This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research - smooth structures, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential forms, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie groups, Lie algebras, and more. The approach is as concrete as possible, with pictures and intuitive discussions of how one should think geometrically about the abstract concepts, while making full use of the powerful tools that modern mathematics has to offer. This second edition has been extensively revised and clarified, and the topics have been substantially rearranged. The book now introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier so that they can be used throughout the book. A few new topics have been added, notably Sard's theorem and transversality, a proof that infinitesimal Lie group actions generate global group actions, a more thorough study of first-order partial differential equations, a brief treatment of degree theory for smooth maps between compact manifolds, and an introduction to contact structures. Prerequisites include a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis.
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This textbook aims to fill the gap between those that offer atheoretical treatment without many applications and those that presentand apply formulas without appropriately deriving them. The balanceachieved will give readers a fundamental understanding of key financialideas and tools that form the basis for building realistic models,including those that may become proprietary. Numerous carefully chosenexamples and exercises reinforce the student's conceptual understandingand facility with applications. The exercises are divided intoconceptual, application-based, and theoretical problems, which probe thematerial deeper.The book is aimed toward advanced undergraduates and first-year graduatestudents who are new to finance or want a more rigorous treatment of themathematical models used within. While no background in finance isassumed, prerequisite math courses include multivariable calculus,probability, and linear algebra. The authors introduce additionalmathematical tools as needed. The entire textbook is appropriate for asingle year-long course on introductory mathematical finance. Theself-contained design of the text allows for instructor flexibility intopics courses and those focusing on financial derivatives. Moreover,the text is useful for mathematicians, physicists, and engineers whowant to learn finance via an approach that builds their financialintuition and is explicit about model building, as well as businessschool students who want a treatment of finance that is deeper but not overly theoretical. 504 pp. Englisch. N° de réf. du vendeur 9781493937813
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Buch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - This textbook aims to fill the gap between those that offer atheoretical treatment without many applications and those that presentand apply formulas without appropriately deriving them. The balanceachieved will give readers a fundamental understanding of key financialideas and tools that form the basis for building realistic models,including those that may become proprietary. Numerous carefully chosenexamples and exercises reinforce the student's conceptual understandingand facility with applications. The exercises are divided intoconceptual, application-based, and theoretical problems, which probe thematerial deeper.The book is aimed toward advanced undergraduates and first-year graduatestudents who are new to finance or want a more rigorous treatment of themathematical models used within. While no background in finance isassumed, prerequisite math courses include multivariable calculus,probability, and linear algebra. The authors introduce additionalmathematical tools as needed. The entire textbook is appropriate for asingle year-long course on introductory mathematical finance. Theself-contained design of the text allows for instructor flexibility intopics courses and those focusing on financial derivatives. Moreover,the text is useful for mathematicians, physicists, and engineers whowant to learn finance via an approach that builds their financialintuition and is explicit about model building, as well as businessschool students who want a treatment of finance that is deeper but not overly theoretical. N° de réf. du vendeur 9781493937813
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