Peter D Lax's Books

Linear Algebra and Its Applications

By: Peter D. Lax

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Linear Algebra and Its Applications

By: Peter D. Lax

This set features Linear Algebra and Its Applications, Second Edition (978-0-471-75156-4) Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems. Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces. Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including: The QR algorithm for finding the eigenvalues of a self-adjoint matrix The Householder algorithm for turning self-adjoint matrices into tridiagonal form The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices. Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals. and Functional Analysis (978-0-471-55604-6) both by Peter D. Lax.

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394

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John Wiley & Sons

Published Date

ISBN 10

0471751561

ISBN 13

9780471751564

Functional Analysis

By: Peter D. Lax

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Functional Analysis

By: Peter D. Lax

Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more. Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables. Includes an appendix on the Riesz representation theorem.

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608

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John Wiley & Sons

Published Date

ISBN 10

0471556041

ISBN 13

9780471556046

Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves

By: Peter D. Lax

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Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves

By: Peter D. Lax

This book deals with the mathematical side of the theory of shock waves. The author presents what is known about the existence and uniqueness of generalized solutions of the initial value problem subject to the entropy conditions. The subtle dissipation introduced by the entropy condition is investigated and the slow decay in signal strength it causes is shown.

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SIAM

Published Date

ISBN 10

0898711770

ISBN 13

9780898711776

Selected Papers II

By: Peter D Lax

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Selected Papers II

By: Peter D Lax

A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honors including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields. Two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious student of these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selecta will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own.

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620

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387229264

ISBN 13

9780387229263

Recent Mathematical Methods in Nonlinear Wave Propagation

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), held in Montecatini Terme, Italy, May 23-31, 1994

By: Guy Boillat,Constantin M. Dafermos,Peter D. Lax,Tai-Ping Liu

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Recent Mathematical Methods in Nonlinear Wave Propagation

Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.), held in Montecatini Terme, Italy, May 23-31, 1994

By: Guy Boillat,Constantin M. Dafermos,Peter D. Lax,Tai-Ping Liu

These lecture notes of the courses presented at the first CIME session 1994 by leading scientists present the state of the art in recent mathematical methods in Nonlinear Wave Propagation.

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149

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Springer

Published Date

ISBN 10

3540495657

ISBN 13

9783540495659

Recent Advances in Partial Differential Equations, Venice 1996

Proceedings of a Conference in Honor of the 70th Birthdays of Peter D. Lax and Louis Nirenberg : June 10-14, 1996, Venice, Italy

By: Peter D. Lax,L. Nirenberg,Renato Spigler

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Recent Advances in Partial Differential Equations, Venice 1996

Proceedings of a Conference in Honor of the 70th Birthdays of Peter D. Lax and Louis Nirenberg : June 10-14, 1996, Venice, Italy

By: Peter D. Lax,L. Nirenberg,Renato Spigler

Lax and Nirenberg are two of the most distinguished mathematicians of our times. Their work on partial differential equations (PDEs) over the last half-century has dramatically advanced the subject and has profoundly influenced the course of mathematics. A huge part of the development in PDEs during this period has either been through their work, motivated by it or achieved by their postdocs and students. A large number of mathematicians honored these two exceptional scientists in a week-long conference in Venice (June 1996) on the occasion of their 70th birthdays. This volume contains the proceedings of the conference, which focused on the modern theory of nonlinear PDEs and their applications. Among the topics treated are turbulence, kinetic models of a rarefied gas, vortex filaments, dispersive waves, singular limits and blow-up solutions, conservation laws, Hamiltonian systems and others. The conference served as a forum for the dissemination of new scientific ideas and discoveries and enhanced scientific communication by bringing together such a large number of scientists working in related fields. THe event allowed the international mathematics community to honor two of its outstanding members.

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407

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American Mathematical Soc.

Published Date

ISBN 10

0821806572

ISBN 13

9780821806579

Linear Algebra and Its Applications

By: Peter D. Lax

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Linear Algebra and Its Applications

By: Peter D. Lax

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261

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John Wiley & Sons

Published Date

ISBN 10

1118626923

ISBN 13

9781118626924

Functional Analysis

By: Peter D. Lax

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Functional Analysis

By: Peter D. Lax

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451

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John Wiley & Sons

Published Date

ISBN 10

1118626745

ISBN 13

9781118626740

The First 90 Days in Government

Critical Success Strategies for New Public Managers at All Levels

By: Peter H. Daly,Michael Watkins,Cate Reavis

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The First 90 Days in Government

Critical Success Strategies for New Public Managers at All Levels

By: Peter H. Daly,Michael Watkins,Cate Reavis

More than 250,000 public sector managers in the United States take on new positions each year and many more aspire to leadership. Each will confront special challenges—from higher public profiles to a greater number of stakeholders to volatile political environments—that will make their transitions even more challenging than in the business world. Now Michael Watkins, author of the bestselling book The First 90 Days, applies his proven leadership transition framework to the public sector. Watkins and coauthor Peter Daly address the crucial differences between the private and public sectors that go to the heart of how success and failure are defined, measured, and rewarded or penalized. This concise, practical book provides a roadmap that will help new government leaders at all levels accelerate their transitions by overcoming nine transition challenges, ranging from clarifying expectations to defining goals to building a team to managing personal stress. The authors also offer detailed strategies for avoiding major “transition traps.” Zeroing in on the challenges faced by new government leaders, The First 90 Days in Government is the indispensable guide for anyone seeking to lead and succeed in the public sector.

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284

Publisher

Harvard Business Press

Published Date

ISBN 10

142213105X

ISBN 13

9781422131053

Direct Methods in Control Problems

By: Peter Falb

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Direct Methods in Control Problems

By: Peter Falb

Various general techniques have been developed for control and systems problems, many of which involve indirect methods. Because these indirect methods are not always effective, alternative approaches using direct methods are of particular interest and relevance given the advances of computing in recent years. The focus of this book, unique in the literature, is on direct methods, which are concerned with finding actual solutions to problems in control and systems, often algorithmic in nature. Throughout the work, deterministic and stochastic problems are examined from a unified perspective and with considerable rigor. Emphasis is placed on the theoretical basis of the methods and their potential utility in a broad range of control and systems problems. The book is an excellent reference for graduate students, researchers, applied mathematicians, and control engineers and may be used as a textbook for a graduate course or seminar on direct methods in control.

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312

Publisher

Springer Nature

Published Date

ISBN 10

0817647236

ISBN 13

9780817647230

Airline Operations Control

By: Peter J. Bruce,Chris Mulholland

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Airline Operations Control

By: Peter J. Bruce,Chris Mulholland

This text is among the first to reveal the intricacies of an airline’s Operations Control Centre; especially the thought processes, information flows, and strategies taken to mitigate disruptions. Airline Operations Control provides a deep level of description, explanation and detail into the activities of a range of highly professional and expert staff managing the ‘sharp’ end of the airline. It aims to fill a void as little is understood about this area, and very little is written for practitioners in the airline business. The book offers a comprehensive look at the make-up of the Operations Centre, its component sections, and the processes that occur both in preparing for and executing the current day’s schedules. Several chapters provide real-life scenarios and demonstrate how Operations Centres manage evolving situations – what they need to take into account, and how they need to have Plan B and Plan C ready when things don’t go right. This book is designed to deliver knowledge gains to both new and experienced aviation industry practitioners with regards to vital operational aspects. Additionally, it also offers students of air transport management a readily accessible and real-world-perspective guide to a crucial function present within every airline.

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220

Publisher

Routledge

Published Date

ISBN 10

1351136283

ISBN 13

9781351136280

Calculus With Applications

By: Peter D. Lax,Maria Shea Terrell

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Calculus With Applications

By: Peter D. Lax,Maria Shea Terrell

Burstein, and Lax's Calculus with Applications and Computing offers meaningful explanations of the important theorems of single variable calculus. Written with students in mathematics, the physical sciences, and engineering in mind, and revised with their help, it shows that the themes of calculation, approximation, and modeling are central to mathematics and the main ideas of single variable calculus. This edition brings the innovation of the first edition to a new generation of students. New sections in this book use simple, elementary examples to show that when applying calculus concepts to approximations of functions, uniform convergence is more natural and easier to use than point-wise convergence. As in the original, this edition includes material that is essential for students in science and engineering, including an elementary introduction to complex numbers and complex-valued functions, applications of calculus to modeling vibrations and population dynamics, and an introduction to probability and information theory.

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509

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Springer Science & Business Media

Published Date

ISBN 10

1461479460

ISBN 13

9781461479468

Parametrized Homotopy Theory

By: J. Peter May,Johann Sigurdsson

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Parametrized Homotopy Theory

By: J. Peter May,Johann Sigurdsson

This book develops rigorous foundations for parametrized homotopy theory, which is the algebraic topology of spaces and spectra that are continuously parametrized by the points of a base space. It also begins the systematic study of parametrized homology and cohomology theories. The parametrized world provides the natural home for many classical notions and results, such as orientation theory, the Thom isomorphism, Atiyah and Poincare duality, transfer maps, the Adams and Wirthmuller isomorphisms, and the Serre and Eilenberg-Moore spectral sequences. But in addition to providing a clearer conceptual outlook on these classical notions, it also provides powerful methods to study new phenomena, such as twisted $K$-theory, and to make new constructions, such as iterated Thom spectra. Duality theory in the parametrized setting is particularly illuminating and comes in two flavors. One allows the construction and analysis of transfer maps, and a quite different one relates parametrized homology to parametrized cohomology. The latter is based formally on a new theory of duality in symmetric bicategories that is of considerable independent interest. The text brings together many recent developments in homotopy theory. It provides a highly structured theory of parametrized spectra, and it extends parametrized homotopy theory to the equivariant setting. The theory of topological model categories is given a more thorough treatment than is available in the literature. This is used, together with an interesting blend of classical methods, to resolve basic foundational problems that have no nonparametrized counterparts.

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456

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821839225

ISBN 13

9780821839225

Recent Advances in Nonlinear Partial Differential Equations and Applications

Conference in Honor of Peter D. Lax and Louis Nirenberg on Their 80th Birthdays, June 7-10, 2006, Universidad de Castilla-La Mancha at Palacio Lorenzana, Toledo, Spain

By: Luis López Bonilla

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Recent Advances in Nonlinear Partial Differential Equations and Applications

Conference in Honor of Peter D. Lax and Louis Nirenberg on Their 80th Birthdays, June 7-10, 2006, Universidad de Castilla-La Mancha at Palacio Lorenzana, Toledo, Spain

By: Luis López Bonilla

The articles of this book are written by leading experts in partial differential equations and their applications, who present overviews here of recent advances in this broad area of mathematics. The formation of shocks in fluids, modern numerical computation of turbulence, the breaking of the Einstein equations in a vacuum, the dynamics of defects in crystals, effects due to entropy in hyperbolic conservation laws, the Navier-Stokes and other limits of the Boltzmann equation, occupancy times for Brownian motion in a two dimensional wedge, and new methods of analyzing and solving integrable systems are some of this volume's subjects. The reader will find an exposition of important advances without a lot of technicalities and with an emphasis on the basic ideas of this field.

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250

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American Mathematical Soc.

Published Date

ISBN 10

0821842110

ISBN 13

9780821842119

The World Heroin Market

Can Supply Be Cut?

By: Letizia Paoli,Victoria A. Greenfield,Peter Reuter

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The World Heroin Market

Can Supply Be Cut?

By: Letizia Paoli,Victoria A. Greenfield,Peter Reuter

Heroin is universally considered the world's most harmful illegal drug. This is due not only to the damaging effects of the drug itself, but also to the spread of AIDS tied to its use. Burgeoning illegal mass consumption in the 1960s and 1970s has given rise to a global market for heroin and other opiates of nearly 16 million users. The production and trafficking of opiates have caused crime, disease, and social distress throughout the world, leading many nations to invest billions of dollars trying to suppress the industry. The failure of their efforts has become a central policy concern. Can the world heroin supply actually be cut, and with what consequences? The result of a five-year-long research project involving extensive fieldwork in six Asian countries, Colombia, and Turkey, this book is the first systematic analysis of the contemporary world heroin market, delving into its development and structure, its participants, and its socio-economic impact. It provides a sound and comprehensive empirical base for concluding that there is little opportunity to shrink the global supply of heroin in the long term, and explains why production is concentrated in a handful of countries--and is likely to remain that way. On the basis of these findings, the authors identify a key set of policy opportunities, largely local, and make suggestions for leveraging them. This book also offers new insights into market conditions in India, Tajikistan, and other countries that have been greatly harmed by the production and trafficking of illegal opiates. A deft integration of economics, sociology, history, and policy analysis, The World Heroin Market provides a rigorous and vital look into the complex--and resilient--global heroin trade.

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392

Publisher

Oxford University Press

Published Date

ISBN 10

0190207949

ISBN 13

9780190207946

Scattering Theory, Revised Edition

By: Peter D. Lax,Ralph S. Phillips

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Scattering Theory, Revised Edition

By: Peter D. Lax,Ralph S. Phillips

This revised edition of a classic book, which established scattering theory as an important and fruitful area of research, reflects the wealth of new results discovered in the intervening years. This new, revised edition should continue to inspire researchers to expand the application of the original ideas proposed by the authors.

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329

Publisher

Academic Press

Published Date

ISBN 10

0080873383

ISBN 13

9780080873381

Recent Advances in Partial Differential Equations, Venice 1996

Proceedings of a Conference in Honor of the 70th Birthdays of Peter D. Lax and Louis Nirenberg : June 10-14, 1996, Venice, Italy

By: Peter D. Lax,L. Nirenberg,Renato Spigler

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Recent Advances in Partial Differential Equations, Venice 1996

Proceedings of a Conference in Honor of the 70th Birthdays of Peter D. Lax and Louis Nirenberg : June 10-14, 1996, Venice, Italy

By: Peter D. Lax,L. Nirenberg,Renato Spigler

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407

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821806572

ISBN 13

9780821806579

Complex Proofs of Real Theorems

By: Peter D. Lax,Lawrence Zalcman

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Complex Proofs of Real Theorems

By: Peter D. Lax,Lawrence Zalcman

Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, ``The shortest and best way between two truths of the real domain often passes through the imaginary one.'' Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, Muntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane-Zelazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime number theorem. Four brief appendices provide all necessary background in complex analysis beyond the standard first year graduate course. Lovers of analysis and beautiful proofs will read and reread this slim volume with pleasure and profit.

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106

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821875590

ISBN 13

9780821875599

Flora of Turkey, Volume 4

By: Davis Peter Davis

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Flora of Turkey, Volume 4

By: Davis Peter Davis

Flora of Turkey, Volume 4

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Page Count

658

Publisher

Edinburgh University Press

Published Date

ISBN 10

1474466095

ISBN 13

9781474466097

The Rogers & Littleton Guide to America's Douchiest Colleges

By: H. L. Rogers,Peter Littleton

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The Rogers & Littleton Guide to America's Douchiest Colleges

By: H. L. Rogers,Peter Littleton

The question isn't whether or not one will be a douchebag in college--the more pertinent question for prospective students is, "What kind of douchebag do you aspire to be?" Here to help is the only college guide to rank and recommend schools based on their level of douchiness.

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145

Publisher

Chronicle Books

Published Date

ISBN 10

0811878872

ISBN 13

9780811878876

Scattering Theory

Pure and Applied Mathematics, Vol. 26

By: Peter D. Lax,Ralph S. Phillips

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Scattering Theory

Pure and Applied Mathematics, Vol. 26

By: Peter D. Lax,Ralph S. Phillips

Scattering Theory describes classical scattering theory in contrast to quantum mechanical scattering theory. The book discusses the formulation of the scattering theory in terms of the representation theory. The text also explains the relation between the behavior of the solution of the perturbed problem at small distances for large positive times and the analytic continuation of the scattering matrix. To prove the representation theorem, the text cites the methods used by Masani and Robertson in their work dealing with stationary stochastic processes. The book also applies the translation representation theory to a wave equation to obtain a comparison of the asymptotic properties of the free space solution with those of the solution in an exterior domain. The text discusses the solution of the wave equation in an exterior domain by fitting this problem into the abstract framework to get a verification of the hypotheses in some other theorems. The general theory of scattering can be applied to symmetric hyperbolic systems in which all sound speeds are different from zero, as well as to the acoustic equation which has a potential that can cause an energy form to become indefinite. The book is suitable for proponents of analytical mathematics, particle physics, and quantum physics.

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289

Publisher

Elsevier

Published Date

ISBN 10

1483223639

ISBN 13

9781483223636

Flora of Turkey, Volume 3

By: Davis Peter Davis

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Flora of Turkey, Volume 3

By: Davis Peter Davis

Flora of Turkey, Volume 3

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628

Publisher

Edinburgh University Press

Published Date

ISBN 10

1474466087

ISBN 13

9781474466080

Hyperbolic Partial Differential Equations

By: Peter D. Lax

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Hyperbolic Partial Differential Equations

By: Peter D. Lax

The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. -- Back cover.

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234

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American Mathematical Soc.

Published Date

ISBN 10

0821835769

ISBN 13

9780821835760

Differential Equations: La Pietra 1996

La Pietra 1996 : Conference on Differential Equations Marking the 70th Birthdays of Peter Lax and Louis Nirenberg, July 3-7, 1996, Villa La Pietra, Florence, Italy

By: Peter D. Lax,S. R. S. Varadhan

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Differential Equations: La Pietra 1996

La Pietra 1996 : Conference on Differential Equations Marking the 70th Birthdays of Peter Lax and Louis Nirenberg, July 3-7, 1996, Villa La Pietra, Florence, Italy

By: Peter D. Lax,S. R. S. Varadhan

The 11 papers discuss analysis, partial differential equations, applied mathematics, and scientific computing, focusing on the work of Peter Lax and Louis Nirenberg, whose 70th birthdays occasioned the conference. Specific topics include viscosity solutions for the porous medium equation, holomorphic curves in contact dynamics, and minimizing volume among Lagrangian submanifolds. No index. Member prices are $31 for institutions and $23 or individuals. Annotation copyrighted by Book News, Inc., Portland, OR.

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233

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821806106

ISBN 13

9780821806104

Flora of Turkey, Volume 1

By: Peter Davis

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Flora of Turkey, Volume 1

By: Peter Davis

Flora of Turkey, Volume 1

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581

Publisher

Edinburgh University Press

Published Date

ISBN 10

1474466052

ISBN 13

9781474466059

Preliminaries to Linguistic Phonetics

By: Peter Ladefoged

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Preliminaries to Linguistic Phonetics

By: Peter Ladefoged

This book is about some of the phonetic events that occur in the languages of the world. The data described consist mainly of contrasts observable at the systematic phonetic level in a wide variety of languages.

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129

Publisher

University of Chicago Press

Published Date

ISBN 10

022622189X

ISBN 13

9780226221892

Teaching American English Pronunciation - Oxford Handbooks for Language Teachers

By: Susan Ehrlich,Peter Avery

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Teaching American English Pronunciation - Oxford Handbooks for Language Teachers

By: Susan Ehrlich,Peter Avery

As an ESL teacher, have you looked at the phonetics textbooks on the market and decided that they don't directly address your needs? Unlike pronunciation books aimed at students of linguistics or at learners of English, Teaching American English Pronunciation has been written specifically for ESL teachers. It doesn't only give academic descriptions, but also helps you to improve your students' pronunciation effectively.

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266

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Oxford University Press

Published Date

ISBN 10

0194342689

ISBN 13

9780194342681

Applications of Lie Groups to Differential Equations

By: Peter J. Olver

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Applications of Lie Groups to Differential Equations

By: Peter J. Olver

This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

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524

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Springer Science & Business Media

Published Date

ISBN 10

1468402749

ISBN 13

9781468402742

Adaptive Numerical Solution of PDEs

By: Peter Deuflhard,Martin Weiser

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Adaptive Numerical Solution of PDEs

By: Peter Deuflhard,Martin Weiser

This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence. Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted. The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.

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