Book Description
This book is an introductory graduate text dealing with many of the perturbation methods currently used by applied mathematicians, scientists, and engineers. The author has based his book on a graduate course he has taught several times over the last ten years to students in applied mathematics, engineering sciences, and physics. The only prerequisite for the course is a background in differential equations. Each chapter begins with an introductory development involving ordinary differential equations. The book covers traditional topics, such as boundary layers and multiple scales. However, it also contains material arising from current research interest. This includes homogenization, slender body theory, symbolic computing, and discrete equations. One of the more important features of this book is contained in the exercises. Many are derived from problems of up- to-date research and are from a wide range of application areas.
Customer Reviews:
nice introduction.......2006-05-30
I found this book explains the ideas very well and also provides examples that help to understand the methods. I also liked all the exercies at the end of each chapter. This is one book that anyone who studies applied mathematics should have on their bookshelf.
Best available introduction to perturbation methods.......2004-05-20
I have read several books on perturbation methods, and this book absolutely the best. Perturbation methods are used in problems where the equations (algebraic, ODEs, or PDEs) involve a small parameter, or that evolve on multiple time scales that differ by orders of magnitude. The basic idea is to build an approximate solution to the equation based on a series expansion involving the small parameter. Usually two or more series expansions are built and then combined to yield a solution to the equation that incorporates dynamics on both the slow and fast time scales (for example).
The first two chapters introduce the basic concepts of asymptotic expansions. Several informative, though relatively simple, examples are developed in detail to illustrate the techniques. The third chapter introduces techniques for solving problems involving multiple scales. Chapters four and five discuss the WKB method and homogenization techniques. The final chapter shows how perturbation methods can be used in conjunction with techniques from dynamical systems analysis, especially stability analysis and bifurcation theory.
The contents of the book are extremely well-chosen and pertinent. Many of the problems and techniques are based on realistic physical systems, and represent the types of problems an applied mathematician is likely to encounter in practice. The book's prose is clear and informative. Only occasionally did I feel that the author had explained something poorly or left out an important piece of information.
There are of course a couple of problems with the book. First, most of the exercises are significantly more difficult than the examples, and no hints or solutions are given. This can be a draw-back if you are using the book for self-study. There are a number of typos and errors in the text, though the author's website has a list of errata. Finally, solving perturbation problems in practice often involves subtle tricks, and unfortunately, this book does not discuss or give examples of many of those tricks.
Overall, this is definitely the best introductory book on perturbation methods. You should definitely consider this book if you work in applied math or with differential equations.
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Perturbation Methods and Semilinear Elliptic Problems on R^n (Progress in Mathematics)
Antonio Ambrosetti , and
Andrea Malchiodi
Manufacturer: Birkhäuser Basel
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Nonlinear Analysis and Semilinear Elliptic Problems (Cambridge Studies in Advanced Mathematics)
ASIN: 3764373210 |
Book Description
The aim of this monograph is to discuss several elliptic problems on R
n with two main features: they are variational and perturbative in nature, and standard tools of nonlinear analysis based on compactness arguments cannot be used in general. For these problems, a more specific approach that takes advantage of such a perturbative setting seems to be the most appropriate. The first part of the book is devoted to these abstract tools, which provide a unified frame for several applications, often considered different in nature.
Such applications are discussed in the second part, and include semilinear elliptic
problems on R
n, bifurcation from the essential spectrum, the prescribed scalar
curvature problem, nonlinear Schrödinger equations, and singularly perturbed
elliptic problems in domains. These topics are presented in a systematic and
unified way.
Book Description
The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists.
Currently available in the Series:
T. W. Anderson
The Statistical Analysis of Time Series
T. S. Arthanari & Yadolah Dodge
Mathematical Programming in Statistics
Emil Artin
Geometric Algebra
Norman T. J. Bailey
The Elements of Stochastic Processes
with Applications to the Natural Sciences
Robert G. Bartle
The Elements of Integration and
Lebesgue Measure
George E. P. Box & Norman R. Draper
Evolutionary Operation: A Statistical Method for Process Improvement
George E. P. Box & George C. Tiao
Bayesian Inference in Statistical Analysis
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Finite Groups of Lie Type: Conjugacy Classes
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R. W. Carter
Simple Groups of Lie Type
William G. Cochran & Gertrude M. Cox
Experimental Designs, Second Edition
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Differential and Integral Calculus, Volume I
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Differential and Integral Calculus, Volume II
Richard Courant & D. Hilbert
Methods of Mathematical Physics, Volume I
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Planning of Experiments
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Representation Theory of Finite Groups and
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Charles W. Curtis & Irving Reiner
Methods of Representation Theory
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Charles W. Curtis & Irving Reiner
Methods of Representation Theory
with Applications to Finite Groups
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Cuthbert Daniel
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Theory of Probability, Volume I
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Sample Design in Business Research
Customer Reviews:
Good and delineating theory for perturbation method.......2006-03-27
understandable for engineers with good reasoning and a little mathematical knowledge
Book Description
In this book the author presents the theory and techniques underlying perturbation methods in a manner that will make the book widely appealing to readers in a broad range of disciplines. Methods of algebraic equations, asymptotic expansions, integrals, PDEs, strained coordinates, and multiple scales are illustrated by copious use of examples drawn from many areas of mathematics and physics. The philosophy adopted is that there is no single or best method for such problems, but that one may exploit the small parameter given some experience and understanding of similar perturbation problems. The author does not look to perturbation methods to give quantitative answers but rather uses them to give a physical understanding of the subtle balances in a complex problem.
Customer Reviews:
Starting Perturbations.......2005-01-30
This is a nice place to start when learning basic perturbation methods. There are numerous examples and the material is clearly presented. However, there are weak points. One is brevity, as pointed out by the first reviewer. The coverage of the subject of perturbation methods is minimal and some of the topics that are covered are done so with little depth. Another drawback is the emphasis, when discussing applications, on fluids and to a lesser extent mechanics. This makes it somewhat old fashioned. The greatest drawback is the exercises. It is impossible to learn mathematics, and perturbation methods in particular, without doing lots of problems. This text, unfortunately, falls far short in the number and range of problems it provides the reader.
Great Intro to Perturbation Methods.......2000-09-14
This is a wonderful first introduction to perturbation methods. Extremley readable, my only criticism of this text is its brevity. In some places, it lacks detail and doesn't go very deeply into several areas. However, it is the type of book that one can easily pick up, read and learn something usefull. The author's do lot's of examples and once this text is mastered, the student is certaintly ready to read Kevorkian and Cole's classic text on the subject.
Book Description
Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this unique book deliniates boundary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in the context of the general theory, as well as a final discussion of the more advanced problems. Precise estimates and excursions into the theoretical background makes this workbook valuable to both the applied sciences and mathematics fields. As a bonus in its last chapter the book includes a collection of rare and useful pieces of literature, such as the summary of the Perturbation theory of Matrices.
Detailed illustrations, stimulating examples and exercises as well as a clear explanation of the underlying theory makes this workbook ideal for senior undergraduate and beginning graduate students in applied mathematics as well as science and engineering fields.
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Algebraic Methods in Nonlinear Perturbation Theory (Applied Mathematical Sciences)
V.N. Bogaevski , and
A. Povzner
Manufacturer: Springer
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ASIN: 0387974911 |
Book Description
This book will be of interest for everybody working on perturbation theory in differential equations. The book requires only a standard mathematical background for engineers and does not require reference to the special literature. Topics which are covered include: matrix perturbation theory; systems of ordinary differential equations with small parameter; reconstruction and equations in partial derivatives. Boundary problems are not discussed in this volume. The reader will find many examples throughout the book.
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Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems
J.J.H. Miller L.G. Vulkov , and
G.I. Shishkin
Manufacturer: Nova Science Publishers
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ASIN: 1560728485 |
Book Description
To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.
Book Description
Everything is going perfectly for Kuga, a top designer at a hip ad agency, until his friend introduces him to Nagisa, a uniquely beautiful man. Desperate for a way to get closer to the fetching newcomer, Kuga asks Nagisa to become the spokesmodel for the launch of his new unisex apparel campaign. With Nagisa aboard, Kuga is certain the campaign will be a success, but deep in his heart he knows that he actually craves something far more intimate than a business relationship.
Book Description
Turgenev was the most liberal-spirited and unqualifiedly humane of all the great nineteenth-century Russian novelists, and in Virgin Soil, his biggest and most ambitious work, he sought to balance his deep affection for his country and his people with his growing apprehensions about what their future held in store. At the heart of the book is the story of a young man and a young woman, torn between love and politics, who struggle to make headway against the complacency of the powerful, the inarticulate misery of the powerless, and the stifling conventions of provincial life. This rich and complex book, at once a love story, a devastating, and bitterly funny social satire, and, perhaps most movingly of all, a heartfelt celebration of the immense beauty of the Russian countryside, is a tragic masterpiece in which one of the world's finest novelists confronts the enduring question of the place of happiness in a political world.
Download Description
TURGENEV was the first writer who was able, having both Slavic and universal imagination enough for it, to interpret modern Russia to the outer world, and Virgin Soil was the last word of his greater testament. It was the book in which many English readers were destined to make his acquaintance about a generation ago, and the effect of it was, like Swinburne's Songs Before Sunrise, Mazzini's Duties of Man, and other congenial documents, to break up the insular confines in which they had been reared and to enlarge their new horizon.
Customer Reviews:
GARNETT UNFAIR TO TURGENEV.......2007-01-06
"Virgin Soil" (1877) was Turgenev's last, longest, but far from greatest novel. A recurring theme through all his fiction is the contrast between the romantic Russian liberalism of the 1840s, which Turgenev regarded as ineffectual, and the hard-headed populism of the 1860s and 70s. After the 1861 emancipation of the serfs (some 80% of Russia at the time), University students wanted to "go to the people" and enlighten them. When they got there, they found an unbridgeable chasm between the middle class and rural workers, who suspiciously had agitators arrested. Many of these spent years in solitary confinement, and the bitterness of their thwarted hopes for reform poisoned Russian politics and made violent revolution more likely. "Virgin Soil" begins with one such cell of radicals in St. Petersburg in 1868, and follows them to the countryside where they interact with both liberal and reactionary gentry, as well as with clear-headed Bolsheviks of the future. Little happens, and the thin, drawn-out plot lacks the economy, texture, and pungency of "Fathers and Sons." This is a decidedly second-drawer effort. To make matters worse, New York Review Books has reissued it in the incompetent, hackwork translation of Constance Garnett (1862-1946), presumably because it was in the public domain. I cannot judge her handling of Russian (though Nabokov did: "dried dung," he called her work) but her English is not even professional: NYRB could have spent some of the money they saved on a free translation by hiring a line editor to correct her egregious errors in syntax, grammar, and punctuation. It might have been better having no edition of "Virgin Soil" on the market at all.
More Russian Nihilism.......2005-04-11
"To turn over virgin soil it is necessary to use a deep plough going well into the earth, not a surface plough gliding lightly over the top."-From a Farmer's Notebook.
Virgin Soil, by Ivan Sergevich Tugenev, is another Russian revolutionist novel. The dubious main character, Nejdanov, is a young poet who tries to help spread the socialistic propaganda to the poor peasants. They must dig deep into the mother earth of Russia to plant the seeds of communism. Nejdanov is accused of being a traitor and gives useless speeches, while his lover, Mariana tries desperately to get him to accept her. Markelov, an older member of the cause, goes to the extreme to arm the peasants and start a revolution and is locked up. Solomin (the real hero), is a cool minded, patient revolutionist who thinks of the peasants as barn animals. He is Turgenev's ideal insurgent. While the main character, Nejdanov is described as, "...the idealist of realism". The book ends with death and imprisonment and an overall unhappy feeling.
Not the most exciting read, just another Russian novel full of depressing nihilist and revolutionist. Tugenev's other great work, Fathers and Sons, is a far more interesting novel, and I highly recommend it.
explanations of all sorts only lead to confusion.......2004-10-07
This is the third of Ivan Turgenev's novels that I have read. He is such a wonderful novelist that the things I dislike about some of his female characters (he must have had SUCH a tough time of it!) tends to get obscured. Surely there can't be women in the world that manipulative and self-obsessed! But I'll avoid the risk of confusing things - yes, the title of my review is a quote - and just mention that there are nice women in each of the novels that I have read, as well as the less attractive, but ever so alluring ones.
Common to all three Turgenev novels that I have read is rejection - rejection of women by men. But the rejection has nothing to do with the men thinking the women are inadequate. It is the men who see themselves as unworthy and, for me with my Western eyes, their 'reasons' are SO tenuous. And yet, for all that I do see the 'sense' in it - I have seen the world in the same way myself.
The outcome for me of this novel was unsatisfactory for another reason that I will not attempt to explain. But it is understandable for me why this outcome was plotted by the author - unlike that of DH Lawrence in another book I reviewed recently.
Perhaps Joseph Conrad is correct in 'Under Western Eyes' and those of us with Western eyes will never really understand the Russian - I have certainly tried both personally and in literature. And I have to say I am floundering a bit. Nevertheless, for the sheer joy of reading a brilliantly crafted novel I unreservedly recommend 'Virgin Soil'.
Other recommendations:
'Memoirs of a Revolutionist' by Peter Kropotkin
'Fathers and Sons' by Ivan Turgenev
'Spring Torrents' by Ivan Turgenev
'Under Western Eyes' by Joseph Conrad
Quintessential Turgenev.......2001-03-14
Encompassing social commentary, a (albeit fairly simplistic) love story, and a homage to Russia's beauty, this work does not fail the lover of Turgenev. Certainly this might not necessarily be the best work with which to begin one's odyssey through Turgenev, but this very effectively pulls together all the familiar elements of his writing. Turgenev is not known for his plot development, and this is again the case here: very little actually occurs. The absence of plot and of action, however, is not to say that this dry, boring drivel. Rather, Turgenev's material, this work in particular, becomes a pleasant marriage of the classic novel with the novel of ideas.
His commentary, both political and human, is both trapped in the amber of history and universally relevant (a lovely dichotomy) to the human condition. "Virgin Soil" is a very fine story, and the translation is flowing and literate (having no Russian, I cannot speak to how accurately this might reflect the original).
Do not start your Turgenev tour with this.......2001-01-28
Having read all of Turgenev's major works, this would be the best one to close one's odyseesy of Turgenev works as it provides his finally achieved view of the desparate situation of then Russia and the skepticism toward the revolutionary movements aiming at social re-engineering. Story is very simple, and no significant action was involved, but a minimum knowlwedge of Russian literature, changing revolutionary movements and intelligentsia situation is required to grasp the width of the topics and issues covered.
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- Collectivisation in the Soviet Union
|
Virgin Soil Upturned: Book 1
Mikhail Aleksandrovich Sholokhov , and
R. C. Daglish
Manufacturer: University Press of the Pacific
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ASIN: 0898751136 |
Book Description
Mikhail Sholokhov is rightly considered both in his own country and abroad the foremost Soviet novelist of his generation.
Born in 1905, in a working Cossack family, Sholokhov's most impressionable years were those of the Russian Revolution and Civil War, which he had described with penetrating insight.
In 1926, he began his great epic of the Civil War And Quite Flows the Don, and , to use his own words, “found himself” as a writer “in that arduous and joyful creative work”. And Quite Flows the Don was completed in 1940. The first book of Virgin Soil Upturned came out in 1932. The second was competed in 1960. In 1957 Sholokhov wrote a story, The Fate of a Man, which has become world famous. Also, he was working on They Fought for Their Country, a novel about Soviet people in the Second World War. Sholokhov is truly a writer of the people. His books have been printed in more than thirty-two million copies and translated into sixty-four languages.
Through the scene is set in a small Cossack village, Sholokhov's scope is no less great than in his other work, for the fate of his characters is the fate of a whole nation undergoing the greatest social revolution in its history.
A process of change had been set afoot that was to spread into every corner of Cossack life. Outworn traditions and habits were swept aside, personalities and ideas that had taken generations to form were either broken or made anew and all this in the face of bitter opposition from those who could not or would not change.
With a telling humanity Sholokhov depicts the faults and strivings, the suffering and laughter both of the fighters for progress with whom he himself has such deep ties, and their opponents.
This book has a fundamental message for those who wish to understand the stresses and strains of Soviet life from the 1930's to the present day.
Customer Reviews:
Collectivisation in the Soviet Union.......2002-05-22
The Communist official Siemion Davidov arrives in the Don community of Gremyachy Log in order to start a collective farm. The community divides between those for the collective farm, and those (mainly the better-off farmers or "kulaks") fiercely opposed to it.
The subject of collectivisation in the rural Soviet Union will no doubt be as dry as old bones to many readers - that was my reaction too as I started the book. However, the Sholokhov explores many complicated issues:
* the view that all property is theft versus the inviolability of private property rights;
* do oppressive landowners deserve any loyalty from their workers?
* the conflict of essentially modernising forces (personified by Davidov, whose background is industrial-urban) with backward "traditional" rural Russia (personified by the locals); and even
* the catastrophic effects of contradictory dictats issued from the centre.
Sholokhov's position (I thought) was esssentialy pro-collectivisation, although he does not spare the reader the real problems associated with it. What does let the book down somewhat is that it's very uneven - there are long passages in which the characters tell anecdotes from their past, some meant to be humerous, others poignant. I thought most of these did not work well and were a distraction. Of course, it's fundamentally a bleak novel - the subject matter makes this almost inevitable. Luckily enough, I seemed to be in the mood!
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Red Virgin Soil: Soviet Literature in the 1920's (SRLT)
Robert A. Maguire
Manufacturer: Northwestern University Press
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ASIN: 081011741X |
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- Introduction to the Theory of Distributions
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- $J$-holomorphic Curves and Symplectic Topology (Colloquium Publications (Amer Mathematical Soc))
- Latent Curve Models : A Structural Equation Perspective (Wiley Series in Probability and Statistics)
- Lattices and Ordered Algebraic Structures (Universitext)
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