Some Modern Mathematics For Physicists And Other Outsiders

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Some Modern Mathematics for Physicists and Other Outsiders

Author : Paul Roman
Publisher : Elsevier
ISBN 13 : 1483187373
Total Pages : 426 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Some Modern Mathematics for Physicists and Other Outsiders by : Paul Roman

Download or read book Some Modern Mathematics for Physicists and Other Outsiders written by Paul Roman and published by Elsevier. This book was released on 2014-05-09 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some Modern Mathematics for Physicists and Other Outsiders: An Introduction to Algebra, Topology, and Functional Analysis, Volume 1 focuses on the operations, principles, methodologies, and approaches employed in algebra, topology, and functional analysis. The publication first offers information on sets, maps, and algebraic composition laws and systems. Discussions focus on morphisms of algebraic systems, sequences and families, cardinal numbers, ordered sets and maps, equivalence relations and maps, composite functions and inverses, operations with sets, and relations in sets. The text then ponders on special algebraic systems, topological spaces, and topological spaces with special properties. Topics include complete metric spaces, compact spaces, separable and connected spaces, homeomorphism and isometry, convergence, continuity, general structure of topological spaces, rings and fields, linear spaces, linear algebras, and nonassociative algebras. The book elaborates on the theory of integration and measure spaces, including measurable spaces, general properties of the integral, and measureable functions. The publication is a valuable reference for theoretical physicists, research engineers, and scientists who are concerned with structural problems.

Some Modern Mathematics for Physicists and Other Outsiders

Author : Paul Roman
Publisher :
ISBN 13 :
Total Pages : 666 pages
Book Rating : 4.:/5 (487 download)

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Book Synopsis Some Modern Mathematics for Physicists and Other Outsiders by : Paul Roman

Download or read book Some Modern Mathematics for Physicists and Other Outsiders written by Paul Roman and published by . This book was released on 1975 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt:

From Micro to Macro Quantum Systems

Author : K. Kong Wan
Publisher : World Scientific
ISBN 13 : 1860946259
Total Pages : 712 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis From Micro to Macro Quantum Systems by : K. Kong Wan

Download or read book From Micro to Macro Quantum Systems written by K. Kong Wan and published by World Scientific. This book was released on 2006 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditional quantum theory has a very rigid structure, making it difficult to accommodate new properties emerging from novel systems. This book presents a flexible and unified theory for physical systems, from micro and macro quantum to classical. This is achieved by incorporating superselection rules and maximal symmetric operators into the theory. The resulting theory is applicable to classical, microscopic quantum and non-orthodox mixed quantum systems of which macroscopic quantum systems are examples. A unified formalism also greatly facilitates the discussion of interactions between these systems. A scheme of quantization by parts is introduced, based on the mathematics of selfadjoint and maximal symmetric extensions of symmetric operators, to describe point interactions. The results are applied to treat superconducting quantum circuits in various configurations.This book also discusses various topics of interest such as the asymptotic treatment of quantum state preparation and quantum measurement, local observables and local values, Schrdinger's cat states in superconducting systems, and a path space formulation of quantum mechanics.This self-contained book is complete with a review of relevant geometric and operator theories, for example, vector fields and operators, symmetric operators and their maximal symmetric extensions, direct integrals of Hilbert spaces and operators.

The Structures of Mathematical Physics

Author : Steven P. Starkovich
Publisher : Springer Nature
ISBN 13 : 3030734498
Total Pages : pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis The Structures of Mathematical Physics by : Steven P. Starkovich

Download or read book The Structures of Mathematical Physics written by Steven P. Starkovich and published by Springer Nature. This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.

Quantum Mechanics

Author : K. Kong Wan
Publisher : CRC Press
ISBN 13 : 1351333364
Total Pages : 720 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Quantum Mechanics by : K. Kong Wan

Download or read book Quantum Mechanics written by K. Kong Wan and published by CRC Press. This book was released on 2019-07-09 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical formalism of quantum theory in terms of vectors and operators in infinite-dimensional complex vector spaces is very abstract. The definitions of many mathematical quantities used do not seem to have an intuitive meaning, which makes it difficult to appreciate the mathematical formalism and understand quantum mechanics. This book provides intuition and motivation to the mathematics of quantum theory, introducing the mathematics in its simplest and familiar form, for instance, with three-dimensional vectors and operators, which can be readily understood. Feeling confident about and comfortable with the mathematics used helps readers appreciate and understand the concepts and formalism of quantum mechanics. This book is divided into four parts. Part I is a brief review of the general properties of classical and quantum systems. A general discussion of probability theory is also included which aims to help in understanding the probability theories relevant to quantum mechanics. Part II is a detailed study of the mathematics for quantum mechanics. Part III presents quantum mechanics in a series of postulates. Six groups of postulates are presented to describe orthodox quantum systems. Each statement of a postulate is supplemented with a detailed discussion. To make them easier to understand, the postulates for discrete observables are presented before those for continuous observables. Part IV presents several illustrative applications, which include harmonic and isotropic oscillators, charged particle in external magnetic fields and the Aharonov–Bohm effect. For easy reference, definitions, theorems, examples, comments, properties and results are labelled with section numbers. Various symbols and notations are adopted to distinguish different quantities explicitly and to avoid misrepresentation. Self-contained both mathematically and physically, the book is accessible to a wide readership, including astrophysicists, mathematicians and philosophers of science who are interested in the foundations of quantum mechanics.

Lectures on Selected Topics in Mathematical Physics

Author : William A Schwalm
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1643273507
Total Pages : 114 pages
Book Rating : 4.6/5 (432 download)

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Book Synopsis Lectures on Selected Topics in Mathematical Physics by : William A Schwalm

Download or read book Lectures on Selected Topics in Mathematical Physics written by William A Schwalm and published by Morgan & Claypool Publishers. This book was released on 2019-03-08 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a sequel to Lectures on Selected Topics in Mathematical Physics: Introduction to Lie theory with applications. This volume is devoted mostly to Lie groups. Lie algebras and generating functions, both for standard special functions and for solution of certain types of physical problems. It is an informal treatment of these topics intended for physics graduate students or others with a physics background wanting a brief and informal introduction to the subjects addressed in a style and vocabulary not completely unfamiliar.

Quantum Theory: Concepts and Methods

Author : A. Peres
Publisher : Springer Science & Business Media
ISBN 13 : 0306471205
Total Pages : 450 pages
Book Rating : 4.3/5 (64 download)

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Book Synopsis Quantum Theory: Concepts and Methods by : A. Peres

Download or read book Quantum Theory: Concepts and Methods written by A. Peres and published by Springer Science & Business Media. This book was released on 2006-06-01 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many excellent books on quantum theory from which one can learn to compute energy levels, transition rates, cross sections, etc. The theoretical rules given in these books are routinely used by physicists to compute observable quantities. Their predictions can then be compared with experimental data. There is no fundamental disagreement among physicists on how to use the theory for these practical purposes. However, there are profound differences in their opinions on the ontological meaning of quantum theory. The purpose of this book is to clarify the conceptual meaning of quantum theory, and to explain some of the mathematical methods which it utilizes. This text is not concerned with specialized topics such as atomic structure, or strong or weak interactions, but with the very foundations of the theory. This is not, however, a book on the philosophy of science. The approach is pragmatic and strictly instrumentalist. This attitude will undoubtedly antagonize some readers, but it has its own logic: quantum phenomena do not occur in a Hilbert space, they occur in a laboratory.

Real and Functional Analysis

Author : Vladimir I. Bogachev
Publisher : Springer Nature
ISBN 13 : 3030382192
Total Pages : 586 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Real and Functional Analysis by : Vladimir I. Bogachev

Download or read book Real and Functional Analysis written by Vladimir I. Bogachev and published by Springer Nature. This book was released on 2020-02-25 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.

Advanced Mathematics for Applications

Author : Andrea Prosperetti
Publisher : Cambridge University Press
ISBN 13 : 1139492683
Total Pages : 743 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Advanced Mathematics for Applications by : Andrea Prosperetti

Download or read book Advanced Mathematics for Applications written by Andrea Prosperetti and published by Cambridge University Press. This book was released on 2011-01-06 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough presentation.

Groups, Systems and Many-Body Physics

Author : Peter Dal Cin
Publisher : Springer Science & Business Media
ISBN 13 : 3663068250
Total Pages : 429 pages
Book Rating : 4.6/5 (63 download)

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Book Synopsis Groups, Systems and Many-Body Physics by : Peter Dal Cin

Download or read book Groups, Systems and Many-Body Physics written by Peter Dal Cin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors of the present book share the view that groups and semigroups playa funda mental role in the structure of the complex systems which they are studying. A serious effort was made to implement this point of view by presenting the fundamental concepts pertaining to groups and semigroups before going into the various fields of application. The first two chapters are written in this spirit. The following seven chapters deal with groups in relation to specific systems and lead from basic notions to high-level applications. The systems under study are in all cases characterized by a high degree of complexity as found in the physics of many degrees of freedom and in the theory of automata and systems. In 1977 the authors from the University of Tiibingen (M. Dal Cin, G. John, P. Kramer, A. Rieckers, K. Scheerer and H. Stumpf) organized an International Summer School on Groups and Many-Body Physics. The lectures presented at this School dealt specifically with this interplay of groups and complex systems. The contributions of this book cover the fields which were treated in a condensed form at the Summer School.

Statistical Mechanics

Author : G Morandi
Publisher : World Scientific Publishing Company
ISBN 13 : 9813102675
Total Pages : 668 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Statistical Mechanics by : G Morandi

Download or read book Statistical Mechanics written by G Morandi and published by World Scientific Publishing Company. This book was released on 2001-05-17 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the foundations of classical thermodynamics, with emphasis on the use of differential forms of classical and quantum statistical mechanics, and also on the foundational aspects. In both contexts, a number of applications are considered in detail, such as the general theory of response, correlations and fluctuations, and classical and quantum spin systems. In the quantum case, a self-contained introduction to path integral methods is given. In addition, the book discusses phase transitions and critical phenomena, with applications to the Landau theory and to the Ginzburg–Landau theory of superconductivity, and also to the phenomenon of Bose condensation and of superfluidity. Finally, there is a careful discussion on the use of the renormalization group in the study of critical phenomena. Request Inspection Copy

Nonlocality in Quantum Physics

Author : Andrey Anatoljevich Grib
Publisher : Springer Science & Business Media
ISBN 13 : 1461546877
Total Pages : 223 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Nonlocality in Quantum Physics by : Andrey Anatoljevich Grib

Download or read book Nonlocality in Quantum Physics written by Andrey Anatoljevich Grib and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlocality phenomena exhibited by entangled quantum systems are certainly one of the most extraordinary aspects of quantum theory. This book discusses this phe nomenon according to several points of view, i.e., according to different interpretations of the mathematics of the quantum formalism. The several interpretations of the Copenhagen interpretation, the many worlds, the de Broglie-Bohm, quantum logics, the decohering by the environment approach and the histories approach interpretations are scrutinized and criticized in detail. Recent results on cryptography, quantum bit commitment, quantum erasers and teleportation are also presented and discussed. In preparing the book we benefited from discussions with many people, but we would like, in particular, to express our gratitude to Professor B. d'Espagnat for his useful comments and suggestions. We are grateful also to Ms. L. Gentry EI-Dash for the English revision, to Dr. 1. E. Maiorino for the production of the figures and a careful reading of the manuscript, and for the statI of Plenum for advice and for having produced a nice book. Finally, the authors thank FAPESP (contract no. I 99612657-0) for a grant making this book possible. A. A. ORIB AND W. A. RODRIGUES, JR.

Theoretical Foundations of Cosmology

Author : Micha? Heller
Publisher : World Scientific
ISBN 13 : 9789810207564
Total Pages : 170 pages
Book Rating : 4.2/5 (75 download)

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Book Synopsis Theoretical Foundations of Cosmology by : Micha? Heller

Download or read book Theoretical Foundations of Cosmology written by Micha? Heller and published by World Scientific. This book was released on 1992 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book's principal aim is to clarify fundamental concepts, decipher mathematical structures used to model space-time and relativistic worlds, and to disclose their physical meaning. After each chapter, philosophical implications of the presented material are commented upon.Both special and general theories of relativity are presented in the book with the stress on their global aspects. Although global mathematical methods are extensively used throughout the book, the definitions of new concepts, short comments and examples make reading smooth without the need to consult other textbooks or review papers.

Methods of Inverse Problems in Physics

Author : Dilip N. Ghosh Roy
Publisher : CRC Press
ISBN 13 : 9780849362583
Total Pages : 506 pages
Book Rating : 4.3/5 (625 download)

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Book Synopsis Methods of Inverse Problems in Physics by : Dilip N. Ghosh Roy

Download or read book Methods of Inverse Problems in Physics written by Dilip N. Ghosh Roy and published by CRC Press. This book was released on 1991-03-14 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interesting volume focuses on the second of the two broad categories into which problems of physical sciences fall-direct (or forward) and inverse (or backward) problems. It emphasizes one-dimensional problems because of their mathematical clarity. The unique feature of the monograph is its rigorous presentation of inverse problems (from quantum scattering to vibrational systems), transmission lines, and imaging sciences in a single volume. It includes exhaustive discussions on spectral function, inverse scattering integral equations of Gel'fand-Levitan and Marcenko, Povzner-Levitan and Levin transforms, Møller wave operators and Krein's functionals, S-matrix and scattering data, and inverse scattering transform for solving nonlinear evolution equations via inverse solving of a linear, isospectral Schrodinger equation and multisoliton solutions of the K-dV equation, which are of special interest to quantum physicists and mathematicians. The book also gives an exhaustive account of inverse problems in discrete systems, including inverting a Jacobi and a Toeplitz matrix, which can be applied to geophysics, electrical engineering, applied mechanics, and mathematics. A rigorous inverse problem for a continuous transmission line developed by Brown and Wilcox is included. The book concludes with inverse problems in integral geometry, specifically Radon's transform and its inversion, which is of particular interest to imaging scientists. This fascinating volume will interest anyone involved with quantum scattering, theoretical physics, linear and nonlinear optics, geosciences, mechanical, biomedical, and electrical engineering, and imaging research.

A Course of Mathematics for Engineerings and Scientists

Author : Brian H. Chirgwin
Publisher : Elsevier
ISBN 13 : 1483154807
Total Pages : 362 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis A Course of Mathematics for Engineerings and Scientists by : Brian H. Chirgwin

Download or read book A Course of Mathematics for Engineerings and Scientists written by Brian H. Chirgwin and published by Elsevier. This book was released on 2013-10-22 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course of Mathematics for Engineers and Scientists offers a mathematics course for undergraduate students reading science and engineering at British and Commonwealth Universities and colleges. The aim of this volume is to generalize and develop the ideas and methods of earlier volumes so that the student can appreciate and use the mathematical methods required in the more advanced parts of physics and engineering. This book begins with elementary ideas of vector algebra which are generalized and developed in two ways. The first is an account of vector analysis and the differential and integral operations and theorems concerning vectors. These ideas find their first generalization in tensor analysis and the transformation of coordinates, including orthogonal curvilinear coordinates. The second development is to matrices, where the properties of arrays of elements, linear equations, and quadratic forms are shown to be the generalizations of elementary algebra and, using 'vector space', of familiar geometrical ideas to n dimensions. The solution of differential equations by series provides a general method for the solution of ordinary and some partial differential equations. A discussion of the properties of the solutions in the light of the Sturm-Liouville theory introduces the conceptions of eigenvalues and orthogonal functions, forming a link with matrices. A chapter on the special functions gives some of the better known properties of Bessel, Legendre, Laguerre, and Hermite functions, which commonly occur in the solution of boundary and initial value problems.

A Course of Mathematics for Engineers and Scientists

Author : Brian H. Chirgwin
Publisher : Elsevier
ISBN 13 : 1483139867
Total Pages : 383 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis A Course of Mathematics for Engineers and Scientists by : Brian H. Chirgwin

Download or read book A Course of Mathematics for Engineers and Scientists written by Brian H. Chirgwin and published by Elsevier. This book was released on 2013-09-03 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course of Mathematics for Engineers and Scientists, Volume 3: Theoretical Mechanics introduces the concepts of virtual work, generalized coordinates and the derivation of generalized forces from the potential energy function. This book is composed of 10 chapters and begins with the principles of mechanics, plane statistics, virtual work, and continuously distributed forces. The succeeding chapters deal with the motion of a particle and the uniplanar motion of a rigid body, as well as the concept of particle dynamics. These topics are followed by discussions of the motions of interacting particles and the principles of stability. The final chapter describes the impulsive motion of a system of particles and collision between bodies. This book will be of value to mathematics and engineering students.

Mathematical Methods

Author : Brian H. Chirgwin
Publisher : Elsevier
ISBN 13 : 1483181936
Total Pages : 560 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Mathematical Methods by : Brian H. Chirgwin

Download or read book Mathematical Methods written by Brian H. Chirgwin and published by Elsevier. This book was released on 2014-06-05 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Methods is an introductory course on mathematical methods for students aiming for a first degree in engineering or science. Topics covered include differentiation and integration and their applications; the geometry of two dimensions, and complex numbers. Statistics and probability are also discussed. Comprised of eight chapters, this volume begins with an introduction to fundamental concepts, including the roots of equations; elementary two-dimensional coordinate geometry; limits and continuity; inequalities and quadratic forms; mathematical induction; and convergence. The discussion then turns to the techniques of differentiation and integration and their applications; the geometry of two dimensions; and complex numbers and their roots, together with trigonometric expansions. The book concludes with a chapter on statistics and probability, paying particular attention to the properties of a frequency distribution; some special probability distributions; normal distribution and the error function; and some probability problems. This monograph is intended for students taking a course in engineering or science.