Description :
This work of translation of the classic Russian textbook emphasizes a fresh modern approach to the geometric qualitative theory of ordinary differential equations. The subject matter of this book is dominated by two central ideas and their ramifications: the theorem on rectifiability of a vector field and the theory of one-parameter groups of linear transformations. While the author has taken the liberty to omit some of the more specialized topics usually included in books on ordinary differential equations, the applications of these equations to mechanics, on the contrary, have been considered in more detail than the customary approach.
KEY FEATURES
• Emphasizes the geometrical and intuitive aspects while familiarizing the students with the concepts of flows on manifolds and tangent bundles.
• Presents a wealth of topics accompanied by many thought-provoking examples, problems and figures.
• Assumes the reader to possess a knowledge not beyond the scope of the standard elementary courses on analysis and linear algebra.
This college-level textbook treats the subject of ordinary differential equations in an entirely new way. A wealth of topics is presented masterfully, accompanied by many thought-provoking examples, problems, and 259 figures. The author emphasizes the geometrical and intuitive aspects and at the same time familiarizes the student with concepts, such as flows and manifolds and tangent bundles, traditionally not found in textbooks of this level. The exposition is guided by applications taken mainly from mechanics. One can expect this book to bring new life into this old subject.
—American Scientist
Content :
Preface. Frequently Used Notation. Basic Concepts. Basic Theorems. Linear Systems. Proofs of the Basic Theorems. Differential Equations on Manifolds. Sample Examination Problems. Bibliography. Index.
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