Book Description

This comprehensive book presents a rigorous and state-of-the-art treatment of variational inequalities and complementarity problems in finite dimensions. This class of mathematical programming problems provides a powerful framework for the unified analysis and development of efficient solution algorithms for a wide range of equilibrium problems in economics, engineering, finance, and applied sciences. New research material and recent results, not otherwise easily accessible, are presented in a self-contained and consistent manner. The book is published in two volumes, with the first volume concentrating on the basic theory and the second on iterative algorithms. Both volumes contain abundant exercises and feature extensive bibliographies. Written with a wide range of readers in mind, including graduate students and researchers in applied mathematics, optimization, and operations research as well as computational economists and engineers, this book will be an enduring reference on the subject and provide the foundation for its sustained growth. ... Read more

Reviews (2)

Piece of Junk or lasting book?
This book contains a lot of information, but a sampling I took revealed that a lot of it is false. Does that say anything about the book? You decide.

koyaanisqatsi
This comprehensive book presents a rigorous and state-of-the-art treatment of variational inequalities and complementarity problems in finite dimensions. This class of mathematical programming problems provides a powerful framework for the unified analysis and development of efficient solution algorithms for a wide range of equilibrium problems in economics, engineering, finance, and applied sciences. New research material and recent results, not otherwise easily accessible, are presented in a self-contained and consistent manner. The book is published in two volumes, with the first volume concentrating on the basic theory and the second on iterative algorithms. Both volumes contain abundant exercises and feature extensive bibliographies. Written with a wide range of readers in mind, including graduate students and researchers in applied mathematics, optimization, and operations research as well as computational economists and engineers, this book will be an enduring reference on the subject and provide the foundation for its sustained growth.

if you believe this, i have a bridge to sell you. ... Read more

Book Description

This book is devoted to geometric methods in the theory of differential equations with quadratic right-hand sides (Riccati-type equations), which are closely related to the calculus of variations and optimal control theory. Connections of the calculus of variations and the Riccati equation with the geometry of Lagrange-Grassmann manifolds and classical Cartan-Siegel homogeneity domains in a space of several complex variables are considered. In the study of the minimization problem for a multiple integral, a quadratic partial differential equation that is an analogue of the Riccati equation in the calculus of varatiations is studied. This book is based on lectures given by the author ower a period of several years in the Department of Mechanics and Mathematics of Moscow State University. The book is addressed to undergraduate and graduate students, scientific researchers and all specialists interested in the problems of geometry, the calculus of variations, and differential equations. ... Read more

Book Description

The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained. Audience: Advanced students and researchers. ... Read more

Book Description

This book explores the standard problem-solving techniques of multivariable mathematics — integrating vector algebra ideas with multivariable calculus and differential equations. Provides many routine, computational exercises illuminating both theory and practice.Offers flexibility in coverage — topics can be covered in a variety of orders, and subsections (which are presented in order of decreasing importance) can be omitted if desired. Provides proofs and includes the definitions and statements of theorems to show how the subject matter can be organized around a few central ideas. Includes new sections on: flow lines and flows; centroids and moments; arc-length and curvature; improper integrals; quadratic surfaces; infinite series—with application to differential equations; and numerical methods. Presents refined method for solving linear systems using exponential matrices. ... Read more

Reviews (3)

Sometimes it takes a second read, or third, or fourth....
I liked this book because it is written at a slightly more sophisticated level than most lower division math books. Admittedly, it is difficult to understand some of the proofs and examples on the first read. It just takes some time, after a second or third read, before the text begins to make sense. Then you'll realize the examples are presented quite well and you have everything you need to solve the problem sets. And you know you've learned the material well if you understand the text and you can do the problems, which are oriented more to make you think than compute.

A coherent view of multivariable mathematics
For those with sufficient preparation (say, a good BC Calculus course and an enjoyment of mathematics), this text offers a very fine presentation of multivariable calculus. Certainly, some of the material is challenging and some of the exercises require insight, but after finishing this book, or substantial portions of it, you will have a coherent view of multivariable calculus, as well as some appreciation of significant, but elementary, applications of linear algebra. I particularly recommend this text to those who have learned multivariable calculus in one of the "fat" three semester calculus texts, and feel that, although they could solve all the problems, they don't really have any sense of what the subject is all about. This text has a distinguished history: it is the latest incarnation of a vector calculus text (Calculus of Vector Functions) first published in 1962 by Crowell and Williamson. Spivak described that text (and I hope Dover someday reissues the third edition) as "one of the first, and still one of the nicest, treatments of advanced calculus using linear algebra."

Naughty Book
This book was used for a two-course introductory math series at Stanford in 1996-7 and 1997-8. The book drew so many complaints that it was abandoned after two years. Personally, I found it difficult to understand many of the formal proofs and explanations provided. Many shortcuts were taken in solving the example problems which made them difficult to follow. The answers to problems in the back of the book were frequently incorrect. This is a poorly written book for all students except those extremely insightful in mathematics. ... Read more

Book Description

Based on a third-year course for French students of physics, this book is a graduate text in functional analysis emphasizing applications to physics. It introduces Lebesgue integration, Fourier and Laplace transforms, Hilbert space theory, theory of distribution a la Laurent Schwartz, linear operators, and spectral theory. It contains numerous examples and completely worked out exercises. ... Read more

Book Description

Reflecting the significant contributions of Russian mathematicians to the field, this book contains a selection of papers on tensor and vector analysis. It is divided into three parts, covering Hamiltonian systems, Riemannian geometry and calculus of variations, and topology. The range of applications of these topics is very broad, as many modern geometrical problems recur across a wide range of fields, including mechanics and physics as well as mathematics.
Many of the approaches to problems presented in this volume will be novel to the Western reader, although questions are of global interest. The main achievements of the Russian school are placed in the context of the development of each individual subject. ... Read more

Reviews (1)

Gives Russian mathematicians their due
Tensor and vector analysis in a Euclidean space gives very elegant and powerful tools for the study of physical systems. Most of the papers in this book will be of interest to physicists. The emphasis is not so much on pure mathematics, but on studying real problems in physics. Quite possibly, engineers dealing in control systems theory and complex dynamical systems may also benefit from some papers.

The book is useful at a graduate and postgraduate level, in bringing forth ideas that go well beyond the standard graduate texts on this subject.

It also helps gives Russian mathematicians their proper due outside Russia. During the Cold War, their contributions were often unknown outside the Soviet Bloc. ... Read more

Book Description

The word holor is a term coined by the authors to describe a mathematical entity that is made up of one or more independent quantities, and includes complex numbers, scalars, vectors, matrices, tensors, quaternions, and other hypernumbers. Holors, thus defined have been known for centuries, but each has been developed more or less independently, accompanied by separate nomenclature and theory. This book demonstrates how these complicated subjects can be made simple by using a single notation that applies to all holors, both tensor and nontensor. The authors consider all possible types of holors and develop holor algebra and holor calculus in the most general sense. Thus the reader will learn to develop a new holor that fits the application, rather than forcing an application onto a holor representation that is known but that does not perfectly describe the application. The discussion includes nontensors having no transformation and holors that transform in more complicated ways than allowed with ordinary tensors. This opens up the possibility to devise a holor for a new physical application, without being limited to a few conventional types of holor. This book should establish a method by which students and teachers can learn vector and tensor analysis via a uniform treatment. Graduate students and professionals in engineering, physics. applied mathematics, chemistry, biology, psychology, and other analytical sciences should find this to be a useful and innovative work. ... Read more

Reviews (2)

illuminates the field
While the notation at first seems burdensome, it resolves to be one of the elegant strengths in this groundbreaking but underappreciated text. If you've experienced tensors, you will wish you'd started here. While the text is of necessity dense, and rife with formulas, notation, and peculiarly named categories of holors, it is obviously not meant for anyone without a great deal of math already under their belt. It clarifies previously ambiguous distinctions under tensor theory, and leads to many "aha" moments. Rigorous and comprehensive. The only book on the subject, literally.

Tensor theory for physics or math lovers
A must for every SR/GR fan. Worth the price. This book is very well organized and easy for someone to understand after a decent intorduction to vector calculus. It includes a well writen historical perspective, a detailed intorduction to tensor nomenclature, an above average treatment of basic tensor theory (transformations, direvitaves, and even integrals), and a strong introduction to non-metric (linearly-connected) spaces. ... Read more

Book Description

Once again keeping a keen ear to the needs of the evolving calculus community, Stewart created this text at the suggestion and with the collaboration of professors in the mathematics department at Texas A&M University. With an early introduction to vectors and vector functions, the approach is ideal for engineering students who use vectors early in their curriculum. Stewart begins by introducing vectors in Chapter 1, along with their basic operations, such as addition, scalar multiplication, and dot product. The definition of vector functions and parametric curves is given at the end of Chapter 1 using a two-dimensional trajectory of a projectile as motivation. Limits, derivatives, and integrals of vector functions are interwoven throughout the subsequent chapters.As with the other texts in his Calculus series, in Early Vectors Stewart makes us of heuristic examples to reveal calculus to students. His examples stand out because they are not just models for problem solving or a means of demonstrating techniques - they also encourage students to develop an analytic view of the subject. This heuristic or discovery approach in the examples give students an intuitive feeling for analysis.In the Preliminary Edition, Stewart incorporates a focus on problem solving; meticulously attends to accuracy; patiently explains the concepts and examples; and includes the same carefully graded problems that make his other texts work so well for a wide range of students. ... Read more

Book Description

Linear Vector Spaces and Cartesian Tensors is primarily concerned with the theory of finite dimensional Euclidian spaces. It makes a careful distinction between real and complex spaces, with an emphasis on real spaces, and focuses on those elements of the theory that are especially important in applications to continuum mechanics. The geometric content of the theory and the distinction between matrices and tensors are emphasized, and absolute- and component-notation are both employed. While the mathematics is rigorous, the style is casual.

Chapter 1 deals with the basic notion of a linear vector space; many examples of such spaces are given, including infinite-dimensional ones. The idea of a linear transformation of a vector space into itself is introduced and explored in Chapter 2. Chapter 3 deals with linear transformations on finite dimensional real Euclidean spaces (i.e., Cartesian tensors), focusing on symmetric tensors, orthogonal tensors, and the interaction of both in the kinetically important polar decomposition theorem. Chapter 4 exploits the ideas introduced in the first three chapters in order to construct the theory of tensors of rank four, which are important in continuum mechanics. Finally, Chapter 5 concentrates on applications of the earlier material to the kinematics of continua, to the notion of isotropic materials, to the concept of scalar invariant functions of tensors, and to linear dynamical systems. Exercises and problems of varying degrees of difficulty are included at the end of each chapter. Two appendices further enhance the text: the first is a short list of mathematical results that students should already be familiar with, and the second contains worked out solutions to almost all of the problems.

Offering many unusual examples and applications, Linear Vector Spaces and Cartesian Tensors serves as an excellent text for advanced undergraduate or first year graduate courses in engineering mathematics and mechanics. Its clear writing style also makes this work useful as a self-study guide. ... Read more

Reviews (1)

Excellent for Sophmores in Physics
Although the book has a flavor towards continuum mechanics, the necessary concepts of linearity needed for the working physicist are presented in an elegant manner. The problems contribute a major understanding and expansion of the topics presented in the chapter. This book in conjuction with Finite-dimensional vector spaces by Halmos will present the reader the view from the top necessary to continue with topics such as Hilbert Spaces and Quantum Mechanics. I highly recommend this book. ... Read more

Book Description

Over the past decade, wavelets and frames have emerged asincreasingly powerful tools of analysis on $n$-dimensionEuclidean space. Both wavelets and frames were studied initiallyby using classical Fourier analysis. However, in recent yearsmore abstract tools have been introduced, for example, fromoperator theory, abstract harmonic analysis, von Neumannalgebras, etc.

The editors of this volume organized a Special Session on thefunctional and harmonic analysis of wavelets at the San Antonio(TX) Joint Mathematics Meetings. The goal of the session was tofocus research attention on these newly-introduced tools and toshare the organizers' view that this modern application holdsthe promise of providing some deeper understanding andfascinating new structures in pure functional analysis. Thisvolume presents the fruitful results of the lively discussionsthat took place at the conference. ... Read more

Book Description

Book Description

Progress in mathematics is based on a thorough understanding of the mathematical objects under consideration, and yet many textbooks and monographs proceed to discuss general statements and assume that the reader can and will provide the mathematical infrastructure of examples and counterexamples. This book makes a deliberate effort to correct this situation: it is a collection of examples. The following table of contents describes its breadth and reveals the underlying motivation--differential geometry--in its many facets: Riemannian, symplectic, K*adahler, hyperK*adahler, as well as complex and quaternionic. ... Read more

Reviews (2)

Frustrating
I have never been so frustrated by a textbook as I have been by this one. It fleshes out the most basic outlines of the topic, then gives a handful of examples (which tend to be unhelpful and riddled with errors) before moving on to the next topic. The number of typographical errors is astounding and makes getting through the examples an exercise in futility. The exercises are mind-numbing in their computational complexity without really challenging the student's understanding of the material. If you're in a class where use of Mathematica is discourage (like I was), beware!

Unfinished
This book is small, expensive and relatively bad. While there are plenty of errors to be annoyed by (everything from incorrect solutions to syntax errors in the mathematics), my main qualm with the book comes from the poorly motivated text. While the underlying structure is suitable, the overall exposition is crap. The text reads like lecture notes, and I don't think it is quite up to the standard of a textbook. The exercises also need some work; there should be more exercises that are more interesting. As a mathematics major I am not all too impressed with it, but a student of an applied science may like it more. Although in this form I don't think it is suitable for any audience.

If you want to learn Vector Calculus, I would suggest the multivariable/vector analysis sections of Stewart's Calculus text. That is where I learned the material. Vector Calculus by Marsden also seems promising, but I have not read it all yet. ... Read more

Book Description

By looking at the processes of change over time - by carrying out longitudinal studies - researchers answer questions about learning, development, educational growth, social change and medical outcomes.

However, longitudinal research has many faces and no one approach answers all the questions about changes, event occurrences and stability over time. Longitudinal Data Analysis covers all the main approaches (such as analysis of variance and log-linear approaches) as well as newer approaches (such as structural equation modelling and multilevel modelling) to enable the reader to get a thorough understanding of the approach and make appropriate decisions about which technique can be applied to the research problem. Each method is accessibly presented with the following features;

- Conceptual explanations are used to keep complex technical and statistical terms to a minimum.

- Examples are used for each approach to show how the various models and methods can be applied to particular classes of problems.

- Issues of design, measurement and significance are intregrated into the presentation of each method.

- A standard notation is used throughout.

Book Description

Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Rad. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The third edition gives a survey on new developments in the field. References have been updated and a small number of mistakes have been rectified. ... Read more

Book Description

This systematic and self-contained treatment of the theory of three-dimensional spinors and their applications fills an important gap in the literature. Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, spinors are developed in this work for three-dimensional spaces in a language analogous to the spinor formalism used in relativistic spacetime.

Unique features of this work:

* Systematic, coherent exposition throughout

* Introductory treatment of spinors, requiring no previous knowledge of spinors or advanced knowledge of Lie groups

* Three chapters devoted to the definition, properties and applications of spin-weighted functions, with all background given.

* Detailed treatment of spin-weighted spherical harmonics, properties and many applications, with examples from electrodynamics, quantum mechanics, and relativity

* Wide range of topics, including the algebraic classification of spinors, conformal rescalings, connections with torsion and Cartan's structural equations in spinor form, spin weight, spin-weighted operators and the geometrical meaning of the Ricci rotation coefficients

* Bibliography and index

This work will serve graduate students and researchers in mathematics and mathematical and theoretical physics; it is suitable as a course or seminar text, as a reference text, and may also be used for self-study. ... Read more