Power Geometry In Algebraic And Differential Equations PDF Download
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| Author | : A.D. Bruno |
| Publisher | : Elsevier |
| Total Pages | : 397 |
| Release | : 2000-08-03 |
| Genre | : Mathematics |
| ISBN | : 0080539335 |
Download Power Geometry in Algebraic and Differential Equations Book in PDF, ePub and Kindle
The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed. The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems. The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.
| Author | : Galina Filipuk |
| Publisher | : Birkhäuser |
| Total Pages | : 472 |
| Release | : 2017-06-23 |
| Genre | : Mathematics |
| ISBN | : 3319528424 |
Download Analytic, Algebraic and Geometric Aspects of Differential Equations Book in PDF, ePub and Kindle
This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.
| Author | : John W. Dettman |
| Publisher | : Courier Corporation |
| Total Pages | : 442 |
| Release | : 2012-10-05 |
| Genre | : Mathematics |
| ISBN | : 0486158314 |
Download Introduction to Linear Algebra and Differential Equations Book in PDF, ePub and Kindle
Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.
| Author | : Jeremy Gray |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 357 |
| Release | : 2010-01-07 |
| Genre | : Mathematics |
| ISBN | : 0817647732 |
Download Linear Differential Equations and Group Theory from Riemann to Poincare Book in PDF, ePub and Kindle
This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry. The text for this second edition has been greatly expanded and revised, and the existing appendices enriched. The exercises have been retained, making it possible to use the book as a companion to mathematics courses at the graduate level.
| Author | : Agostino Prastaro |
| Publisher | : World Scientific |
| Total Pages | : 762 |
| Release | : 1996-06-20 |
| Genre | : Science |
| ISBN | : 9814499498 |
Download Geometry Of Pdes And Mechanics Book in PDF, ePub and Kindle
This volume presents the theory of partial differential equations (PDEs) from a modern geometric point of view so that PDEs can be characterized by using either technique of differential geometry or algebraic geometry. This allows us to recognize the richness of the structure of PDEs. It presents, for the first time, a geometric theory of non-commutative (quantum) PDEs and gives a general application of this theory to quantum field theory and quantum supergravity.
| Author | : P.H. Kersten |
| Publisher | : Springer |
| Total Pages | : 349 |
| Release | : 2011-10-03 |
| Genre | : Mathematics |
| ISBN | : 9789401065658 |
Download Geometric and Algebraic Structures in Differential Equations Book in PDF, ePub and Kindle
The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Bäcklund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became clear that some basic and quite general geometrical and algebraic structures govern this property of integrability. Nowadays the geometrical and algebraic approach to partial differential equations constitutes a special branch of modern mathematics. In 1993, a workshop on algebra and geometry of differential equations took place at the University of Twente (The Netherlands), where the state-of-the-art of the main problems was fixed. This book contains a collection of invited lectures presented at this workshop. The material presented is of interest to those who work in pure and applied mathematics and especially in mathematical physics.
| Author | : John Oprea |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 469 |
| Release | : 2019-02-06 |
| Genre | : |
| ISBN | : 147045050X |
Download Differential Geometry and Its Applications Book in PDF, ePub and Kindle
Differential Geometry and Its Applications studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. That mix of ideas offers students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. Differential Geometry and Its Applications emphasizes that this visualization goes hand in hand with understanding the mathematics behind the computer construction. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.
| Author | : Galina Filipuk |
| Publisher | : Springer |
| Total Pages | : 274 |
| Release | : 2018-09-24 |
| Genre | : Mathematics |
| ISBN | : 3319991485 |
Download Formal and Analytic Solutions of Diff. Equations Book in PDF, ePub and Kindle
These proceedings provide methods, techniques, different mathematical tools and recent results in the study of formal and analytic solutions to Diff. (differential, partial differential, difference, q-difference, q-difference-differential.... ) Equations. They consist of selected contributions from the conference "Formal and Analytic Solutions of Diff. Equations", held at Alcalá de Henares, Spain during September 4-8, 2017. Their topics include summability and asymptotic study of both ordinary and partial differential equations. The volume is divided into four parts. The first paper is a survey of the elements of nonlinear analysis. It describes the algorithms to obtain asymptotic expansion of solutions of nonlinear algebraic, ordinary differential, partial differential equations, and of systems of such equations. Five works on formal and analytic solutions of PDEs are followed by five papers on the study of solutions of ODEs. The proceedings conclude with five works on related topics, generalizations and applications. All contributions have been peer reviewed by anonymous referees chosen among the experts on the subject. The volume will be of interest to graduate students and researchers in theoretical and applied mathematics, physics and engineering seeking an overview of the recent trends in the theory of formal and analytic solutions of functional (differential, partial differential, difference, q-difference, q-difference-differential) equations in the complex domain.
| Author | : Ernst Hairer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 526 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662050188 |
Download Geometric Numerical Integration Book 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.
| Author | : Heinrich G.W. Begehr |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 316 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475737416 |
Download Analysis and Applications - ISAAC 2001 Book in PDF, ePub and Kindle
This collection of survey articles gives and idea of new methods and results in real and complex analysis and its applications. Besides several chapters on hyperbolic equations and systems and complex analysis, potential theory, dynamical systems and harmonic analysis are also included. Newly developed subjects from power geometry, homogenization, partial differential equations in graph structures are presented and a decomposition of the Hilbert space and Hamiltonian are given. Audience: Advanced students and scientists interested in new methods and results in analysis and applications.
