This book is an introduction to Cartan's approach to differential geometry. Two central methods in Cartan's geometry are the theory of exterior differential systems and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems. It begins with the classical geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics.One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. The book features an introduction to $G$-structures and a treatment of the theory of connections. The Cartan machinery is also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as PDEs and algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields.
Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. It begins with the classical differential geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally, with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics. One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. As well, the book features an introduction to G-structures and a treatment of the theory of connections. The techniques of EDS are also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as geometry of PDE systems and complex algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields. The second edition features three new chapters: on Riemannian geometry, emphasizing the use of representation theory; on the latest developments in the study of Darboux-integrable systems; and on conformal geometry, written in a manner to introduce readers to the related parabolic geometry perspective.
The Second Edition of the definitive text on systemic clinical supervision has been fully updated and now includes a range of practical online resources. New edition of the definitive text on systemic clinical supervision, fully updated and revised, with a wealth of case studies throughout Supported by a range of practical online resources New material includes coverage of systemic supervision outside MFT and international training contexts – such as healthcare, schools and the military Top-level contributors include those practicing academic, agency, and privately contracted supervision with novice to experienced therapists The editors received a prestigious award in 2015 from the American Family Therapy Academy for their contribution to systemic supervision theory and practice
Based on fifty years of clinical and classroom experience, a comprehensive basic helping skills textbook for undergraduates as well as master's degree students in counseling, psychology, social work, or pastoral counseling.
Markov processes are among the most important stochastic processes for both theory and applications. This book develops the general theory of these processes, and applies this theory to various special examples.
Since its conception by Allen Ivey in the mid-1960s, microcounseling has grown from a methodology for teaching basic counseling skills to a conceptual framework for the multicultural intentional helper. Microcounseling has proven to be a very effective training paradigm with a wide variety of individuals from various cultures and contexts. This text presents not only the latest thinking on microcounseling but, more specifically, outlines the major theoretical constructs and concepts of the microcounseling model. These constructs and concepts are framed within the context of the culturally effe.
Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. It begins with the classical differential geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally, with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics. One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. As well, the book features an introduction to G-structures and a treatment of the theory of connections. The techniques of EDS are also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as geometry of PDE systems and complex algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields. The second edition features three new chapters: on Riemannian geometry, emphasizing the use of representation theory; on the latest developments in the study of Darboux-integrable systems; and on conformal geometry, written in a manner to introduce readers to the related parabolic geometry perspective.
This book not only provides a lot of solid information about real analysis, it also answers those questions which students want to ask but cannot figure how to formulate. To read this book is to spend time with one of the modern masters in the subject. --Steven G. Krantz, Washington University, St. Louis One of the major assets of the book is Korner's very personal writing style. By keeping his own engagement with the material continually in view, he invites the reader to a similarly high level of involvement. And the witty and erudite asides that are sprinkled throughout the book are a real pleasure. --Gerald Folland, University of Washingtion, Seattle Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician. Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique.
Research Paper (undergraduate) from the year 2007 in the subject Business economics - Business Management, Corporate Governance, grade: 1,3, University of Cooperative Education Bad Mergentheim, language: English, abstract: Never before in history has the convergence of companies been that intense like in the year 2006. Gaining market share immediately, cutting costs through consolidation, expanding product lines or obtaining reputation are just a few ideas behind an acquisition or merger. Mergers and acquisitions rose in US Dollars to a new high from the peak in the year 2000 with 31.022 mergers and acquisitions and a capital flow of 3.332 billion US Dollars to 29.008 M&As and 3.568 US Dollars dated by 28th November 2006. An interesting aspect is that four out of the five largest transactions in 2006 did take place in Europe and not in America. Germany has the fourth largest merger and acquisitions market in the world with 1.488 transactions and a volume of 145,1 billion US Dollars in 2005. According to an analyst from Goldman Sachs, one of the biggest players in the M&A business, the M&A market is going to stabilize on the high level of 2006 also in the continuing years. Mergers and acquisitions are not a new topic in the age of globalization but with rising competition, price wars and merging markets it seems for many companies the only backdoor. However every second transaction is value-destroying and the aimed synergies remain a vision and never get realized. Bigger, stronger and more profitable are the key arguments for mergers and creating competitive advantage due to economies of scale. The core challenge often heard by management is to 85 % the integration process. Especially cultural differences are not taken into account properly. The centre stage of this study is to analyse how corporate culture and mergers melt together or collide and the reasons why so many companies fail. It covers the steps of a merger process and how the corporate culture can be aligned. The study can not examine explicitly the integration process like the due diligence method but it is a brief overview on what to be aware of when thinking about summing up synergies in mergers and acquisitions with different corporate cultures. It reveals that in the M&A business you can not set up the equation that one plus one is equal to two.
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