Excursions in Calculus: An Interplay of the Continuous and the Discrete (Dolciani Mathematical Expositions)
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Author: Robert M. Young

The purpose of this book is to explore the rich and elegant interplay that exists between the two main currents of mathematics, the continuous and the discrete. Such fundamental notions in discrete mathematics as induction, recursion, combinatorics, number theory, discrete probability, and the algorithmic point of view as a unifying principle are continually explored as they interact with traditional calculus. The book is addressed primarily to welltrained calculus students and those who teach them, but it can also serve as a supplement in a traditional calculus course for anyone who wants to see more. The problems, taken for the most part from probability, analysis, and number theory, are an integral part of the text. There are over 400 problems presented in this book.
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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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Understanding Geometry
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Author: Kathy Richardson

This valuable teachers resource provides teachers with classroom tested activities that help children develop indepth understandings about 2D and 3D geometry concepts and spatial awareness. Understanding Geometry is more than a book about geometry activities. Kathy provides the following resources for teachers:  Background information on what we need to know about geometry  Assessment and observation moments are highlighted  Geometry Terminology Glossary  Planning Guide for Grades K3  Task Cards
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Orbit and Constellation Design and Management (Space Technology Library, Vol. 13)  Renewed Edition
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Author: James R Wertz
Brand: Brand: Microcosm, Inc

Orbit and Constellation Design and Management (OCDM) provides greatly expanded detail on many topics first introduced in the 2 of the earlier Wertz works  Spacecraft Attitude Determination and Control (SADC) and Space Mission Analysis and Design (SMAD). If these two books got you started in mission engineering and you need more detail on the key area of Spacecraft Orbit and Attitude Systems (SOAS), then this book provides more detail in SOAS requirements definition, mission geometry, orbit and constellation design, relative motion of satellites, observation and measurement systems engineering, orbit control and management, and similar topics.
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Topologies and Uniformities (Springer Undergraduate Mathematics Series)
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Author: I.M. James
Brand: Brand: Springer

A substantially revised edition of the UTM volume, with a view to making the book far more accessible to undergraduates. It contains a larger number of detailed explanations and exercises, together with fully worked solutions to the essential problems and a new chapter on the historical aspects.
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Multidimensional Real Analysis II: Integration (Cambridge Studies in Advanced Mathematics)
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Author: J. J. Duistermaat

Volume 2 provides a comprehensive review of integral analysis in multidimensional Euclidean space.
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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
Brand: John W Morgan

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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Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets (Texts in Applied Mathematics)
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Author: Claude Gasquet

The object of this book is twofold  on the one hand it conveys to mathematical readers a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations. On the other hand, it presents physics readers with a body of theory in which the wellknown formulae find their justification. The basic study of fundamental notions, such as Lebesgue integration and theory of distribution, allow the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis timefrequency analysis (gabor transforms and wavelets). The whole is rounded off with a large number of exercises as well as selected workedout solutions.
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Introduction to Topology
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Author: Crump W. Baker
Brand: Brand: Krieger Pub Co

This text is intended for a onesemester undergraduate course in topology. The fundamental concepts of general topology are covered rigorously but at a gentle pace and an elementary level. It is accessible to students with only an elementary calculus background. In particular, abstract algebra is not a prerequisite. The first chapter develops the elementary concepts of sets and functions, and in Chapter 2 the general topological space is introduced. Subspaces, continuity, and homeomorphisms are covered in Chapter 3. The remaining chapters cover product spaces, connected spaces, separation properties, and metric spaces.
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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.

