This book presents a complete theory of ordinary differential equations, with many illustrative examples and interesting exercises. A rigorous treatment is offered in this book with clear proofs for the theoretical results and with detailed solutions for the examples and problems. This book is intended for undergraduate students who major in mathematics and have acquired a prerequisite knowledge of calculus and partly the knowledge of a complex variable, and are now reading advanced calculus and linear algebra. Additionally, the comprehensive coverage of the theory with a wide array of examples and detailed solutions, would appeal to mathematics graduate students and researchers as well as graduate students in majors of other disciplines. As a handy reference, advanced knowledge is provided in this book with details developed beyond the basics; optional sections, where main results are extended, offer an understanding of further applications of ordinary differential equations.
This systematically-organized text on the theory of differential equations deals with the basic concepts and the methods of solving ordinary differential equations.
[5] C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978. [6] G. F. Carrier and C. E. Pearson, Ordinary Differential Equations, Ginn/Blaisdell, Waltam, MA., 1968.
Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear ...
This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.
The book is divided into four parts. The first covers fundamental existence, uniqueness, smoothness with respect to data, and nonuniqueness.
This book has developed from courses given by the authors and probably contains more material than will ordinarily be covered in a one-year course. It is hoped that the book...
Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters.
Chapter 5 describes the linearization technique for analyzing the behavior of a nonlinear system in a neighborhood of a ... Chapter 9 comprises the elementary theory of Hamiltonian systems and includes proofs of Arnold's Theorem, ...
Ordinary differential equations (ODEs) play an important role in many problems in mathematics, engineering, physics and other applied sciences. This book covers analytical and numerical aspects of the study of...
This graduate-level textbook offers students a rapid introduction to the language of ordinary differential equations followed by a careful treatment of the central topics of the qualitative theory.