Download or read book Algebraic Methods in Quantum Chemistry and Physics written by Francisco M. Fernandez and published by CRC Press. This book was released on 1995-10-24 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Methods in Quantum Chemistry and Physics provides straightforward presentations of selected topics in theoretical chemistry and physics, including Lie algebras and their applications, harmonic oscillators, bilinear oscillators, perturbation theory, numerical solutions of the Schrödinger equation, and parameterizations of the time-evolution operator. The mathematical tools described in this book are presented in a manner that clearly illustrates their application to problems arising in theoretical chemistry and physics. The application techniques are carefully explained with step-by-step instructions that are easy to follow, and the results are organized to facilitate both manual and numerical calculations. Algebraic Methods in Quantum Chemistry and Physics demonstrates how to obtain useful analytical results with elementary algebra and calculus and an understanding of basic quantum chemistry and physics.
Download or read book General Algebraic Methods in Mathematics and Physics written by Hans Schwerdtfeger and published by . This book was released on 1949 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebraic Methods in Physics written by Yvan Saint-Aubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book pays tribute to two pioneers in the field of Mathematical physics, Jiri Patera and Pavel Winternitz of the CRM. Each has contributed more than forty years to the subject of mathematical physics, particularly to the study of algebraic methods.
Download or read book Algebraic Methods in Statistical Mechanics and Quantum Field Theory written by Dr. Gérard G. Emch and published by Courier Corporation. This book was released on 2014-08-04 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematic algebraic approach offers a careful formulation of the problems' physical motivations as well as self-contained descriptions of the mathematical methods for arriving at solutions. 1972 edition.
Download or read book Basic Algebra written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. The presentation includes blocks of problems that introduce additional topics and applications to science and engineering to guide further study. Many examples and hundreds of problems are included, along with a separate 90-page section giving hints or complete solutions for most of the problems.
Download or read book Introduction To Non linear Algebra written by Morozov Alexei and published by World Scientific Publishing Company. This book was released on 2007-10-02 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text presents the new domain of consistent non-linear counterparts for all basic objects and tools of linear algebra, and develops an adequate calculus for solving non-linear algebraic and differential equations. It reveals the non-linear algebraic activity as an essentially wider and diverse field with its own original methods, of which the linear one is a special restricted case.This volume contains a detailed and comprehensive description of basic objects and fundamental techniques arising from the theory of non-linear equations, which constitute the scope of what should be called non-linear algebra. The objects of non-linear algebra are presented in parallel with the corresponding linear ones, followed by an exposition of specific non-linear properties treated with the use of classical (such as the Koszul complex) and original new tools. This volume extensively uses a new diagram technique and is enriched with a variety of illustrations throughout the text. Thus, most of the material is new and is clearly exposed, starting from the elementary level. With the scope of its perspective applications spreading from general algebra to mathematical physics, it will interest a broad audience of physicists; mathematicians, as well as advanced undergraduate and graduate students.
Download or read book Linear Methods written by David Hecker and published by CRC Press. This book was released on 2018-08-06 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Methods: A General Education Course is expressly written for non-mathematical students, particularly freshmen taking a required core mathematics course. Rather than covering a hodgepodge of different topics as is typical for a core mathematics course, this text encourages students to explore one particular branch of mathematics, elementary linear algebra, in some depth. The material is presented in an accessible manner, as opposed to a traditional overly rigorous approach. While introducing students to useful topics in linear algebra, the book also includes a gentle introduction to more abstract facets of the subject. Many relevant uses of linear algebra in today’s world are illustrated, including applications involving business, economics, elementary graph theory, Markov chains, linear regression and least-squares polynomials, geometric transformations, and elementary physics. The authors have included proofs of various important elementary theorems and properties which provide readers with the reasoning behind these results. Features: Written for a general education core course in introductory mathematics Introduces elementary linear algebra concepts to non-mathematics majors Provides an informal introduction to elementary proofs involving matrices and vectors Includes useful applications from linear algebra related to business, graph theory, regression, and elementary physics Authors Bio: David Hecker is a Professor of Mathematics at Saint Joseph's University in Philadelphia. He received his Ph.D. from Rutgers University and has published several journal articles. He also co-authored several editions of Elementary Linear Algebra with Stephen Andrilli. Stephen Andrilli is a Professor in the Mathematics and Computer Science Department at La Salle University in Philadelphia. He received his Ph.D. from Rutgers University and also co-authored several editions of Elementary Linear Algebra with David Hecker.
Download or read book Geometrical and Algebraic Aspects of Nonlinear Field Theory written by S. de Filippo and published by Elsevier. This book was released on 2012-12-02 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experts in general relativity, particle physics and mathematical physics discuss aspects of their recent research. The main emphasis is on the geometrical and algebraic methods used in solving a wide range of problems.
Download or read book Basic Methods Of Soliton Theory written by Ivan V Cherednik and published by World Scientific. This book was released on 1996-08-22 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 25 years of its existence Soliton Theory has drastically expanded our understanding of “integrability” and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.Differential algebra (local conservation laws, Bäcklund-Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann-Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin-Gordon, and Nonlinear Schrödinger equation.
Download or read book Mathematical Methods written by Sadri Hassani and published by Springer Science & Business Media. This book was released on 2008-10-27 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.
Download or read book Numerical Methods for Grid Equations written by A.A. Samarskij and published by Birkhäuser. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The finite-difference solution of mathematical-physics differential equations is carried out in two stages: 1) the writing of the difference scheme (a differ ence approximation to the differential equation on a grid), 2) the computer solution of the difference equations, which are written in the form of a high order system of linear algebraic equations of special form (ill-conditioned, band-structured). Application of general linear algebra methods is not always appropriate for such systems because of the need to store a large volume of information, as well as because of the large amount of work required by these methods. For the solution of difference equations, special methods have been developed which, in one way or another, take into account special features of the problem, and which allow the solution to be found using less work than via the general methods. This work is an extension of the book Difference M ethod3 for the Solution of Elliptic Equation3 by A. A. Samarskii and V. B. Andreev which considered a whole set of questions connected with difference approximations, the con struction of difference operators, and estimation of the ~onvergence rate of difference schemes for typical elliptic boundary-value problems. Here we consider only solution methods for difference equations. The book in fact consists of two volumes.
Download or read book Algebraic and Geometric Methods in Mathematical Physics written by Anne Boutet de Monvel and published by Springer. This book was released on 2013-01-22 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
Download or read book Clifford Algebras written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers.
Download or read book Algebraic and Geometric Structures in Current Algebra Theory written by Robert Hermann and published by Scholarly Press. This book was released on 1969 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper begins the general mathematical study of 'current algebras' by elementary particle physicists. They are defined abstractly as infinite dimensional real Lie algebras, whose underlying vector space is a module over the ring of test-functions. Preliminary remarks about classification of these objects and general geometric and algebraic methods of their construction are made. As preparation, certain facts about differential operators on arbitrary modules are presented. In addition, remarks about the differential-geometric nature of the 'energy-momentum tensor' and conformal symmetry are made. Finally, a global transformation group is constructed whose Lie algebra is one of the simplest current algebras.
Download or read book New Mathematical Methods for Physics written by Jean-Francois Pommaret and published by . This book was released on 2018-06 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of "group" has been introduced in mathematics for the first time by E. Galois (1830) and slowly passed from algebra to geometry with the work of S. Lie on Lie groups (1880) and Lie pseudogroups (1890) of transformations. The concept of a finite length differential sequence, now called the Janet sequence, had been described for the first time by M. Janet (1920). Then, the work of D. C. Spencer (1970) has been the first attempt to use the formal theory of systems of partial differential equations (PDE) in order to study the formal theory of Lie pseudogroups. However, the linear and nonlinear Spencer sequences for Lie pseudogroups, though never used in physics, largely supersede the "Cartan structure equations " (1905) and are quite different from the "Vessiot structure equations " (1903), introduced for the same purpose but never acknowledged by E. Cartan or successors. Meanwhile, mixing differential geometry with homological algebra, M. Kashiwara (1970) created "algebraic analysis" in order to study differential modules and double duality. By chance, unexpected arguments have been introduced by the brothers E. and F. Cosserat (1909) in order to revisit elasticity and by H. Weyl (1918) in order to revisit electromagnetism through a unique differential sequence only depending on the structure of the conformal group of space-time.The classical Galois theory deals with certain finite algebraic extensions and establishes a bijective order reversing correspondence between the intermediate fields and the subgroups of a group of permutations called the Galois group of the extension. It has been the dream of many mathematicians at the end of the nineteenth century to generalize these results to systems of linear or algebraic PDE and the corresponding finitely generated differential extensions, in order to be able to add the word differential in front of any classical statement. The achievement of the Picard-Vessiot theory by E. Kolchin and coworkers between 1950 and 1970 is now well-known. However, the work of Vessiot on the differential Galois theory (1904), that is on the possibility to extend the classical Galois theory to systems of algebraic PDE and algebraic Lie pseudogroups, namely groups of transformations solutions for systems of algebraic PDE, has also never been acknowledged. His main idea has been to notice that the Galois theory (old and new) is a study of principal homogeneous spaces (PHS) for algebraic groups or pseudogroups described by what he called "automorphic systems" of PDE.The purpose of this book is first to revisit Gauge Theory and General Relativity in light of the latest developments just described and then to apply the differential Galois theory in order to revisit various domains of mechanics (Shell theory, Chain theory, Frenet-Serret formulas, Hamilton-Jacobi equations). All the results presented are new. (Nova)
Download or read book Lectures in General Algebra written by A. G. Kurosh and published by Elsevier. This book was released on 2014-07-10 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the convenience of constructing a single theory from the results of group experiments and ring experiments which are known to follow simple corollaries. The text also presents algebraic structures that are not of binary nature. From this parallelism arise other concepts, such as that of the lattices, complete lattices, and modular lattices. The book then proves the Schmidt-Ore theorem, and also describes linear algebra, as well as the Birkhoff-Witt theorem on Lie algebras. The text also addresses ordered groups, the Archimedean groups and rings, and Albert's theorem on normed algebras. This book can prove useful for algebra students and for professors of algebra and advanced mathematicians.
Download or read book Space Time Algebra written by David Hestenes and published by Birkhäuser. This book was released on 2015-04-25 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, and enables physicists to understand topics in engineering, and engineers to understand topics in physics (including aspects in frontier areas), in a way which no other single mathematical system could hope to make possible. There is another aspect to Geometric Algebra, which is less tangible, and goes beyond questions of mathematical power and range. This is the remarkable insight it gives to physical problems, and the way it constantly suggests new features of the physics itself, not just the mathematics. Examples of this are peppered throughout ‘Space-Time Algebra’, despite its short length, and some of them are effectively still research topics for the future. From the Foreward by Anthony Lasenby
