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Operator Functions and Localization of Spectra is the first book that presents a systematic exposition of bounds for the spectra of various linear nonself-adjoint operators in a Hilbert space, having discrete and continuous spectra. In particular bounds for the spectra of integral, differential and integro-differential operators, as well as finite and infinite matrices are established. The volume also presents a systematic exposition of estimates for norms of operator-valued functions and their applications.

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The symplectic eigenvalue problem is helpful, e.g., inanalyzing a number of different questions that arise in linear controltheory for discrete-time systems. Industrial production andtechnological processes may suffer from unwanted behavior, e.g.,losses in the start-up and change-over phases of operation, pollution,emission of harmful elements, and production of unwanted by-products.Control techniques offer the possibility of analyzing such processesin order to detect the underlying causes of the unwanted behavior.This monograph describes up-to-date techniques for solving small tomedium-sized as well as large and sparse symplectic eigenvalueproblems. The text presents all developed algorithms inMatlab-programming style and numerical examples to demonstrate theirabilities, all of which makes the text accessible to graduate studentsin applied mathematics and control engineering, as well as toresearchers in these areas. ... Read more

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This book covers recent results in linear algebra with indefinite inner product. It includes applications to differential and difference equations with symmetries, matrix polynomials and Riccati equations. These applications are based on linear algebra in spaces with indefinite inner product. The latter forms an independent branch of linear algebra called indefinite linear algebra. This new subject is presented following the principles of a standard linear algebra course.

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Text for researchers, algorithm designers, and advanced graduate students in related fields, featuring as yet unpublished results on structured matrices and polynomials. Features systematic presentation and a user-friendly style to accommodate all readers. DLC: Matrices--Data processing. ... Read more

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Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of research that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential and difference equations, approximation theory, cohomology, and module theory.

This book, written by two distinguished authors, engages a broad audience by proving the a strong foudation. This book may be used in the classroom setting as well as a reference for researchers.

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The symplectic eigenvalue problem is helpful, e.g., inanalyzing a number of different questions that arise in linear controltheory for discrete-time systems. Industrial production andtechnological processes may suffer from unwanted behavior, e.g.,losses in the start-up and change-over phases of operation, pollution,emission of harmful elements, and production of unwanted by-products.Control techniques offer the possibility of analyzing such processesin order to detect the underlying causes of the unwanted behavior.This monograph describes up-to-date techniques for solving small tomedium-sized as well as large and sparse symplectic eigenvalueproblems. The text presents all developed algorithms inMatlab-programming style and numerical examples to demonstrate theirabilities, all of which makes the text accessible to graduate studentsin applied mathematics and control engineering, as well as toresearchers in these areas. ... Read more

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This volume combines an illustration of the theory of tensors and the foundations of continuum mechanics. Firstly, a detailed tensor analysis is developed in Cartesian and general coordinates. Definitions, propositions, and examples relative to operations on tensors, canonical isomorphism, Euclidean vector spaces, exterior algebra, point spaces, metric element, Christoffel symbols, covariant and absolute derivatives, adjoint, differential operators, and many other concepts are introduced in a rigorous and practical way. The topic is not merely viewed as an autonomous mathematical discipline, but as a preparation for theories of physics such as general relativity theory, fluid-dynamics, engineering, and differential geometry. Secondly, developed in symbiosis with tensor analysis, continuum mechanics thoroughly covers Lagrangian and Eulerian descriptions, deformations, kinematics of continua, fundamental laws, principle of virtual work, linear elasticity and more. This work lays the groundwork for more technical subjects as strength of materials, plasticity, viscoelasticity, and nonlinear continuum mechanics. The material is presented with great pedagogical care, a summary of formulae and a glossary of symbols are provided, as well as ninety-five solved problems. The book is suitable as a text for third year students of mathematics, physics and engineering, and for anyone wishing to acquire insight into the mathematics of mechanics, the mathematics of physics, the mathematics of engineering, continuum mechanics, elasticity and viscoelasticity, linear and multilinear algebra, or matrix theory. ... Read more

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Tensor Analysis and Nonlinear Tensor Functions embraces the basic fields of tensor calculus: tensor algebra, tensor analysis, tensor description of curves and surfaces, tensor integral calculus, the basis of tensor calculus in Riemannian spaces and affinely connected spaces, - which are used in mechanics and electrodynamics of continua, crystallophysics, quantum chemistry etc. The book suggests a new approach to definition of a tensor in space 3, which allows us to show a geometric representation of a tensor and operations on tensors. Based on this approach, the author gives a mathematically rigorous definition of a tensor as an individual object in arbitrary linear, Riemannian and other spaces for the first time. It is the first book to present a systematized theory of tensor invariants, a theory of nonlinear anisotropic tensor functions and a theory of indifferent tensors describing the physical properties of continua. The book will be useful for students and postgraduates of mathematical, mechanical engineering and physical departments of universities and also for investigators and academic scientists working in continuum mechanics, solid physics, general relativity, crystallophysics, quantum chemistry of solids and material science. ... Read more

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Matrix and polynomial computations are fundamental to the theory and practice of computing. The authors present here a systematic treatment of algorithms and complexity in these two related areas. Its study of computations with Toeplitz matrices and other dense structured matrices demonstrates the links between numerical and algebraic approaches to computation. The authors begin with classical fundamental problems and gradually introduce the reader to current research. In particular, the book provides improved parallel algorithms for computations with structured matrices and their further applications to some fundamental computations with matrices and polynomials. The book is designed as a text for advanced graduates in mathematics and computer science. ... Read more

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This work presents some classical as well as some very recentresults and techniques concerning the spectral geometry correspondingto the Laplace--Beltrami operator and the Hodge--de Rhamoperators. It treats many topics that are not usually dealt with in this field,such as the continuous dependence of the eigenvalues with respect tothe Riemannian metric in the C-topology, and some of theirconsequences, such as Uhlenbeck's genericity theorem; examples ofnon-isometric flat tori in all dimensions greater than or equal tofour; Gordon's classical technique for constructing isospectral closedRiemannian manifolds; a detailed presentation of Sunada's techniqueand Pesce's approach to isospectrality; Gordon and Webb's example ofnon-isometric convex domains in Rn (n>=4) thatare isospectral for both Dirichlet and Neumann boundary conditions;the Chanillo--Treves estimate for the first positiveeigenvalue of the Hodge--de Rham operator, etc. Significantapplications are developed, and many open problems, references andsuggestions for further reading are given. Several themes foradditional research are pointed out. Audience: This volume is designed as an introductory text formathematicians and physicists interested in global analysis, analysison manifolds, differential geometry, linear and multilinear algebra,and matrix theory. It is accessible to readers whose backgroundincludes basic Riemannian geometry and functional analysis. Thesemathematical prerequisites are covered in the first two chapters, thusmaking the book largely self-contained. ... Read more

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Breadth of scope is unique

Author is a widely-known and successful textbook author

Unlike many recent textbooks on chaotic systems that have superficial treatment, this book provides explanations of the deep underlying mathematical ideas

No technical proofs, but an introduction to the whole field that is based on the specific analysis of carefully selected examples

Includes a section on cellular automata

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Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilities of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level.

The authors are leading researchers in  Computational Mathematics who have written various successful books.

Product Description

Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilitites of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level.

The authors are leading researchers in Computational Mathematics who have written various successful books.