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It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing approximate solutions, fails catastrophically due to the problem of small denominators. It then goes on to describe chaotic motion using the tools of discrete maps and Poincar  sections. This leads to the two great landmarks of chaos theory, the Poincar -Birkhoff theorem and the so-called KAM theorem, one of the signal results in modern mathematics. The book concludes with an appendix discussing the relevance of the KAM theorem to the ergodic hypothesis and the second law of thermodynamics.Lectures on Nonlinear Mechanics and Chaos Theory is written in the easy conversational style of a great teacher. It features numerous computer-drawn figures illustrating the behavior of nonlinear systems. It also contains homework exercises and a selection of more detailed computational projects. The book will be valuable to students and faculty in physics, mathematics, and engineering.See Press Release: Problems in mechanics open the door to the orderly world of chaos","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49695557484817,"sku":"DVDB0013H3JV6VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/B0013H3JV6.jpg?v=1751068291"},{"product_id":"summer-grandeur-dvd-with-bob-ross-dvd-0720867010034","title":"Bob Ross the Joy of Painting: Grandeur of Summer","description":"\u003cp\u003eWhat does it take to be Present? Sydney Platt takes us on an inner journey exploring the many facets of Presence, with one goal in mind: Reconnecting with the Essence of Who You Truly Are. \u003c\/p\u003e \u003cp\u003eStepping Into Presence is an experiential guide, not just a book for the mind. From its premise that the main obstacle to Being Present is a deep sense of Disconnection from the soul, what it takes to live in presence is explored from many perspectives. This involves delving into all the dimensions of human existence: Spirit, Thought, Emotion, and Physical senses (STEP). \u003c\/p\u003e \u003cp\u003eIf you wholeheartedly engage yourself in its pages, it is expected that you will: \u003c\/p\u003e \u003cp\u003eUnderstand how your deepest fears originate and function under the radar to keep you out of the present. \u003cbr\u003e Discover why the Personality is the most powerful force that blocks the full expression of who you truly are. \u003cbr\u003e Get savvy to the hidden agenda of your personality, and learn to sidestep its unconscious motives and unproductive directives. \u003cbr\u003e Become more aware of how you disconnect from the flow of Life and all its dimensions. \u003cbr\u003e Explore ways to resonate with the qualities of Presence, so you can be happier, calmer, and more fully present. \u003c\/p\u003e \u003cp\u003eCalm allows us to process our experience completely and helps us access the resources present within the well of our soul. - from Chapter 21\u003c\/p\u003e \u003cp\u003eSydney Platt has written a remarkably thorough guide to personal transformation, weaving together many systems of consciousness.At the completion of each section, she provides lovely meditations and prayers to help manifest the transformations. 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Taking the term to encompass both a literary tradition of satirical works, mostly on totalitarianism, as well as real despotisms and societies in a state of disastrous collapse, this volume redefines the central concepts and the chronology of the genre and offers a paradigm-shifting understanding of the subject. \u003cp\u003e\u003c\/p\u003ePart One assesses the theory and prehistory of 'dystopia'. By contrast to utopia, conceived as promoting an ideal of friendship defined as enhanced sociability', dystopia is defined by estrangement, fear, and the proliferation of 'enemy' categories. A natural history of dystopia thus concentrates upon the centrality of the passion or emotion of fear and hatred in modern despotisms. The work of Le Bon, Freud, and others is used to show how dystopian groups use such emotions. Utopia and dystopia are portrayed not as opposites, but as extremes on a spectrum of sociability, defined by a heightened form of group identity. The prehistory of the process whereby enemies are demonised is explored from early conceptions of monstrosity through Christian conceptions of the devil and witchcraft, and the persecution of heresy. \u003cp\u003e\u003c\/p\u003ePart Two surveys the major dystopian moments in twentieth century despotisms, focussing in particular upon Nazi Germany, Stalinism, the Chinese Cultural Revolution, and Cambodia under Pol Pot. The concentration here is upon the political religion hypothesis as a key explanation for the chief excesses of communism in particular. \u003cp\u003e\u003c\/p\u003ePart Three examines literary dystopias. It commences well before the usual starting-point in the secondary literature, in anti-Jacobin writings of the 1790s. Two chapters address the main twentieth-century texts usually studied as representative of the genre, Aldous Huxley's \u003cem\u003eBrave New World\u003c\/em\u003e and George Orwell's \u003cem\u003eNineteen Eighty-Four\u003c\/em\u003e. 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