Differential Equations: Theory and Applications: with Maple®Springer Science & Business Media, 29/06/2013 - 680 من الصفحات This book was written as a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as time-honored and important applications of this theory. His torically, these were the applications that spurred the development of the mathematical theory and in hindsight they are still the best applications for illustrating the concepts, ideas, and impact of the theory. While the book is intended for traditional graduate students in mathe matics, the material is organized so that the book can also be used in a wider setting within today's modern university and society (see "Ways to Use the Book" below). In particular, it is hoped that interdisciplinary programs with courses that combine students in mathematics, physics, engineering, and other sciences can benefit from using this text. Working professionals in any of these fields should be able to profit too by study of this text. An important, but optional component of the book (based on the in structor's or reader's preferences) is its computer material. The book is one of the few graduate differential equations texts that use the computer to enhance the concepts and theory normally taught to first- and second-year graduate students in mathematics. I have made every attempt to blend to gether the traditional theoretical material on differential equations and the new, exciting techniques afforded by computer algebra systems (CAS), like Maple, Mathematica, or Matlab. |
المحتوى
1 | |
11 | |
Techniques Concepts and Examples | 33 |
The Flow | 75 |
OneDimensional Systems | 117 |
Linear Algebra | 157 |
Linear Systems | 163 |
32 | 177 |
45 | 205 |
Stability Theory | 275 |
Integrable Systems | 329 |
Newtonian Mechanics | 361 |
72 | 412 |
82 | 420 |
92 | 427 |
Motion on a Submanifold | 463 |
طبعات أخرى - عرض جميع المقتطفات
Differential Equations: Theory and Applications <span dir=ltr>David Betounes</span> لا تتوفر معاينة - 2014 |
عبارات ومصطلحات مألوفة
asymptotically b₁ body center of mass Chapter complex conservation laws constant corresponding curves of F defined definition determine diagonal differential equation discussion domain dynamical systems easy eigenspace eigenvalues eigenvectors equations of motion equivalent example exercise Existence and Uniqueness fixed points flow map formula function F fundamental matrix geometric given gives graph hyperbolic initial conditions integrable systems integral curve intersection interval of existence inverse Jordan form k₁ level curves Liapunov function linear system linearly independent matrix exponential maximum intervals N-body problem notation Note open set orbit origin particles phase portrait Picard iterates plot polar coordinates positive proof Proposition r₁ satisfies semigroup semigroup property shown in Figure sketch solution solve stability Suppose system x technique transformation v₁ vector field velocity worksheet zero