Mathematical Analysis: A Straightforward Approach, 2nd Edition
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Author: K.G. Binmore
Brand: Cambridge University Press

For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation.
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Trans Mast Geometry Jacobs
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Author: Harold R. Jacobs

This is the book for making transparencies to go along with the Jacob's geometry 7th printing, 2nd edition, ISBN #071671745X student text.


Multidimensional Real Analysis I: Differentiation (Cambridge Studies in Advanced Mathematics)
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Author: J. J. Duistermaat
Brand: Brand: Cambridge University Press

Volume 1 provides a comprehensive review of differential analysis in multidimensional Euclidean space.
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SpaceFilling Curves (Universitext)
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Author: Hans Sagan

The subject of spacefilling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most interesting and perplexing results were still to come. Besides, Sierpiriski's paper was written in Polish and published in a journal that is not readily accessible (Sierpiriski [2]). Most of the early literature on the subject is in French, German, and Polish, providing an additional raison d'etre for a comprehensive treatment in English. While there was, understandably, some intensive research activity on this subject around the turn of the century, contributions have, nevertheless, continued up to the present and there is no end in sight, indicating that the subject is still very much alive. The recent interest in fractals has refocused interest on spaceĀ filling curves, and the study of fractals has thrown some new light on this small but venerable part of mathematics. This monograph is neither a textbook nor an encyclopedic treatment of the subject nor a historical account, but it is a little of each. While it may lend structure to a seminar or proseminar, or be useful as a supplement in a course on topology or mathematical analysis, it is primarily intended for selfstudy by the aficionados of classical analysis.


Yet Another Introduction to Analysis
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Author: Victor Bryant
Brand: Brand: Cambridge University Press

Mathematics education in schools has seen a revolution in recent years. Students everywhere expect the subject to be wellmotivated, relevant and practical. When such students reach higher education, the traditional development of analysis, often divorced from the calculus they learned at school, seems highly inappropriate. Shouldn't every step in a first course in analysis arise naturally from the student's experience of functions and calculus in school? And shouldn't such a course take every opportunity to endorse and extend the student's basic knowledge of functions? In Yet Another Introduction to Analysis, the author steers a simple and wellmotivated path through the central ideas of real analysis. Each concept is introduced only after its need has become clear and after it has already been used informally. Wherever appropriate, new ideas are related to common topics in math curricula and are used to extend the reader's understanding of those topics. In this book the readers are led carefully through every step in such a way that they will soon be predicting the next step for themselves. In this way students will not only understand analysis, but also enjoy it.
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The SeibergWitten Equations and Applications to the Topology of Smooth FourManifolds (Mathematical Notes, Vol. 44)
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Author: John W. Morgan
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The recent introduction of the SeibergWitten invariants of smooth fourmanifolds has revolutionized the study of those manifolds. The invariants are gaugetheoretic in nature and are close cousins of the muchstudied SU(2)invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the SeibergWitten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the SeibergWitten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the SeibergWitten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)case, the SeibergWitten moduli spaces are shown to be compact. The SeibergWitten invariant is then essentially the homology class in the space of configurations represented by the SeibergWitten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.
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The Geometry of FourManifolds (Oxford Mathematical Monographs)
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Author: S. K. Donaldson

The last ten years have seen rapid advances in the understanding of differentiable fourmanifolds, not least of which has been the discovery of new 'exotic' manifolds. These results have had farreaching consequences in geometry, topology, and mathematical physics, and have proven to be a mainspring of current mathematical research. This book provides a lucid and accessible account of the modern study of the geometry of fourmanifolds. Consequently, it will be required reading for all those mathematicians and theoretical physicists whose research touches on this topic. The authors present both a thorough treatment of the main lines of these developments in fourmanifold topologynotably the definition of new invariants of fourmanifoldsand also a wideranging treatment of relevant topics from geometry and global analysis. All of the main theorems about YangMills instantons on fourmanifolds are proven in detail. On the geometric side, the book contains a new proof of the classification of instantons on the foursphere, together with an extensive discussion of the differential geometry of holomorphic vector bundles. At the end of the book the different strands of the theory are brought together in the proofs of results which settle longstanding problems in fourmanifolds topology and which are close to the frontiers of current research. Coauthor Donaldson is the 1994 corecipient of the prestigious Crafoord Prize.


Asymptotics and MellinBarnes Integrals (Encyclopedia of Mathematics and its Applications)
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Author: R. B. Paris
Brand: Brand: Cambridge University Press

Asymptotics and MellinBarnes Integrals provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behavior of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of MellinBarnes integrals that is otherwise not available in standard references on asymptotics.
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A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library)
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Author: G. N. Watson
Brand: Cambridge University Press

The late Professor G.N. Watson wrote his monumental treatise on the theory of Bessel functions in 1922 with two objects in view. The first was the development of applications of the fundamental processes of the theory of complex variables, and the second was compiling a collection of results of value for mathematicians and physicists who encounter Bessel functions in the course of their researches. The completeness of the theoretical account, combined with the wide scope of the collection of practical examples have resulted in a book that will be indispensable for pure mathematicians, applied mathematicians, and physicists.
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Seifert and Threlfall: A Textbook of Topology
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Author: H. Seifert

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