’d, Ordinary Differential Equations) does not help the student in later making a transition to qualitative considerations of nonlinear ODEs, and it prevents an appreciation of how special the standard linear solution techniques are. C&P also avoids complex analysis; while this is good for a student who has not studied complex variables, the lack of complex analysis means that C&P only inverts Laplace transforms with tables (not contour integration) and has no treatment at all of Fourier transforms. Also, the emphasis on problems means that some very important techniques (like variation of parameters) show up only in the problems.Whether or not this book is a worthwhile buy depends on the reader. It is great for learning a number of applied-mathematical techniques by the Socratic method. However, it fails as an encyclopedic reference, a mathematician’s textbook, or a gateway to nonlinear dynamical systems theory. At any rate, it is a unique book, and at least a portion of science/engineering students would benefit from it.

⭐Excellent text but subtle and requires concentration and commitment. Skimming will not work with this book. George Carrier has an international reputation in this area.

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