Bücher der Reihe Modern Birkhauser Classics

The author introduces the four representations of a scalar linear system and establishes the major results of a similar theory for multivariable systems appearing in a succeeding volume (Part II: Multivariable Linear Systems and Projective Algebraic Geometry).

Over the past several decades, we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous materials. This work has implications for many physical problems involving optimal design, composite materials, and coherent phase transitions.

"An introduction to the ideas of algebraic geometry in the motivated context of system theory." This describes this two volume work which has been specifically written to serve the needs of researchers and students of systems, control, and applied mathematics. Without sacrificing mathematical rigor, the author makes the basic ideas of algebraic geometry accessible to engineers and applied scientists. The emphasis is on constructive methods and clarity rather than on abstraction. While familiarity with Part I is helpful, it is not essential, since a considerable amount of relevant material is included here.Part I, Scalar Linear Systems and Affine Algebraic Geometry, contains a clear presentation, with an applied flavor , of the core ideas in the algebra-geometric treatment of scalar linear system theory. Part II extends the theory to multivariable systems. After delineating limitations of the scalar theory through carefully chosen examples, the author introduces seven representations of a multivariable linear system and establishes the major results of the underlying theory. Of key importance is a clear, detailed analysis of the structure of the space of linear systems including the full set of equations defining the space. Key topics also covered are the Geometric Quotient Theorem and a highly geometric analysis of both state and output feedback. Prerequisites are the basics of linear algebra, some simple topological notions, the elementary properties of groups, rings, and fields, and a basic course in linear systems. Exercises, which are an integral part of the exposition throughout, combined with an index and extensive bibliography of related literature make this a valuable classroom tool or good self-study resource. The present, softcover reprint is designed to make this classic textbook available to a wider audience."The exposition is extremely clear. In order to motivate the general theory, the author presents a number of examples of two or three input-, two-output systems in detail. I highly recommend this excellent book to all those interested in the interplay between control theory and algebraic geometry." ¿Publicationes Mathematicae, Debrecen"This book is the multivariable counterpart of Methods of Algebraic Geometry in Control Theory, Part I¿. In the first volume the simpler single-input¿single-output time-invariant linear systems were considered and the corresponding simpler affine algebraic geometry was used as the required prerequisite. Obviously, multivariable systems are more difficult and consequently the algebraic results are deeper and less transparent, but essential in the understanding of linear control theory¿. Each chapter contains illustrative examples throughout and terminates with some exercises for further study." ¿Mathematical Reviews

This textbook presents the basic concepts and methods of fluid mechanics, including Lagrangian and Eulerian descriptions, tensors of stresses and strains, continuity, momentum, energy, thermodynamics laws, and similarity theory.  The models and their solutions are presented within a context of the mechanics of multiphase media.  The treatment fully utilizes the computer algebra and software system Mathematica® to both develop concepts and help the reader to master modern methods of solving problems in fluid mechanics.Topics and features:Glossary of over thirty Mathematica® computer programsExtensive, self-contained appendix of Mathematica® functions and their useChapter coverage of mechanics of multiphase heterogeneous mediaDetailed coverage of theory of shock waves in gas dynamicsThorough discussion of aerohydrodynamics of ideal and viscous fluidsand gasesComplete worked examples with detailed solutionsProblem-solving approachFoundations of Fluid Mechanics with Applications is a complete and accessible text or reference for graduates and professionals in mechanics, applied mathematics, physical sciences, materials science, and engineering.  It is an essential resource for the study and use of modern solution methods for problems in fluid mechanics and the underlying mathematical models.  The present, softcover reprint is designed to make this classic textbook available to a wider audience.

This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations of logic programming. It presents applications and themes of computer science research such as resolution, automated deduction, and logic programming in a rigorous but readable way.

The second of two volumes, this text compiles survey articles borne of a landmark 1999 Tel Aviv conference dedicated to probing the importance, the methods, the past and future of mathematics as well as the connection between mathematics and related areas.

Originally published in 1985, this classic textbook is an English translation of Einfuhrung in die kommutative Algebra und algebraische Geometrie. It presents areas of commutative algebra that are best understood together.

In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus.

This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. Part two, which is Chapter 2, characterizes the development of cardinal arith metic in the seventies, which was led by Galvin, Hajnal, and Silver.

The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. The Self-Avoiding Walk provides the first unified account of the known rigorous results for the self-avoiding walk, with particular emphasis on its critical behavior.

Originally published in 1999, Wavelets Made Easy offers a lucid and concise explanation of mathematical wavelets. The third part explains the Fourier transform and then demonstrates how to apply basic Fourier analysis to designing and analyzing mathematical wavelets.

This book is a publication in Swiss Seminars, a subseries of Progress in Mathematics. It is an expanded version of the notes from a seminar on intersection cohomology theory, which met at the University of Bern, Switzerland, in the spring of 1983.

Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods.

First published in 2003, this is an accessible and thorough treatment of implicit and inverse function theorems and their applications. The book documents and places in context a substantial body of concepts that have played an role in modern mathematics.

Winner of the 1983 National Book Award, The Mathematical Experience conveyed the power and beauty of its topic to a broad audience. The study version added exercises and other classroom aids. This softcover edition includes new epilogues by the original authors.

1 Aim and General Description of the Anthology The purpose of this anthology is to introduce the English speaking public to the wide spectrum of texts authored predominently by physicists portraying the ac tual and perceived role of physics in the Nazi state.

The book treats four fundamental problems: the number of primes below a given limit, the approximate number of primes, the recognition of primes and the factorization of large numbers.

To this reviewer's knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming....

This book is a study of how a particular vision of the unity of mathematics, often called geometric function theory, was created in the 19th century. The central focus is on the convergence of three mathematical topics: the hypergeometric and related linear differential equations, group theory, and on-Euclidean geometry.

Schroedinger Equations and Diffusion Theory addresses the question "What is the Schroedinger equation?" in terms of diffusion processes, and shows that the Schroedinger equation and diffusion equations in duality are equivalent.

The advent of H -control was a truly remarkable innovation in multivariable theory. It enhanced the application by deepening the theory mathematically and logically, not by weakening it as was done by the reformers of modern control theory in the early 1970s.

Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate.

This book is devoted to one of the fastest developing fields in modern control theory - the so-called H-infinity optimal control theory. The book can be used for a second or third year graduate level course in the subject, and researchers working in the area will find the book useful as a standard reference.

The first of two volumes, this text compiles survey articles borne of a landmark 1999 Tel Aviv conference dedicated to probing the importance, the methods, the past and future of mathematics as well as the connection between mathematics and related areas.

- Acta Scientiarum MathematicarumAvramov lecture: "... - Zentralblatt MATHValla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory."

A compact, moderately general book which encompasses many fluid models of current interest...The book is written very clearly and contains a large number of exercises and their solutions.

The second in a series of three volumes that survey the theory of theta functions, this volume emphasizes the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations.