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Author: A. W. Joshi Publisher: New Age International ISBN: 9788122405637 Category : Mathematics Languages : en Pages : 364
Book Description
The First Part Of This Book Begins With An Introduction To Matrices Through Linear Transformations On Vector Spaces, Followed By A Discussion On The Algebra Of Matrices, Special Matrices, Linear Equations, The Eigenvalue Problem, Bilinear And Quadratic Forms, Kronecker Sum And Product Of Matrices. Other Matrices Which Occur In Physics, Such As The Rotation Matrix, Pauli Spin Matrices And Dirac Matrices, Are Then Presented. A Brief Account Of Infinite Matrices From The Point Of View Of Matrix Formulation Of Quantum Mechanics Is Also Included. The Emphasis In This Part Is On Linear Dependence And Independence Of Vectors And Matrices, Linear Combinations, Independent Parameters Of Various Special Matrices And Such Other Concepts As Help The Student In Obtaining A Clear Understanding Of The Subject. A Simplified Proof Of The Theorem That A Common Set Of Eigenvectors Can Be Found For Two Commuting Matrices Is Given. The Second Part Deals With Cartesian And General Tensors. Many Physical Situations Are Discussed Which Require The Use Of Second And Higher Rank Tensors, Such As Effective Mass Tensor, Moment Of Inertia Tensor, Stress, Strain And Elastic Constants, Piezoelectric Strain Coefficient Tensor, Etc. Einsteins Summation Convention Is Explained In Detail And Common Errors Arising In Its Use Are Pointed Out. Rules For Checking The Correctness Of Tensor Equations Are Given. This Is Followed By Four-Vectors In Special Relativity And Covarient Formulation Of Electrodynamics. This Part Comes To An End With The Concept Of Parallel Displacement Of Vectors In Riemannian Space And Covariant Derivative Of Tensors, Leading To The Curvature Tensors And Its Properties.Appendix I Has Expanded And Two New Appendices Have Been Added In This Edition.
Author: Miroslav Fiedler Publisher: Springer ISBN: 9789024729579 Category : Mathematics Languages : en Pages : 308
Book Description
This is an updated translation of a book published in Czech by the SNTL - Publishers of Technical Literature in 1981. In developing this book, it was found reasonable to consider special matrices in general sense and also to include some more or less auxiliary topics that made it possible to present some facts or processes more demonstratively. An example is the graph theory. Chapter 1 contains the definitions of basic concepts of the theory of matrices, and fundamental theorems. The Schur complement is defined here in full generality and using its properties we prove the theorem on the factorization of a partitioned matrix into the product of a lower block triangular matrix with identity diagonal blocks, a block diagonal matrix, and an upper block triangular matrix with identity diagonal blocks. The theorem on the Jordan normal form of a matrix is gi¥en without proof. Chapter 2 is concerned with symmetric and Hermitian matrices. We prove Schur's theorem and, using it, we establish the fundamental theorem describing the factorization of symmetric or Hermitian matrices. Further, the properties of positive definite and positive semidefinite matrices are studied. In the conclusion, Sylvester's law of inertia of quadratic forms and theorems on the singular value decomposition and polar decomposition are proved. Chapter 3 treats the mutual connections between graphs and matrices.
Author: Miroslav Fiedler Publisher: Courier Corporation ISBN: 0486783480 Category : Mathematics Languages : en Pages : 386
Book Description
This revised and corrected second edition of a classic on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference. 1986 edition.
Author: M. C. Jain Publisher: Alpha Science International, Limited ISBN: Category : Mathematics Languages : en Pages : 240
Book Description
The theory of vector spaces and matrices is an essential part of the mathematical background required by physicists. This book is written primarily as a text for the undergraduate and postgraduate students and as a reference for physicists. Special emphasis is given to topics relevant to physics, e.g., linear independence and dependence of vectors, inner product, orthonormality, matrices as representations of linear transformations on vector spaces, similarity, eigenvalues, eigenvectors and diagonalization of matrices etc. The role of orthogonal, Hermitian and unitary matrices in physics is highlighted. A large number of solved problems and exercises, with enough hints/solutions, are provided to make the book self sufficient.
Author: Gupta B.D. Publisher: Vikas Publishing House ISBN: 8125930965 Category : Science Languages : en Pages : 1448
Book Description
Mathematics is an essential ingredient in the education of a student of mathematics or physics of a professional physicist, indeed in the education of any professional scientist or engineer. The purpose of Mathematical Physics is to provide a comprehensive study of the mathematics underlying theoretical physics at the level of graduate and postgraduate students and also have enough depth for others interested in higher level mathematics relevant to specialized fields. It is also intended to serve the research scientist or engineer who needs a quick refresher course in the subject. The Fourth Edition of the book has been thoroughly revised and updated keeping in mind the requirements of students and the latest UGC syllabus.
Author: Günter Ludyk Publisher: Springer Science & Business Media ISBN: 3642357989 Category : Science Languages : en Pages : 202
Book Description
This book is an introduction to the theories of Special and General Relativity. The target audience are physicists, engineers and applied scientists who are looking for an understandable introduction to the topic - without too much new mathematics. The fundamental equations of Einstein's theory of Special and General Relativity are derived using matrix calculus, without the help of tensors. This feature makes the book special and a valuable tool for scientists and engineers with no experience in the field of tensor calculus. In part I the foundations of Special Relativity are developed, part II describes the structure and principle of General Relativity. Part III explains the Schwarzschild solution of spherical body gravity and examines the "Black Hole" phenomenon. Any necessary mathematical tools are user friendly provided, either directly in the text or in the appendices.
Author: Evgeny V. Doktorov Publisher: Springer Science & Business Media ISBN: 1402061404 Category : Science Languages : en Pages : 413
Book Description
This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. Throughout, the text exploits the "linear experience" of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions.
Author: Danilo Babusci Publisher: World Scientific ISBN: 9811201595 Category : Science Languages : en Pages : 478
Book Description
The book covers different aspects of mathematical methods for Physics. It is designed for graduate courses but a part of it can also be used by undergraduate students. The leitmotiv of the book is the search for a common mathematical framework for a wide class of apparently disparate physical phenomena. An important role, within this respect, is provided by a nonconventional formulation of special functions and polynomials. The proposed methods simplify the understanding of the relevant technicalities and yield a unifying view to their applications in Physics as well as other branches of science.The chapters are not organized through the mathematical study of specific problems in Physics, rather they are suggested by the formalism itself. For example, it is shown how the matrix formalism is useful to treat ray Optics, atomic systems evolution, QED, QCD and Feynman diagrams. The methods presented here are simple but rigorous. They allow a fairly substantive tool of analysis for a variety of topics and are useful for beginners as well as the more experienced researchers.
Author: Suresh Chandra Publisher: Alpha Science Int'l Ltd. ISBN: 9781842651650 Category : Mathematics Languages : en Pages : 182
Book Description
Mathematical Physics is a vast topic which will need several volumes to cover. This text however discusses Vector Spaces, Matrices, Special Functions, Fourier Series, Fourier Transform and Laplace Transform this forming a complete set for postgraduate and engineering students. Each of the topics is developed in a systematic manner.
Author: Ruben Aldrovandi
Author: Ruben Aldrovandi
Author: A. W. Joshi
Author: Miroslav Fiedler
Author: Miroslav Fiedler
Author: M. C. Jain
Author: Gupta B.D.
Author: Günter Ludyk
Author: Evgeny V. Doktorov
Author: Danilo Babusci
Author: Suresh Chandra