From the reviews: "... As an encyclopaedia article, this book does not seek to serve as a textbook, nor to replace the original articles whose results it describes. The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising. ... The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview. ..." American Mathematical Monthly, Nov. 1989 "This is a book to curl up with in front of a fire on a cold winter's evening. ..." SIAM Reviews, Sept. 1989
From the reviews: "... As an encyclopaedia article, this book does not seek to serve as a textbook, nor to replace the original articles whose results it describes. The book's goal is to provide an overview, pointing out highlights and unsolved problems, and putting individual results into a coherent context. It is full of historical nuggets, many of them surprising. ... The examples are especially helpful; if a particular topic seems difficult, a later example frequently tames it. The writing is refreshingly direct, never degenerating into a vocabulary lesson for its own sake. The book accomplishes the goals it has set for itself. While it is not an introduction to the field, it is an excellent overview. ..." American Mathematical Monthly, Nov. 1989 "This is a book to curl up with in front of a fire on a cold winter's evening. ..." SIAM Reviews, Sept. 1989
This work describes the fundamental principles, problems, and methods of elassical mechanics focussing on its mathematical aspects. The authors have striven to give an exposition stressing the working apparatus of elassical mechanics, rather than its physical foundations or applications. This appara tus is basically contained in Chapters 1, 3,4 and 5. Chapter 1 is devoted to the fundamental mathematical models which are usually employed to describe the motion of real mechanical systems. Special consideration is given to the study of motion under constraints, and also to problems concerned with the realization of constraints in dynamics. Chapter 3 is concerned with the symmetry groups of mechanical systems and the corresponding conservation laws. Also discussed are various aspects of the theory of the reduction of order for systems with symmetry, often used in applications. Chapter 4 contains abrief survey of various approaches to the problem of the integrability of the equations of motion, and discusses some of the most general and effective methods of integrating these equations. Various elassical examples of integrated problems are outlined. The material pre sen ted in this chapter is used in Chapter 5, which is devoted to one of the most fruitful branches of mechanics - perturbation theory. The main task of perturbation theory is the investigation of problems of mechanics which are" elose" to exact1y integrable problems.
This book begins with the past and present of the subversive technology of artificial intelligence, clearly analyzes the overall picture, latest developments and development trends of the artificial intelligence industry, and conducts in-depth research on the competitive situation of various countries. The book also provides an in-depth analysis of the opportunities and challenges that artificial intelligence brings to individuals, businesses, and society. For readers who want to fully understand artificial intelligence, this book provides an important reference and is a must-read.
The world we live in presents plenty of tricky, impactful, and hard-to make decisions to be taken. Sometimes the available options are ample, at other times they are apparently binary, either way, they often confront us with dilemmas, paradoxes, and even denial of values. In the dawn of the age of intelligence, when robots are gradually taking over most decision making from humans, this book sheds a bit of light on decision rationale. It delves into the limits of these decision processes (for both humans and machines), and it does so by providing a new perspective that is somehow opposed to orthodox economics. All Economics reflections in this book are underlined and linked to Artificial Intelligence. The authors hope that this comprehensive and modern analysis, firmly grounded in the opinions of various ground-breaking Nobel laureate economists, may be helpful to a broad audience interested in how decisions may lead us all to flourishing societies. That is, societies in which economic blunders (caused by over simplification of problems and super estimation of tools) are reduced substantially"--
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