The plan to publish the present book arose while I was preparing a joint work with Gunter Gabisch (Gabisch, G. /Lorenz, H. -W. : Business Cycle Theory. Berlin-Heidel berg-New York: Springer). It turned out that a lot of interesting material could only be sketched in a business cycle text, either because the relevance for business cycle theory was not evident or because the material required an interest in dynamical economics which laid beyond the scope of a survey text for advanced undergraduates. While much of the material enclosed in this book can be found in condensed and sometimes more or less identical form in that business cycle text, the present monograph attempts to present nonlinear dynamical economics in a broader context with economic examples from other fields than business cycle theory. It is a pleasure for me to acknowledge the critical comments, extremely detailed remarks, or suggestions by many friends and colleagues. The responses to earlier versions of the manuscript by W. A. Barnett, M. Boldrin, W. A. Brock, C. Chiarella, C. Dale, G. Feichtinger, P. Flaschel, D. K. Foley, R. M. Goodwin, D. Kelsey, M. Lines, A. Medio, L. Montrucchio, P. Read, C. Sayers, A. Schmutzler, H. Schnabl, G. Silverberg, H. -\'\!. Sinn, J. Sterman, and R. Tscherning not only encouraged me to publish the book in its present form but helped to remove numerous errors (not only typographic ones) and conceptnal misunderstandings and flaws. Particular thanks go to G.
Is the business cycle obsolete?" This often cited title of a book edited by Bronfenbren ner with the implicit affirmation of the question reflected the attitude of mainstream macroeconomics in the Sixties regarding the empirical relevance of cyclic motions of an economy. The successful income policies, theoretically grounded in Keynesian macroec onomics, seemed to have eased or even abolished the fluctuations in West,ern economies which motivated studies of many classical and neoclassical economists for more than 100 years. The reasoning behind the conviction that business cycles would increasingly become irrelevant was rather simple: if an economy fluctuates for whatever reason, then it is almost always possible to neutralize these cyclic motions by means of anti-cyclic demand policies. From the 1950's until the mid-Sixties business cycle theory had often been consid ered either as an appendix to growth theory or as an academic exercise in dynamical economics. The common business cycle models were essentially multiplier-accelerator models whose sensitive dependence on parameter values (in order to be called busi ness cycle models) suggested a rather improbable occurrence of continuing oscillations. The obvious success in compensating business cycles in those days prevented intensive concern with the occurrence of cycles. Rather, business cycle theory turned into sta bilization theory which investigated theoretical possibilities of stabilizing a fluctuating economy. Many macroeconomic textbooks appeared in the Sixties which consequently identified business cycle theory with inquiries on the possibilities to stabilize economies 2 Introduction by means of active fiscal or monetary policies.
Friction contacts are used to transmit forces or to dissipate energy. The aim of this second edition is to describe an efficient procedure to model dynamical contact problems with friction. This procedure is applied to different practical problems and validated by experiments. A thorough understanding of friction phenomena can lead to improvements like the reduction of noise and maintenance costs, increased useful life of machines and improved energy efficiency.
This book reviews the theoretical framework of nonlinear mechanics, covering computational methods, applications, parametric investigations of nonlinear phenomena and mechanical interpretation towards design. Builds skills via increasing levels of complexity.
For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with ordinary differential equations. Unlike most textbooks on the subject, this text includes nonstandard topics such as perturbation methods and differential equations and Mathematica. In addition to the nonstandard topics, this text also contains contemporary material in the area as well as its classical topics. This second edition is updated to be compatible with Mathematica, version 7.0. It also provides 81 additional exercises, a new section in Chapter 1 on the generalized logistic equation, an additional theorem in Chapter 2 concerning fundamental matrices, and many more other enhancements to the first edition. This book can be used either for a second course in ordinary differential equations or as an introductory course for well-prepared students. The prerequisites for this book are three semesters of calculus and a course in linear algebra, although the needed concepts from linear algebra are introduced along with examples in the book. An undergraduate course in analysis is needed for the more theoretical subjects covered in the final two chapters.
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Following on the success of his "Classic Baseball," America's greatest sports photographer is back with a book that chronicles some of the most memorable moments in the history of golf.
In his 40-year career, Iooss has covered major sporting events and taken countless portraits of top personalities. Part travelogue and part memoir, this artistic diary weaves over 150 photos and illustrations, newspaper clippings, and handwritten thoughts into visually arresting collages to chronicle his life and behind-the-scenes work.
Following on the success of his "Classic Baseball," America's greatest sports photographer is back with a book that chronicles some of the most memorable moments in the history of golf.
Explorer Robert E. Peary’s quest for the North Pole—a true Arctic adventure from the #1 New York Times–bestselling author of A Night to Remember. On March 1, 1909, only 413 miles of formidable ice separated Robert E. Peary from realizing his lifelong dream of becoming the first man to set foot on the North Pole. On that dark morning on Canada’s Ellesmere Island, it was cold enough to freeze a bottle of brandy. The ice looked solid enough, but it sat atop seawater—and shifted violently according to the whims of the ocean below. Peary was used to the conditions—he’d barely survived them just three years before when he first tried, and failed, to reach the earth’s northernmost point. But this time around, no amount of peril could dissuade Peary and his party from their expedition. With a cry of “Forward, march!” the journey of a lifetime began. Written with thrilling detail and heart-pounding suspense by the author of Day of Infamy and other bestselling histories, Peary to the Pole is the definitive account of one man’s trek through some of the world’s most treacherous terrain, in search of adventure, discovery, and immortality, a classic for readers of books like In the Kingdom of Ice or The Last Place on Earth.
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