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Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation." --SIAM REVIEW
Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required. The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further study of partial differential equations.
"A book of great value . . . it should have a profound influence upon future research."--Mathematical Reviews. Hardcover edition. The foundations of the study of asymptotic series in the theory of differential equations were laid by Poincaré in the late 19th century, but it was not until the middle of this century that it became apparent how essential asymptotic series are to understanding the solutions of ordinary differential equations. Moreover, they have come to be seen as crucial to such areas of applied mathematics as quantum mechanics, viscous flows, elasticity, electromagnetic theory, electronics, and astrophysics. In this outstanding text, the first book devoted exclusively to the subject, the author concentrates on the mathematical ideas underlying the various asymptotic methods; however, asymptotic methods for differential equations are included only if they lead to full, infinite expansions. Unabridged Dover republication of the edition published by Robert E. Krieger Publishing Company, Huntington, N.Y., 1976, a corrected, slightly enlarged reprint of the original edition published by Interscience Publishers, New York, 1965. 12 illustrations. Preface. 2 bibliographies. Appendix. Index.
This treatment presents most of the methods for solving ordinary differential equations and systematic arrangements of more than 2,000 equations and their solutions. The material is organized so that standard equations can be easily found. Plus, the substantial number and variety of equations promises an exact equation or a sufficiently similar one. 1960 edition.
Based on a one-year course taught by the author to graduates at the University of Missouri, this book provides a student-friendly account of some of the standard topics encountered in an introductory course of ordinary differential equations. In a second semester, these ideas can be expanded by introducing more advanced concepts and applications. A central theme in the book is the use of Implicit Function Theorem, while the latter sections of the book introduce the basic ideas of perturbation theory as applications of this Theorem. The book also contains material differing from standard treatments, for example, the Fiber Contraction Principle is used to prove the smoothness of functions that are obtained as fixed points of contractions. The ideas introduced in this section can be extended to infinite dimensions.
Covers the fundamentals of the theory of ordinary differential equations.

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