Special Functions

Book Description

Special functions, which include the trigonometric functions, have been used for centuries. Their role in the solution of differential equations was exploited by Newton and Leibniz, and the subject of special functions has been in continuous development ever since. In just the past thirty years several new special functions and applications have been discovered. This treatise presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series. It includes both important historical results and recent developments and shows how these arise from several areas of mathematics and mathematical physics. Particular emphasis is placed on formulas that can be used in computation. The book begins with a thorough treatment of the gamma and beta functions that are essential to understanding hypergeometric functions. Later chapters discuss Bessel functions, orthogonal polynomials and transformations, the Selberg integral and its applications, spherical harmonics, q-series, partitions, and Bailey chains. This clear, authoritative work will be a lasting reference for students and researchers in number theory, algebra, combinatorics, differential equations, applied mathematics, mathematical computing, and mathematical physics.

Customer Reviews:

A Modern Whittaker and Watson, Buy It.......2004-10-24

This book is great. It is the best overview I have ever seen of the primary special functions, as seen from a modern viewpoint. Buy it and you will spend many happy hours reading the theorems it contains, and doing the excercizes at the end of each chapter.

A book comes close to " A course of modern analysis ".......2001-08-07

Though this book cannot be compared to Whittaker and Watson's classic book. It comes quite close to it. I just want to comment on the the area covers are too concentrated and the rigorous manner which is the hall mark of " Modern Analysis " is lacking. Anyway, this book deserves 5 stars.

clean and concise.......2001-02-11

It has a very good style of writing for the nature of mathematics. It is clean, no unnecessary explanation or examples. In a way, one can feel something similar to Axler's. It is an excellent reference book. One should keep this book just as Axler's Linear Algebra Done Right, Numerical Recipe, DE Knuth's Art of Programming.

clean and concise.......2001-02-11

Design Theory (Encyclopedia of Mathematics and its Applications)

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Design Theory (Encyclopedia of Mathematics and its Applications)
Thomas Beth , D. Jungnickel , and H. Lenz
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521772311

Book Description

This volume concludes the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to reflect this. In particular, the growing importance of discrete mathematics to many parts of engineering and science have made designs a useful tool for applications, a fact that has been acknowledged here with the inclusion of an additional chapter on applications. The volume is suitable for advanced courses and for reference use, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. Features include exercises and an extensive, updated bibliography of well over 1800 citations.

Control Theory of Partial Differential Equations (Lecture Notes in Pure and Applied Mathematics)

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Control Theory of Partial Differential Equations (Lecture Notes in Pure and Applied Mathematics)

Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Paperback

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Book Description

The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids and elastic structures, and fluid dynamics and the new challenges that they present. Other control theoretic problems include parabolic systems, dynamical Lame systems, linear and nonlinear hyperbolic equations, and pseudo-differential operators on a manifold. This is a valuable tool authored by international specialists in the field.

Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)

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An Excellent Book on Model Order Reduction

Approximation of Large-Scale Dynamical Systems (Advances in Design and Control) (Advances in Design and Control)
Athanasios C. Antoulas
Manufacturer: Society for Industrial and Applied Mathematic
ProductGroup: Book
Binding: Hardcover

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Dynamic Programming and Optimal Control (2 Vol Set)

ASIN: 0898715296
Release Date: 2005-07-13

Product Description

Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However, in the presence of limited computational, accuracy, and storage capabilities, model reduction (system approximation) is often necessary. Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting trade-offs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications. This book is for anyone interested in model reduction. Graduate students and researchers in the fields of system and control theory, numerical analysis, and the theory of partial differential equations/computational fluid dynamics will find it an excellent reference. Contents List of Figures; Foreword; Preface; How to Use this Book; Part I: Introduction. Chapter 1: Introduction; Chapter 2: Motivating Examples; Part II: Preliminaries. Chapter 3: Tools from Matrix Theory; Chapter 4: Linear Dynamical Systems: Part 1; Chapter 5: Linear Dynamical Systems: Part 2; Chapter 6: Sylvester and Lyapunov equations; Part III: SVD-based Approximation Methods. Chapter 7: Balancing and balanced approximations; Chapter 8: Hankel-norm Approximation; Chapter 9: Special topics in SVD-based approximation methods; Part IV: Krylov-based Approximation Methods; Chapter 10: Eigenvalue Computations; Chapter 11: Model Reduction Using Krylov Methods; Part V: SVDKrylov Methods and Case Studies. Chapter 12: SVDKrylov Methods; Chapter 13: Case Studies; Chapter 14: Epilogue; Chapter 15: Problems; Bibliography; Index.

Customer Reviews:

An Excellent Book on Model Order Reduction.......2006-05-10

Dr. Athanasios C. Antoulas is one of the world's leading authorities on model order reduction. In this book he clearly differentiated Singular Value Decomposition (SVD) methods and Krylov subspace projection methods and their explanation in part III and IV is excellent. The fist two chapter of introduction and preliminaries give you sufficient background to understand Part III and IV. The book does require some familiarity with numerical linear algebra and may be difficult for a new comer in the area to follow, however the way it is written it can be used both by engineers and scientist. A must-have book for any one working on model order reduction or dealing with large scale dynamical system. By reading this book I clearly understood the concept of reachability and observability and how it is applied to better understand a dynamical system. Overall a book with excellent source of knowledge, both as text and reference book. My recommendation definitely 5 stars.

Representations and Invariants of the Classical Groups (Encyclopedia of Mathematics and its Applications)

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typical math text
Comprehensive, well organized, very applicable

Representations and Invariants of the Classical Groups (Encyclopedia of Mathematics and its Applications)
Roe Goodman , and Nolan R. Wallach
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521663482

Book Description

More than half a century has passed since Weyl's "The Classical Groups" gave a unified picture of invariant theory that has retained its importance in mathematics and physics to the present day. This book presents an updated version of this theory together with many of the important recent developments. As a text for beginners, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. It makes abundant use of examples and exercises to explain concepts such as root systems, Weyl groups and highest weight theory. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.

Customer Reviews:

typical math text.......2004-07-01

Sadly, this book does not live up to its
reputation and can only be used by those
already having a working knowledege of
the subject. On top of that, the printing
is atrocious in places - unacceptable for
an expensive item.

Comprehensive, well organized, very applicable.......2001-07-12

The book may be considered an update of Weyl's classic from 1946 "The classical groups, their invariants and representations". Naturally the theory has developed immensly since then and a new comprehensive presentation has been urgently overdue. Goodman and Wallach are not only among the most qualified to write this next "classic" on the subject, they also put a phantastic effort into making it comprehensive, readable, and pleasant to use. I found it easy to find needed results and concrete formulae on decompositions of tensors and harmonics, duailty groups and centralizer algebras, mulitiplicity formulae, branching laws, etc.. The results are systematically organized - almost in an "encyclopedial" style. The book also contains rather modern results, such as, for example, new proofs of the Kostant Rallis Theorem or the relations between invariant theory and the Jones knot polynomial.

Book Description

How can one be assured that computer codes that solve differential equations are correct? Standard practice using benchmark testing no longer provides full coverage because today's production codes solve more complex equations using more powerful algorithms. By verifying the order-of-accuracy of the numerical algorithm implemented in the code, one can detect most any coding mistake that would prevent correct solutions from being computed. Verification of Computer Codes in Computational Science and Engineering sets forth a powerful alternative called OVMSP: Order-Verification via the Manufactured Solution Procedure. This procedure has two primary components: using the Method of Manufactured Exact Solutions to create analytic solutions to the fully-general differential equations solved by the code and using grid convergence studies to confirm the order-of-accuracy. The authors present a step-by-step procedural guide to OVMSP implementation and demonstrate its effectiveness. Properly implemented, OVMSP offers an exciting opportunity to identify virtually all coding 'bugs' that prevent correct solution of the governing partial differential equations. Verification of Computer Codes in Computational Science and Engineering shows you how this can be done. The treatment is clear, concise, and suitable both for developers of production quality simulation software and as a reference for computational science and engineering professionals.

Numerical Continuation Methods: An Introduction (Springer Series in Computational Mathematics, Vol 13)

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Numerical Continuation Methods: An Introduction (Springer Series in Computational Mathematics, Vol 13)
Eugene L. Allgower , and Kurt Georg
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Banach Algebras and the General Theory of *-Algebras Volume 2

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Banach Algebras and the General Theory of *-Algebras Volume 2
Theodore W. Palmer
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521366380

Book Description

This second volume of a two-volume set provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. The author emphasizes the roles of *-algebra structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. Proofs are presented in complete detail at a level accessible to graduate students. The books contain a wealth of historical comments, background material, examples, and an extensive bibliography. Together they constitute the standard reference for the general theory of *-algebras. This second volume deals with *-algebras. Noteworthy chapters develop the theory of *-algebras without additional restrictions, going well beyond what has been proved previously in this context and describe locally compact groups and the *-algebras related to them.

Carleman Estimates and Applications to Uniqueness and Control Theory (Progress in Nonlinear Differential Equations and Their Applications)

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Carleman Estimates and Applications to Uniqueness and Control Theory (Progress in Nonlinear Differential Equations and Their Applications)

Manufacturer: Birkhauser
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817642307

Book Description

This volume consists of 14 research articles that are an outgrowth of a scientific meeting held in Cortona on the subject of Carleman Estimates and Control Theory. New results are presented on Carleman estimates and their applications to uniqueness and controllability of partial differential equations and systems. The main topics are unique continuation for elliptic PDEs and systems, control theory and inverse problems. New results on strong uniqueness for second or higher order operators are explored in detail in several papers. In the area of control theory, the reader will find applications of Carleman estimates to stabilization, observability and exact control for the wave and Schrödinger equations. A final paper presents a challenging list of open problems on the topic of controllability of linear and semilinear heat equations. The articles contain exhaustive and essentially self-contained proofs directly accessible to mathematicians, physicists, and graduate students with an elementary background in PDEs. Contributors: L. Aloui, M. Bellassoued, N. Burq, F. Colombini, B. Dehman, C. Grammatico, M. Khenissi, H. Koch, P. Le Borgne, N. Lerner, T. Nishitani, T. Okaji, K.D. Phung, R. Regbaoui, X. Saint Raymond, D. Tataru, E. Zuazua

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"Courageously translated"

Truth never dies, it just gets new teeth

Encore! Add these to your list of great minds.

Great moralist, critic, wit

Dicta and Contradicta
Karl Kraus , and Jonathan McVity
Manufacturer: University of Illinois Press
ProductGroup: Book
Binding: Hardcover

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Half-Truths and One-and-a-Half Truths: Selected Aphorisms

The Waste Books (New York Review Books Classics)

Anti-Freud: Karl Kraus's Criticism of Psychoanalysis and Psychiatry

Karl Kraus: Apocalyptic Satirist: Culture and Catastrophe in Habsburg Vienna

The Notebooks of Joseph Joubert

ASIN: 0252026489

Book Description

"A woman is more than just her exterior. The lingerie is also important."

"The mission of the press is to spread culture while destroying the attention span."

"Art serves to rinse out our eyes."

Uniquely combining humor with profundity and venom with compassion, Dicta and Contradicta is a bonanza of scandalous wit from Vienna's answer to Oscar Wilde.

From the decadent turn of the century to the Third Reich, the acerbic satirist Karl Kraus was one of the most famous-and feared-intellectuals in Europe. Through the polemical and satirical magazine Die Fackel (The torch), which he founded in 1899, Kraus launched wicked but unrelentingly witty attacks on literary and media corruption, sexual repression and militarism, and the social hypocrisy of fin-de-siècle Vienna.

Kraus's barbed aphorisms were an essential part of his running commentary on Viennese culture. These miniature gems, as sharp as diamonds, demonstrate Kraus's highly cultivated wit and his unerring eye for human weakness, flaccidity, and hypocrisy. Kraus shies away from nothing; the salient issues of the day are lined up side by side, as before a firing squad, with such perennial concerns as sexuality, religion, politics, art, war, and literature. By turns antagonistic, pacifistic, realistic, and maddeningly misogynistic, Kraus's aphorisms provide the sting that precedes healing.

For Dicta and Contradicta, originally published in 1909 (with the title Spruche und Widerspruche) and revised in 1923, Kraus selected nearly 1,000 of the scathing aphorisms that had appeared in Die Fackel. In this new translation, Jonathan McVity masterfully renders Kraus's multilayered meanings, preserving the clever wordplay of the German in readable colloquial English. He also provides an introductory essay on Kraus's life and milieu and annotations that clarify many of Kraus's literary and sociohistorical allusions.

Customer Reviews:

"Courageously translated".......2006-03-09

It takes a whole lot of courage to translate the works of Karl Kraus. By just about anybody's standards, he is a bigot and a misogynist, but his bile is not without purpose. He reserves most of his barbed comments for women, criticizing their deceptively weak and ultimately treacherous nature, but also praising them for being strong-willed and defiant. Kraus is a vivisectionist, peeling away our comforting hypocrisies and revealing the ugly truths of life. Nothing escapes his knife, not even religion or education. In the pitch darkness of society's lies, Karl Kraus is a light of truth and wisdom. His words may wound tender egos, but they'll become stronger for it.

Truth never dies, it just gets new teeth.......2004-04-28

Chicken soup for the spleen!

Damn. And I thought I had a bleak perspective and a cutting cacpcity for quick critical insight- Karl leaves me and everyone else in the dirt. A comedian could quite possibly mine an entire erudite, Dennis Miller-esque routine from this book. Kraus' witticisms are as spot-on today as they were when he edited Die Fackel (The Torch), in Vienna about a century ago.

My only beef- it's a lot of dough for not a lot of tree-gut. I mean 918 aphorisms? these aren't sprawling, long-winded Nietzschian aphorisms. They're quick. And this is a page turner... Ah well, it still gets the 5 for being so damn right!

Hey- if you think people (by and large) are lying, manipulative, weak, dishonest scum- this is a book for you. Great essay by the translator too!

Encore! Add these to your list of great minds........2002-12-12

This book heralds the emergence of two great minds.
Karl Kraus, who because of his fearless critique of the media, politics, religion, and the other humbugs of the world Hitler & Co. was trying to shove down the world's throat...and Mr. McVity, who not only translates the difficult work of Kraus brilliantly, but provides, in his concluding essay, a history and examination of Kraus and his world, and great insights into those troubling times, whose wake we are still witnessing... but also rises, in his own writing, to such heights and depths as to be truly humbling. And yet I am excited that such a mind might surface in such a time as this...where content nor form offer much to chew on, beyond the official story and the infantile rant.

Share this wondrous book with your friends, but realize it may return dog-eared, pages now sea-foam green in highlighter. Sharing, after all, is a very Krausian thing to do. Karl Kraus donated much of his proceeds to homeless shelters, low-cost housing, Quakers caring for starving tubercular children, and the like. And Kraus shared ideas and art with his friends Brecht, Wittgenstein, Schoenberg, Rilke, and others whose greatness is already well-known, perhaps because of their being less a thorn in the side of the system.
As Kraus once said, "Art serves to rinse out our eyes."
But I would also suggest that his, and McVity's, art serves to rinse out our ears as well. Especially since our ears are now filled with the likes of...well...you know! But "Kraus named names." Read all about it! And then imagine random names such as Rush, O'Reilly, and others that miraculously make their way to the top of the list, forgetting perhaps that the list is boogerpasted to the wall of a sandbox. [Head shakes left then right. Repeat.]

I am pleased to give this book 5-stars, but regret that I couldn't give it more. As Lin Yutang once said: "I regard the discovery of one's favorite author as the most critical event in one's intellectual development. There is such a thing as affinity of spirits, and among authors of ancient and modern times, one must try to find an author whose spirit is akin with his own."

I eagerly await the next offerings of this protean mind among us, and urge that he not limit himself to translations, as his own writing is such a pleasure, and translations do take so dreadfully long...

Great moralist, critic, wit.......2001-11-22

Kraus is almost unknown to Americans, but he was one of the shining social critics of the 20th century. He was the first major debunker of Freudian nonsense. He wrote brilliantly on language, politics, and culture. He was, like all great critics, fearless.

This book is a mixed presentation, including many quotes that seem outdated or inscrutible. It also has the editor's odd and distorted rendering of Kraus.

If you are unfamilair with Kraus you will be better served by Thomas Szasz's "Anti-Freud : Karl Kraus's Criticism of Psychoanalysis and Psychiatry."...The Szasz book provides fascinating biographical info about Kraus. Szasz has also nicely translated many of Kraus's pithiest and funniest aphorisms.

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Dicta and Contradicta
Karl and Jonathan McVity Kraus
Manufacturer: University of Illinois Press
ProductGroup: Book
Binding: Paperback
ASIN: B000OQ7YH2

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