دانلود کتاب Nonlinear Differential Equations

This concise and widely referenced monograph has served as a text for generations of advanced undergraduate math majors and graduate students. Prepared with an eye toward the needs of applied mathematicians, engineers, and physicists, the treatment is equally valuable as a reference for professionals. After discussing some mathematical preliminaries, author Raimond A. Struble presents detailed treatments of the existence and the uniqueness of a solution of the initial-value problem, properties of solutions, properties of linear systems, stability in nonlinear systems, and two-dimensional systems. Additional chapters examine perturbations of periodic solutions and a general asymptotic method. Numerous exercises appear throughout the book, along with examples that contribute additional material, illustrate theorems and concepts, and provide a link with more practical aspects of the theory.
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This book has been written primarily as a short (one semester) text for an undergraduate-graduate introductory course in nonlinear differential equations. The author has not strived for completeness nor has he attempted to achieve generality. He is primarily interested in having the student or reader obtain a rapid first look at some important aspects of the subject, and in so doing, to prepare him, if he has the inclination, to undertake a more thorough study. After some preliminary considerations (Chapter 1) which introduce the notions of solution, linearity, nonlinearity, trajectories, the phase plane, vector and matrix notation, the author devotes two chapters to existence and uniqueness theorems and regularity properties of solutions in their dependence on initial conditions and parameters. He does this well and with dispatch. Chapter 4 treats the essentials of linear systems in a thoroughly modern fashion. Where theorems are needed whose proofs would add little to the subject at hand, he states the theorem he needs and uses it. It is a good quick introduction to linear systems. The remaining four chapters are a study of nonlinear problems, and he manages to cover with varying degrees of brevity the following: (Chapter 5) stability concepts, theorems which provide sufficient conditions for stability of equilibrium states and periodic solutions, and a brief introduction to Liapunov's method; (Chapter 6) critical points of two-dimensional systems, limit cycles, some qualitative theory leading to the Poincaré-Bendixson theorem; (Chapter 7) perturbations of periodic solutions of nonautonomous and autonomous systems of quasi-harmonic equations; (Chapter 8) an admittedly formal asymptotic procedure for obtaining quantitative information about nonlinear oscillations. Examples illustrate the major concepts and theorems, and the exercises, while not abundant, are adequate. On the whole, the author has succeeded remarkably well in achieving his objectives. It will be a useful textbook, particularly for applied mathematicians, scientists, and engineers, who for nonlinear systems are discovering the necessity of returning to the subject of differential equations. The book provides a useful step from the out-of-date undergraduate texts still being used to the excellent advanced books that have been written in recent years.
Reviewed by [J. P. LaSalle](https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=108850)