A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems.Originally published in 1957.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Product Description: From the earliest days of measure theory, invariant measures have held the interests of geometers and analysts alike, with the Haar measure playing an especially delightful role. The aim of this book is to present invariant measures on topological groups, progressing from special cases to the more general...read more

Product Description: In the past few years, the differential quadrature method has been applied extensively in engineering. This book, aimed primarily at practising engineers, scientists and graduate students, gives a systematic description of the mathematical fundamentals of differential quadrature and its detailed implementation in solving Helmholtz problems and problems of flow, structure and vibration...read more

Product Description: This book focuses primarily on a powerful tool: dimensionality reducing expansion (DRE). The method of DRE is a technique for changing a higher dimensional integration to a lower dimensional one with or without remainder. This work will appeal to a broad audience of students and researchers in pure and applied mathematics, statistics, and physics...read more

Product Description: The goal of geometric numerical integration is the simulation of evolution equations possessing geometric properties over long periods of time. Of particular importance are Hamiltonian partial differential equations typically arising in application fields such as quantum mechanics or wave propagation phenomena...read more

Product Description: Modern Tools to Perform Numerical DifferentiationThe original direct differential quadrature (DQ) method has been known to fail for problems with strong nonlinearity and material discontinuity as well as for problems involving singularity, irregularity, and multiple scales...read more

Product Description: Useful to programmers and stimulating for theoreticians, this text covers the major methods of numerical integration. It offers a balanced presentation: certain sections derive from or allude to deep results of analysis, but most of the final results are expressed in a form accessible to anyone with a background in calculus...read more

Product Description: During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open-ended...read more

Product Description: Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed...read more (view table of contents, read Amazon.com's description)

Product Description: This text discusses computational integration methods and the fundamental mathematical principles they are based on. It includes sections on one-dimensional and multi-dimensional integration formulas, and it deals with issues concerning the construction of numerical integration algorithms...read more

Product Description: Offers the quadrature user a selection of the most effective algorithms in each of the main areas of the subject. Topics range from Simpson's rule and Gaussian quadrature to recent research on irregular oscillatory and singular quadrature...read more

Product Description: Here is an elementary development of the Sinc-Galerkin method with the focal point being ordinary and partial differential equations. This is the first book to explain this powerful computational method for treating differential equations...read more

Product Description: High dimensional integration arises naturally in two major subfields of statistics: multivariate and Bayesian statistics. Indeed, the most common measures of central tendency, variation, and loss are defined by integrals over the sample space, the parameter space, or both...read more

This book is a textbook for graduate or advanced undergraduate students in mathematics and (or) mathematical physics. It is not primarily aimed, therefore, at specialists (or those who wish to become specialists) in integra­ tion theory, Fourier theory and harmonic analysis, although even for these there might be some points of interest in the book (such as for example the simple remarks in Section 15). At many universities the students do not yet get acquainted with Lebesgue integration in their first and second year (or sometimes only with the first principles of integration on the real line ). The Lebesgue integral, however, is indispensable for obtaining a familiarity with Fourier series and Fourier transforms on a higher level; more so than by us­ ing only the Riemann integral. Therefore, we have included a discussion of integration theory - brief but with complete proofs - for Lebesgue measure in Euclidean space as well as for abstract measures. We give some emphasis to subjects of which an understanding is necessary for the Fourier theory in the later chapters. In view of the emphasis in modern mathematics curric­ ula on abstract subjects (algebraic geometry, algebraic topology, algebraic number theory) on the one hand and computer science on the other, it may be useful to have a textbook available (not too elementary and not too spe­ cialized) on the subjects - classical but still important to-day - which are mentioned in the title of this book.

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