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Matrix Methods and Vector Spaces in Physics by Sharma,Sharma Vinod K. Pdf
They have wide applications in a number of subjects ranging from solid state physics, solid/fluid mechanics to relativity and electromagnetics. This well-written book gives, in an easy-to-read style, a step-by-step and comprehensive understanding about the various concepts, theories and applications of vector spaces, matrices and tensors. The book equips the reader with the fundamental knowledge in such subjects as matrix theory, linear algebraic equations, applications of eigenvalues and eigenvectors, diagonalisation process, quadratic forms, Cartesian tensors and more.
Vector Spaces and Matrices in Physics by M. C. Jain Pdf
The theory of vector spaces and matrices is an essential part of the mathematical background required by physicists. Most books on the subject, however, do not adequately meet the requirements of physics courses-they tend to be either highly mathematical or too elementary. Books that focus on mathematical theory may render the subject too dry to hold the interest of physics students, while books that are more elementary tend to neglect some topics that are vital in the development of physical theories. In particular, there is often very little discussion of vector spaces, and many books introduce matrices merely as a computational tool. Vector Spaces and Matrices in Physics fills the gap between the elementary and the heavily mathematical treatments of the subject with an approach and presentation ideal for graduate-level physics students. After building a foundation in vector spaces and matrix algebra, the author takes care to emphasize the role of matrices as representations of linear transformations on vector spaces, a concept of matrix theory that is essential for a proper understanding of quantum mechanics. He includes numerous solved and unsolved problems, and enough hints for the unsolved problems to make the book self-sufficient. Developed through many years of lecture notes, Vector Spaces and Matrices in Physics was written primarily as a graduate and post-graduate textbook and as a reference for physicists. Its clear presentation and concise but thorough coverage, however, make it useful for engineers, chemists, economists, and anyone who needs a background in matrices for application in other areas.
Vector Spaces, Matrices and Tensors in Physics by M. C. Jain Pdf
Vector spaces, matrices, and tensors in physics form an essential part of the mathematical background required by physicists. This book is written primarily as textbook for undergraduate and postgraduate students and as a reference book for working physicists. Special emphasis is given to topics relevant to physics, for example linear independence and dependence of vectors, inner product, orthonormality, matrices as representations of linear transformations on vector spaces, similarity, eigenvalues, eigenvectors, diagonalization of matrices, expressing various physical quantities as tensors, tensorial formulation of vector algebra, calculus and geometry. The role of orthogonal, hermitian and unitary matrices in physics is highlighted.
Author : K. A. I. L. Wijewardena Gamalath Publisher : Cambridge India Page : 244 pages File Size : 48,6 Mb Release : 2007-03 Category : Science ISBN : 9788175964365
Groups, Matrices, and Vector Spaces by James B. Carrell Pdf
This unique text provides a geometric approach to group theory and linear algebra, bringing to light the interesting ways in which these subjects interact. Requiring few prerequisites beyond understanding the notion of a proof, the text aims to give students a strong foundation in both geometry and algebra. Starting with preliminaries (relations, elementary combinatorics, and induction), the book then proceeds to the core topics: the elements of the theory of groups and fields (Lagrange's Theorem, cosets, the complex numbers and the prime fields), matrix theory and matrix groups, determinants, vector spaces, linear mappings, eigentheory and diagonalization, Jordan decomposition and normal form, normal matrices, and quadratic forms. The final two chapters consist of a more intensive look at group theory, emphasizing orbit stabilizer methods, and an introduction to linear algebraic groups, which enriches the notion of a matrix group. Applications involving symm etry groups, determinants, linear coding theory and cryptography are interwoven throughout. Each section ends with ample practice problems assisting the reader to better understand the material. Some of the applications are illustrated in the chapter appendices. The author's unique melding of topics evolved from a two semester course that he taught at the University of British Columbia consisting of an undergraduate honors course on abstract linear algebra and a similar course on the theory of groups. The combined content from both makes this rare text ideal for a year-long course, covering more material than most linear algebra texts. It is also optimal for independent study and as a supplementary text for various professional applications. Advanced undergraduate or graduate students in mathematics, physics, computer science and engineering will find this book both useful and enjoyable.
Mustafa A. Akcoglu,Paul F. A. Bartha,Dzung Minh Ha
Author : Mustafa A. Akcoglu,Paul F. A. Bartha,Dzung Minh Ha Publisher : John Wiley & Sons Page : 480 pages File Size : 43,8 Mb Release : 2011-09-09 Category : Mathematics ISBN : 9781118164594
Analysis in Vector Spaces by Mustafa A. Akcoglu,Paul F. A. Bartha,Dzung Minh Ha Pdf
A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined withrelated computational methods are essential to understanding nearlyall areas of quantitative science. Analysis in Vector Spacespresents the central results of this classic subject throughrigorous arguments, discussions, and examples. The book aims tocultivate not only knowledge of the major theoretical results, butalso the geometric intuition needed for both mathematicalproblem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, terminology,and notation and also provide a basic introduction to set theory,the properties of real numbers, and a review of linear algebra. Anelegant approach to eigenvector problems and the spectral theoremsets the stage for later results on volume and integration.Subsequent chapters present the major results of differential andintegral calculus of several variables as well as the theory ofmanifolds. Additional topical coverage includes: Sets and functions Real numbers Vector functions Normed vector spaces First- and higher-order derivatives Diffeomorphisms and manifolds Multiple integrals Integration on manifolds Stokes' theorem Basic point set topology Numerous examples and exercises are provided in each chapter toreinforce new concepts and to illustrate how results can be appliedto additional problems. Furthermore, proofs and examples arepresented in a clear style that emphasizes the underlying intuitiveideas. Counterexamples are provided throughout the book to warnagainst possible mistakes, and extensive appendices outline theconstruction of real numbers, include a fundamental result aboutdimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra andsingle variable calculus, Analysis in Vector Spaces is anexcellent book for a second course in analysis for mathematics,physics, computer science, and engineering majors at theundergraduate and graduate levels. It also serves as a valuablereference for further study in any discipline that requires a firmunderstanding of mathematical techniques and concepts.
Lectures on Groups and Vector Spaces for Physicists by C J Isham Pdf
These notes are the contents of a lecture course given to third year physics undergraduates at the Imperial College who are taking the theoretical physics option. The subject of “Algebra and Groups” is of considerable importance in a number of branches of modern theoretical physics, and therefore one major objective of the course is to introduce the students to the basic ideas on the subject, bearing in mind the potential applications to quantum theory. However, another equally important aim of the course is to introduce the student to the art of genuine “mathematical” thinking. The notes are therefore written in a more precise mathematical style than is usually the case in courses aimed at physics students. Quite apart from the general educational value of such an exposure to abstract thinking, it is also the case that much modern theoretical physics draws on sophisticated ideas from pure mathematics and therefore it is most important that a perspective graduate student can approach these subjects without experiencing a total culture shock! The course is divided into three parts. The first is a short introduction to general group theory, with particular emphasis being placed on the matrix Lie groups that play such a crucial role in modern theoretical physics. The second part deals with the theory of vector spaces, with particular attention being paid to the theory of Hilbert spaces and the basic analytical techniques that are needed to handle the infinite dimensional situation. The final part of the course is a short introduction to the theory of group representations and the associated theory of characters. Contents:GroupsVector SpacesGroup Representations Readership: Mathematical physicists and mathematicians.
Matrices and Tensors in Physics by A. W. Joshi Pdf
This updated edition contains a good deal of new and relevant material including Bessel inequality, vector spaces of functions, physical laws and invariance principle, invariance in 3-D Newtonian and 4-D Minkowski spaces, fully antisymmetric tensors and their contraction. Discusses normal matrices and features a proof of the general theorem that a matrix posesses a complete set of orthonormal eigenvectors if and only if it is a normal matrix. Over 200 exercises and 100+ solved problems help students grasp the concepts presented.
Author : Arak M. Mathai,Hans J. Haubold Publisher : Walter de Gruyter GmbH & Co KG Page : 670 pages File Size : 41,9 Mb Release : 2017-10-23 Category : Mathematics ISBN : 9783110562590
Linear Algebra by Arak M. Mathai,Hans J. Haubold Pdf
In order not to intimidate students by a too abstract approach, this textbook on linear algebra is written to be easy to digest by non-mathematicians. It introduces the concepts of vector spaces and mappings between them without dwelling on statements such as theorems and proofs too much. It is also designed to be self-contained, so no other material is required for an understanding of the topics covered. As the basis for courses on space and atmospheric science, remote sensing, geographic information systems, meteorology, climate and satellite communications at UN-affiliated regional centers, various applications of the formal theory are discussed as well. These include differential equations, statistics, optimization and some engineering-motivated problems in physics. Contents Vectors Matrices Determinants Eigenvalues and eigenvectors Some applications of matrices and determinants Matrix series and additional properties of matrices
Linear Algebra Thoroughly Explained by Milan Vujicic Pdf
The author of this book was Professor of Theoretical Physics at the University of Belgrade. The book is based on lectures he gave there to both undergraduate and postgraduate students over a period of several decades. It sets out to explain Linear Algebra from its fundamentals to the most advanced level. A special feature of this book is its didactical approach, with a myriad of thoroughly worked examples and excellent illustrations, which allows the reader to approach the subject from any level and to proceed to that of the most advanced applications. Throughout, the subject is explained with painstaking care.
Mathematics for Quantum Mechanics by John David Jackson Pdf
Advanced undergraduates and graduate students studying quantum mechanics will find this text a valuable guide to mathematical methods. Emphasizing the unity of a variety of different techniques, it is enduringly relevant to many physical systems outside the domain of quantum theory. Concise in its presentation, this text covers eigenvalue problems in classical physics, orthogonal functions and expansions, the Sturm-Liouville theory and linear operators on functions, and linear vector spaces. Appendixes offer useful information on Bessel functions and Legendre functions and spherical harmonics. This introductory text's teachings offer a solid foundation to students beginning a serious study of quantum mechanics.
Author : P. K. Chattopadhyay Publisher : New Age International Page : 368 pages File Size : 45,6 Mb Release : 1990 Category : Mathematical physics ISBN : 8122402836
The Book Is Intended As A Text For Students Of Physics At The Master S Level. It Is Assumed That The Students Pursuing The Course Have Some Knowledge Of Differential Equations And Complex Variables. In Addition, A Knowledge Of Physics Upto At Least The B.Sc. (Honours) Level Is Assumed. Throughout The Book The Applications Of The Mathematical Techniques Developed, To Physics Are Emphasized. Examples Are, To A Large Extent, Drawn From Various Branches Of Physics. The Exercises Provide Further Extensions To Such Applications And Are Often ``Chosen`` To Illustrate And Supplement The Material In The Text. They Thus Form An Essential Part Of The TextDistinguishing Features Of The Book: * Emphasis On Applications To Physics. The Examples And Problems Are Chosen With This Aspect In Mind. * More Than One Hundred Solved Examples And A Large Collection Of Problems In The Exercises. * A Discussion On Non-Linear Differential Equations-A Topic Usually Not Found In Standard Texts. There Is Also A Section Devoted To Systems Of Linear, First Order Differential Equations. * One Full Chapter On Linear Vector Spaces And Matrices. This Chapter Is Essential For The Understanding Of The Mathematical Foundations Of Quantum Mechanics And The Material Can Be Used In A Course Of Quantum Mechanics. * Parts Of Chapter-6 (Greens Function) Will Be Useful In Courses On Electrodynamics And Quantum Mechanics. * One Complete Chapter Is Devoted To Group Theory Within Special Emphasis On The Applications In Physics. The Subject Matter Is Treated In Fairly Great Detail And Can Be Used In A Course On Group Theory.
Quantum Mechanics in Matrix Form by Günter Ludyk Pdf
This book gives an introduction to quantum mechanics with the matrix method. Heisenberg's matrix mechanics is described in detail. The fundamental equations are derived by algebraic methods using matrix calculus. Only a brief description of Schrödinger's wave mechanics is given (in most books exclusively treated), to show their equivalence to Heisenberg's matrix method. In the first part the historical development of Quantum theory by Planck, Bohr and Sommerfeld is sketched, followed by the ideas and methods of Heisenberg, Born and Jordan. Then Pauli's spin and exclusion principles are treated. Pauli's exclusion principle leads to the structure of atoms. Finally, Dirac ́s relativistic quantum mechanics is shortly presented. Matrices and matrix equations are today easy to handle when implementing numerical algorithms using standard software as MAPLE and Mathematica.
