Linear Algebra

Linear Algebra

Every student of mathematics needs a sound grounding in the techniques of linear algebra. It forms the basis of the study of linear equations, matrices, linear mappings, and differential equations, and comprises a central part of any course in mathematics. This textbook provides a rigorous introduction to the main concepts of linear algebra which will be suitable for all students coming to the subject for the first time. The book is in two parts: Part One develops the basic theory of vector spaces and linear maps, including dimension, determinants, and eigenvalues and eigenvectors. Part Two goes on to develop more advanced topics and in particular the study of canonical forms for matrices. Professor Berberian is at pains to explain all the ideas underlying the proofs of results as well as to give numerous examples and applications. There is an abundant supply of exercises to reinforce the reader’s grasp of the material and to elaborate on ideas from the text. As a result, this book presents a well-rounded and mathematically sound first course in linear algebra.

Linear Algebra

Maple By Example

Maple By Example

Maple by Example, Third Edition, is a reference/text with CD for beginning and experienced students, professional engineers, and other Maple users. This new edition has been updated to be compatible with the most recent release of the Maple software. Coverage includes built-in Maple commands used in courses and practices that involve calculus, linear algebra, business mathematics, ordinary and partial differential equations, numerical methods, graphics and more. The CD-ROM provides updated Maple input and all text from the book.

Maple By Example

Linear Algebra with Applications, 3rd Edition

Linear Algebra with Applications, 3rd Edition

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Linear Algebra with Applications, 3rd Edition

Introductory Real Analysis

Introductory Real Analysis

Self-contained and comprehensive, this elementary introduction to real and functional analysis is readily accessible to those with background in advanced calculus. It covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, and much more. 350 problems. 1970 edition.

Introductory Real Analysis

Rhythmanalysis

Rhythmanalysis

Rhythmanalysis displays all the characteristics which made Lefebvre one of the most important Marxist thinkers of the twentieth century. In the analysis of rhythms — both biological and social — Lefebvre shows the interrelation of space and time in the understanding of everyday life.With dazzling skills, Lefebvre moves between discussions of music, the commodity, measurement, the media and the city. In doing so he shows how a non-linear conception of time and history balanced his famous rethinking of the question of space. This volume also includes his earlier essays on ‘The Rhythmanaly.

Rhythmanalysis

Semigroups of Linear Operators and Applications to Partial Differential Equations

Semigroups of Linear Operators and Applications to Partial Differential Equations

Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Semigroups of Linear Operators and Applications to Partial Differential Equations

Vector and Geometric Calculus

Vector and Geometric Calculus

This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. It is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one.

Vector and Geometric Calculus

Linear and Geometric Algebra

Linear and Geometric Algebra

This textbook for the first undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. Geometric algebra is an extension of linear algebra. It enhances the treatment of many linear algebra topics. And geometric algebra does much more. Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas. They provide a unified mathematical language for many areas of physics, computer science, and other fields. The book can be used for self study by those comfortable with the theorem/proof style of a mathematics text. This is a second printing, corrected and slightly revised. Visit the book’s web site for more information: http: //faculty.luther.edu/ macdonal/laga I commend Alan Macdonald for his excellent book! His exposition is clean and spare. He has done a fine job of engineering a gradual transition from standard views of linear algebra to the perspective of geometric algebra. The book is sufficiently conventional to be adopted as a textbook by an adventurous teacher without getting flack from colleagues. Yet it leads to gems of geometric algebra that are likely to delight thoughtful students and surprise even the most experienced instructors. — David Hestenes, Distinguished Research Professor, Arizona State University

Linear and Geometric Algebra

Rational Algebraic Curves

Rational Algebraic Curves

The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.

Rational Algebraic Curves

Fault Diagnosis and Fault-Tolerant Control Strategies for Non-Linear Systems

Fault Diagnosis and Fault-Tolerant Control Strategies for Non-Linear Systems

This book presents selected fault diagnosis and fault-tolerant control strategies for non-linear systems in a unified framework. In particular, starting from advanced state estimation strategies up to modern soft computing, the discrete-time description of the system is employed Part I of the book presents original research results regarding state estimation and neural networks for robust fault diagnosis. Part II is devoted to the presentation of integrated fault diagnosis and fault-tolerant systems. It starts with a general fault-tolerant control framework, which is then extended by introducing robustness with respect to various uncertainties. Finally, it is shown how to implement the proposed framework for fuzzy systems described by the well-known TakagiSugeno models.

Fault Diagnosis and Fault-Tolerant Control Strategies for Non-Linear Systems

Generalized, Linear, and Mixed Models

Generalized, Linear, and Mixed Models

Wiley Series in Probability and Statistics

Generalized, Linear, and Mixed Models

Ultrashort Laser Pulses in Biology and Medicine

Ultrashort Laser Pulses in Biology and Medicine

Sources of ultrashort laser pulses are nowadays commercially available and have entered many areas of research and development. This book gives an overview of biological and medical applications of these laser pulses. The briefness of these laser pulses permits the tracing of the fastest processes in photo-active bio-systems, which is one focus of the book. The other focus is applications that rely on the high peak intensity of ultrashort laser pulses. Examples covered span non-linear imaging techniques, optical tomography, and laser surgery.

Ultrashort Laser Pulses in Biology and Medicine

Elasticity

Elasticity

Elasticity: Theory, Applications, and Numerics, Third Edition, continues its market-leading tradition of concisely presenting and developing the linear theory of elasticity, moving from solution methodologies, formulations, and strategies into applications of contemporary interest, such as fracture mechanics, anisotropic and composite materials, micromechanics, nonhomogeneous graded materials, and computational methods.

Elasticity

Statics of Rods

Statics of Rods

The volume is devoted to the mechanics of rods, which is a branch of the mechanics of deformable bodies. The main goal of the book is to present systematically theoretical fundamentals of the mechanics of rods as well as numerical methods used for practical purposes. The monograph is concerned with the most general statements of the problems in the mechanics of rods. Various types of external loads that a rod may be subject to are discussed. Advanced techniques that includes vector analyses, linear algebra, and distributions is used in the derivation of linear and nonlinear equilibrium equations. The use of these techniques helps us to make transformations and rearrangements of equations more transparent and compact. Theoretical basics of rods interacting with external and internal flows of fluid and the derivation of the formulas for the hydrodynamic and aerodynamic forces are presented.

Statics of Rods

The W3 Algebra

The W3 Algebra

‘W’ algebras are nonlinear generalizations of Lie algebras that arise in the context of two-dimensional conformal field theories when one explores higher-spin extensions of the Virasoro algebra. They provide the underlying symmetry algebra of certain string generalizations which allow the extended world sheet gravity. This book presents such gravity theories, concentrating on the algebra of physical operators determined from an analysis of the corresponding BRST cohomology. It develops the representation theory of ‘W’ algebras needed to extend the standard techniques which were so successful in treating linear algebras. For certain strings corresponding to ‘W’N gravity we show that the operator cohomology has a natural geometric model. This result suggests new directions for the study of ‘W’ geometry.

The W3 Algebra

Lectures on Algebra, Volume 1

Lectures on Algebra, Volume 1

This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author’s fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author’s lectures at Purdue University over the last few years.

Lectures on Algebra, Volume 1

Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes

Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes

The book presents variational methods combined with boundary integral equation techniques in application to a model of dynamic bending of plates with transverse shear deformation. The emphasis is on the rigorous mathematical investigation of the model, which covers a complete study of the well-posedness of a number of initial-boundary value problems, their reduction to time-dependent boundary integral equations by means of suitable potential representations, and the solution of the latter in Sobolev spaces.

Variational and Potential Methods for a Class of Linear Hyperbolic Evolutionary Processes

Applied Mathematics

Applied Mathematics

This is a textbook for a two-semester graduate course in Mathematical Methods in Physics. Most universities give this course, which is often taught jointly with the Engineering or Mathematics Departments. General topics include: group theory, linear equations, matrices, series, functions of complex variables, conformal mapping, special functions, and partial differential equations. Each chapter has numerous homework problems. The section on transforms includes those on Fourier and Laplace, as well as the modern topic of wavelets. The chapters on partial differential equations include: Laplace’s, Poisson’s, Helmholtz, diffusion, and wave equations. Problems are treated in one, two, and three dimensions.

Applied Mathematics

Extending the Linear Model with R

Extending the Linear Model with R

Linear models are central to the practice of statistics and form the foundation of a vast range of statistical methodologies. Julian J. Faraway’s critically acclaimed Linear Models with R examined regression and analysis of variance, demonstrated the different methods available, and showed in which situations each one applies.

Extending the Linear Model with R

The Jacobson Radical of Group Algebras

The Jacobson Radical of Group Algebras

Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results.

The Jacobson Radical of Group Algebras