Geometric Integration Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Integration Theory write by Hassler Whitney. This book was released on 2015-12-08. Geometric Integration Theory available in PDF, EPUB and Kindle. 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.
Geometric Integration Theory
Geometric Integration Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Integration Theory write by Steven G. Krantz. This book was released on 2008-12-15. Geometric Integration Theory available in PDF, EPUB and Kindle. This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.
Geometric Measure Theory
Geometric Measure Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Measure Theory write by Herbert Federer. This book was released on 2014-11-25. Geometric Measure Theory available in PDF, EPUB and Kindle. "This book is a major treatise in mathematics and is essential in the working library of the modern analyst." (Bulletin of the London Mathematical Society)
Geometric Numerical Integration
Geometric Numerical Integration - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Numerical Integration write by Ernst Hairer. This book was released on 2013-03-09. Geometric Numerical Integration available in PDF, EPUB and Kindle. This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. 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. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.
A Concise Introduction to Geometric Numerical Integration
A Concise Introduction to Geometric Numerical Integration - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Concise Introduction to Geometric Numerical Integration write by Sergio Blanes. This book was released on 2017-11-22. A Concise Introduction to Geometric Numerical Integration available in PDF, EPUB and Kindle. Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration. The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations. The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.
