Book Description

Here's the perfect self-teaching guide to help anyone master differential equations--a common stumbling block for students looking to progress to advanced topics in both science and math.Covers First Order Equations, Second Order Equations and Higher, Properties, Solutions, Series Solutions, Fourier Series and Orthogonal Systems, Partial Differential Equations and Boundary Value Problems, Numerical Techniques, and more. ... Read more

Book Description

This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods.

* Treats vector calculus using differential forms
* Presents a very concrete introduction to differential forms
* Develops Stokess theorem in an easily understandable way
* Gives well-supported, carefully stated, and thoroughly explained definitions and theorems.
* Provides glimpses of further topics to entice the interested student ... Read more

Reviews (4)

Very confusing....
This book was a very confusing book on a very confusing topic. I am looking forward to the day that someone can write an understandable treatise on this subject.

Intuitive Book
This is the only book on the subject I know of that gives me a feel for what is going on. To many other books are long on notation and short on insight. Occasionally the book seems to plod but that is a minor problem compared with the dense presentation of other books. Highly recommended.

VERY CLEAR BOOK ON DIFFERENTIAL FORMS
I recommend this book to anyone who wants a quick introduction to differential forms without getting lost in a sea of mathematical formalism. The author explains the ideas very well. The exercises in the book are fairly easy to solve. I haven't noticed any misprints so far as the other reviewer claims but should there by any I am sure they can be corrected with intuition alone. This is a very intuitive book that can serve as a companion text to the authoritative book on "DIFFERENTIAL FORMS" by Edwards which I have also reviewed.

Many Misprints But Still Useful
This book does have many misprints. The author has a partial errata list on his personal web site. The book is still a useful hands on introduction to differential forms.

But why is Amazon.com selling a paperback at a price much more than other sites are selling the hard cover? In fact, is there a paperback? ... Read more

Book Description

This book develops the theory of global attractors for a class of parabolic PDEs that includes reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated in detail.A lengthy chapter on Sobolev spaces provides the framework that allows a rigorous treatment of existence and uniqueness of solutions for both linear time-independent problems (Poisson's equation) and the nonlinear evolution equations which generate the infinite-dimensional dynamical systemss of the title. Attention then switches to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space which determines the asymptotic dynamics. In particular, the concluding chapters investigate in what sense the dynamics restricted to the attractor are themselves "finite-dimensional." The book is intended as a didactic text for first year graduates, and assumes only a basic knowledge of Banach and Hilbert spaces, and a working understanding of the Lebesgue integral. ... Read more

Book Description

This revision of Boyce & DiPrima's market-leading text maintains its classic strengths: a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. Like previous editions, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences.

Student Solutions Manual:

Created as an integral learning aid to Boyce and DiPrima's Elementary Differntial Equations, 8E, this Solutions Manual provides worked out answers to select problems in the text.Using the Solutions Manual as you work your way through the course will ensure that you are doing the work right all along. ... Read more

Book Description

Handbook of Grid Generation addresses the use of grids (meshes) in the numerical solutions of partial differential equations by finite elements, finite volume, finite differences, and boundary elements. Four parts divide the chapters: structured grids, unstructured girds, surface definition, and adaption/quality. An introduction to each section provides a roadmap through the material.This handbook covers:oFundamental concepts and approachesoGrid generation processoEssential mathematical elements from tensor analysis and differential geometry, particularly relevant to curves and surfacesoCells of any shape - Cartesian, structured curvilinear coordinates, unstructured tetrahedra, unstructured hexahedra, or various combinationsoSeparate grids overlaid on one another, communicating data through interpolationoMoving boundaries and internal interfaces in the fieldoResolving gradients and controlling solution erroroGrid generation codes, both commercial and freeware, as well as representative and illustrative grid configurationsHandbook of Grid Generation contains 37 chapters as well as contributions from more than 100 experts from around the world, comprehensively evaluating this expanding field and providing a fundamental orientation for practitioners. ... Read more

Reviews (2)

A disappointment
I bought this book in the hope that it would contain actual implementation details concerning the various methods; specifically prismatic and other unstructured methods. To say the least, this book is thick but it is filled with extraneous fluff without any real details. For instance, the chapter on prismatic grid generation is nothing but a lot of "hand-waving" without any concrete details and I can say the same concerning the rest of the book.

Also, it appears that many of the chapters in the book were included without a strict peer-review process as should be the process for a book of this type.

A broad survey
I bought the book with great interest because of the type of research I am currently involved in. For me, the book is a disappointment. I have seen two types of technical handbooks. One type is the usual handbook of mathematics (or more specialized in integrals or differential equations). This type gives the basic definitions and well-known facts about the concepts and topics. The other type of handbook is more advanced, covering specialized topics in depth. An example is the Handbook of Numerical Analysis, in which a wide range of topics are covered in depth. The reader (e.g. myself) can LEARN the fundemtals of a particular numerical theory by reading the handbook alone. The handbook under review, however, is of neither types. In some sense it is a compilation of review articles of various grid generation techniques while lacking the depth usually seen in such articles. I can imagine the difficulty in presenting grid generation in a systemtic manner as determined by the nature of the field. I did wish that the book could be something similar to the Numerical Receipes: not systematic but practical and very useful. But this is not the case. The book does contain lots of useful references, which probably justify its cost. ... Read more

Book Description

There are dozens of books on ODEs, but none with the elegant geometric insight of Arnol'd's book. Arnol'd puts a clear emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on the routine presentation of algorithms for solving special classes of equations. Of course, the reader learns how to solve equations, but with much more understanding of the systems, the solutions and the techniques. Vector fields and one-parameter groups of transformations come right from the start and Arnol'd uses this "language" throughout the book. This fundamental difference from the standard presentation allows him to explain some of the real mathematics of ODEs in a very understandable way and without hiding the substance. The text is also rich with examples and connections with mechanics. Where possible, Arnol'd proceeds by physical reasoning, using it as a convenient shorthand for much longer formal mathematical reasoning. This technique helps the student get a feel for the subject. Following Arnol'd's guiding geometric and qualitative principles, there are 272 figures in the book, but not a single complicated formula. Also, the text is peppered with historical remarks, which put the material in context, showing how the ideas have developed since Newton and Leibniz. This book is an excellent text for a course whose goal is a mathematical treatment of differential equations and the related physical systems. ... Read more

Reviews (5)

A beauty; a struggle
This has to be one of the most amazing math books I've ever read. Arnol'd seems to do the impossible here - he blends abstract theory with an intuitive exposition while avoiding any tendency to become verbose. By the end of Arnol'd, it's hard not to have a deep understanding of the way that ODEs and their solutions behave.

Arnol'd accomplishes this feat through an intense parsimony of words and topics. Everything in this book builds on the central theme of the relations between vector fields and one-parameter groups of diffeomorphisms, and the topics are illustrated (and often motivated) almost exclusively through problems in classical mechanics, most notably the plane pendulum. Almost no solution techniques are given in this book - expect no mention of integrating factors or Bessel functions. One of the main reasons that the book does so much without bogging down is that the mathematical formalism is minimal and terse - proofs are often one or two lines long, merely mentioning the conceptual justification of a result without detailed, formal constructions.

But the result of this parsimony is that Arnol'd is a very difficult book. To understand every detail and to be able to attempt every problem, I think, basically requires a math degree - lots of linear algebra (for his monumental 116-page chapter on linear systems), a solid background in analysis and topology, and a bit of differential geometry and abstract algebra are prerequsites for a full understanding. (I found the section on the "topological classification of singular points," in particular, nearly incomprehensible with my thin chemistry-major math background.) There are foibles, too, including proofs that satisfy the requirements for some theorem or definition without actually stating what theorem or definition is now applicable. One can detect some mild arrogance in places (after an arduous two-page proof, he mentions "As always in proving obvious theorems, it is easier to carry out the proof of the extension theorem than to read through it.") Also, a few typos can be found here and there, which sometimes result in confusion.

One very curious thing about Arnol'd is that my most brilliant math-major friends find it impenetrable, whereas I know biologists who got through it with no problem. So I guess that, for a mere mortal, reading Arnol'd demands a willingness to have a feel for a big picture without worrying about every epsilon and delta.

So grab a copy of this book, let it flow, and learn about ODEs. It's well worth the effort.

Stimulating
Like his books on classical mechanics, a book that theoretical physicists should read. Unfortunately, the discussion of local integrability is too abstract and there is no distinction made with global integrability. Also irritating: because of a singularity at the origin the damped harmonic oscillator is not recognized as integrable in spite of the existence of a global conservation law, excepting one point in phase space. Integrability is an extremely difficult subject and maybe Arnol'd could have taught us more about it. I've discussed integrability/nonintegrability from a physicist's perspective in my Classical Mechanics (Cambridge, 1997).

excellent, 1st of 2 english versions
Be aware there are 2 versions of this book
available in English; this one from MIT press
is (contrary to one of the reviews above) is
translated from the *first* Russian edition;
there is another version from Springer-Verlag
translated from the *third* Russian edition.
They're translated by different people so
some wording etc is different but otherwise
they're similar, though not identical. The
later edition has some reworked passages
and modest amount of new material, but it's
not a hugely different book.

Both are excellent, are are all the other
books & papers I've seen by V.I. Arnol'd.

An understanding-oriented mathematical textbook on ODEs.
It is hardly needed to add words to the existing positive reviews of the book. In the line of previous comments, I just mention that it is an enjoyable book on a basic subject of great interest also for engineers and physicists. The matter is treated with the evident purpose to make the reader fully aware of the interesting geometrical and dynamic implications of the conclusions reached at each step. It is a nice counterexample for those who believe that, to be rigorous, a mathematical book needs to be very hard to read.

A geometrical approach to differential equations.
This is one of the few original books in the area of differential equations. In his clear style, Arnold presents the basics of differential equations. He is more interested in understanding the solutions than in deriving them by analytical methods. The text is well organized and there seem to be more figures than proofs (although all proofs are there, it just that they do not get in the way). A must, if you are in the area of chaos and dynamical systems. (RM) ... Read more

Book Description

Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra.Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods. ... Read more

Book Description

This revision of Boyce & DiPrima's market-leading text maintains its classic strengths: a contemporary approach with flexible chapter construction, clear exposition, and outstanding problems. Like previous editions, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences. ... Read more

Reviews (12)

Good intro book to accompany a course
I have had the privledge to use this book for an introductory course in differential equations with colleages of Dr. Boyce. This book is well written and contains numerous examples and a plethora of problems. However, a student would do well to have a very firm knowledge of calculus and a quick mathematical mind; some of the methods covered are not candy coated to go down easier. As such, it is important that a strong professor and a strong curriculum accompany this book. This is NOT a good book for self-instruction. However, it is a very useful reference to go back to when dealing with more advanced mathematical topics.

Elementary Diffential Equations by Boyce and DiPrima
This book is excellent for math majors or engineers who have had
a strong background in higher mathematics. The work provides
a step-by-step analysis of the classic problem areas i.e.
initial value problems, solution boundaries, homogeneous and
non-homogeneous solutions, the exponential form, higher order
differential equations, variation of parameters, LaPlace
transformation and other more exotic applications too numerous
to list here. For non-math majors, the book may become difficult

to follow. Therefore; it may help to consult with the Schaum's
Outline in order to supplement this text. Boyce and DiPrima
is more than enough to get you through the Fundamentals of
Engineering Examination. Differential Equations is a subject
which requires students to take copious notes. It pays to
struggle through the homeworks and to plan daily study sessions
of 15 minutes to 1 hour depending upon where you are in the
course. It is well worth the effort to master this course

because the applications to engineering are numerous and profound. Mastery of this subject will provide you with a
life-long skill.

written by math professors for math professors
I am taking a differential equations course for the engineering program at Drexel University and I must say that this is one of the worst text books I have ever come across. I wonder what Boyce and Diprima were smoking as they were writting this book. First of all make sure you brush up on your greek before reading this book, there are more greek symbols in it then there are numbers or letters from the english alphabet. This book is so vague that you may as well consult a magic 8-ball for guidance. Basically, if you buy this book, prepare to fail. It skips so many steps its rediculous. My mind turns to mush every time I open it. For my homework in this course using this book, I just write the giberish my magic 8 ball tells me to. Even the TAs are lost in this book. Consider this a warning and not a rating. STAY AWAY!

University Student's Openion
Please take this advice; I have been using this book for the past four months.

This is a rare occasion. I never take to the time to go to a site and write a review unless there is some outstanding reason. This is my fourth year as an engineering student and while I have had some bad books, I have NEVER had a book this bad. For example, the text almost never gives full examples let alone examples on how to do the practice problems/homework problems. When the text gives example problems, it will randomly skip important steps. Ironically, in a lot of cases, it will skip the step/method that is being covered in the section. Also, the text mainly discusses theory and usually doesn't really show how to solve these equations. Furthermore, the solutions manual is just as bad. Solutions are given in a sloppy manner that are unclear and incomplete. I would not recommend this book to any university as an introductory differential equations text.

Poor choice for an introductory text
Why anyone would choose this text to first introduce students to differential equations is beyond me. I've used this text both as a student and as a TA, and my hatred of it has only grown as I've tutored students out of it. Engineers and scientists don't need the lengthy descriptions provided in this text, which make it difficult to quickly refresh one's memory on a particular method. In addition, this text is suffering from a blight that affects many calculus and differential equations texts--moving important methods and/or concepts into the exercises. The examples are fairly good and provide the only way to figure out what is going on without spending hours reading. Its other redeeming quality is that almost all of the answers are provided in the back of the text, which is helpful to students who will rework problems until they get the right answer. Students should beware that instructors and graders quickly catch on to this fact, so you really need to work through to the right answer, or your score will suffer.

Additionally, this text's price is rising quite rapidly. I don't understand why it is, but the book certainly isn't worth its current price.

Don't buy this book unless you have to! ... Read more

Book Description

This is the only book on spectral methods built around MATLAB programs. Along with finite differences and finite elements, spectral methods are one of the three main technologies for solving partial differential equations on computers. Since spectral methods involve significant linear algebra and graphics they are very suitable for the high level programming of MATLAB. This hands-on introduction is built around forty short and powerful MATLAB programs, which the reader can download from the World Wide Web.

This book presents the key ideas along with many figures, examples, and short, elegant MATLAB programs for readers to adapt to their own needs. It covers ODE and PDE boundary value problems, eigenvalues and pseudospectra, linear and nonlinear waves, and numerical quadrature. ... Read more

Reviews (2)

Loaded with errors, author defensive and arrogant
I found glaring errors starting on page 1. I emailed the author for clarification who agreed that his nomenclature was unclear and misleading (come on Professor, we call them mistakes, errata, etc.). The first chapter is available in his web site, go see for yourself. You'll also find a page of errata, which unfortunately is far from complete. My colleagues and I desperately tried to get Professor Trefethen to clarify his nomenclature, which he quite arrogantly dismissed. His matlab code seems to execute fine, but you'll likely spend a good deal of time dissecting it. Any programmer who must use someone elses code despises poorly commented and optimized code. This book just isn't a good place to start for spectral methods or matlab.

A useful introduction to spectral methods
The author achieves the hard task of explaining the subject in a very simple and, at the same time, intelligent way. The MATLAB m-files are short, educative and full of useful tricks. The book is well motivated, focused in the essentials and easy to read. I am very fond of most of Prof. Trefethen writings and this book is no disappoitment. It contrasts starkly with the lack of mathematical insight in most of the engineering collocation literature, but at the same time has a hands-on approach to the problems. This book should be useful to anybody interested in solving PDE in regular geometries. ... Read more

Book Description

Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) that reinforce ideas and provide insight into more advanced problems. A Student Solutions Manual is also available.

* Comprehensive coverage of frequently used integrals, functions and fundamental mathematical results
* Contents selected and organized to suit the needs of students, scientists, and engineers
* Contains tables of Laplace and Fourier transform pairs
* New section on numerical approximation
* New section on the z-transform
* Easy reference system ... Read more

Reviews (1)

Very Rich Book, but not for the faint of heart
This is a good book for one who already has an advanced knowledge of mathematics and wants a cohesive text that covers many of the fundamental mathematics subjects needed for engineering and science applications (noticeably not including statistics).

The text itself is terse but very rich. Exercises which are quite challenging are included at the end of most sections and odd answers are in the back of the book. A solutions manual would have been a good idea since many problems are difficult. ... Read more

Book Description

A thorough, systematic first course in elementary differential equations for undergraduates in mathematics and science, requiring only basic calculus for a background, and including many exercises designed to develop students’ technique in solving equations. With problems and answers. Index.
... Read more

Reviews (5)

An excellent text ... in 1970, not in 2003
I used this text as a reference over 25 years ago and it was great, for its time. Today, however, there are a number of books available with a more "modern" treatment - ones more likely to provide a more realistic view of the subject matter.

Arguably, ODE is a geometry course in disguise and not a collection of "party tricks" as it is often portrayed in older texts. Analytical methods are clean and easy to convey in the classroom but, frankly, they never appear in the "real world".

If you plan to (or do) encounter ODE's in your chosen field you'd do better to spend lots of time looking at qualitative and numerical techniques, i.e., a more up to date approach.

Coddington did a great job with the subtopics he did address but in the late sixties it would have been difficult, if not impossible, to really provide the reader with a solid feel for the depth and breadth of the subject.

A great Introduction or review.
I took an undergraduate ordinary differential equations class and felt I grasped the subject quite well. I wanted an inexpensive text that I could review the subject with and I decided that I would give Coddington's book a try. I was really pleased with the order in which the text was presented which differed from the course I had taken. The author's seem to put things in a very logical order versus some texts I have seen which really confuse you by the order in which the subjects are presented. Another point that I have to make is the depth that the book has. I learned much more in reviewing this text than I ever did in any diff eq class. It shows the distinction between linear and non-linear diff eq's and covered many other methods which I had not learned previously. This is a great text as a "refresher" or as a course text. I just wish I would have previously used this text to learn ordinary differential equations.

Holy Bible for Introduction to differential equations UG
This book is a holy bible for introduction to differential equations. It is easy to understand and the problems are quite challenging. Dr Coddington knows how to explain the material by systematically order(Easy to tough). His book is not easy to figure out if you just sit without paper,pen and think. But once you are understand his book, no one can teach you differential equations for undergarduate level. Other suggested reading are Theory of ordinary differential equations, Linear ordinary differential equations by Earl Coddington(Both of them), Ordinary Differential Equations by Fritz John,and Ordinary Differential Equations by Edward L Ince. Once the most important statement is: YOU KNOW DIFFERENTIAL EQUATIONS IF YOU UNDERSTAND WHAT IS GOING ON IN CODDINGTON'S AND FRITZ JOHN BOOKS.

One of the Better ODE Texts
This book was used in my "Introduction to Ordinary Differential Equations" class when I was a senior at Louisiana State. I found it to be one of the better texts in differential equations that I have come across. The first chapter is mainly the prerequisite calculus, then the next chapter jumps into first order equations. Then unlike most other books, he jumps straight into second order problems. the biggest plus in the book is the ready use of complex analysis throughout, something which most books avoid altogether, thus allowing the student to get only a partial understanding of the theory needed to solve more advanced problems. Answers are included at the back of the book, problems are clear and well-explained, and there are enough advanced topics covered later in the book (including celestial mechanics) to keep the course interesting for students of all kinds.

Superb introduction to ODE's
This classic book appeared for the first time in the early 1960's, and the world is still waiting to see a better elementary text on ODE's.

It begins with a chapter covering the necessary background to understand the material, and then proceeds to study the first order linear equation. The next step is the 2nd order linear equation and then the n-th order linear equation. The most appreciated feature of this book is that the author shows that the method (an explicit formula!) for solving the n-th order equation is essentially the same as the 1st order one. After solving completely the linear equation the author moves on to the non-linear case, again up to the n-th order. The idea seems quite simple, yet no other customary text introduces ODE's this way. All the other authors begin with the 1st order equation mixing up the linear and the non-linear cases, and continue their exposition following the same fashion, leading the student to misunderstand a very subtle and important feature of analysis (and mathematics): the great difference between linearity and non-linearity. The way this book is written shows clearly this crucial phenomenon.

Another valuable feature of this book is its complex-number approach which leads to straightforward computation of explicit formulas for the solutions of linear equations. Other texts give no more than the sketch of some methods which have to be performed every single time, and most of them don't even justify those methods rigorously.

Conclusion: Superb book. Excellent as a course text.

Please read my other reviews at my member page (click on my name above). ... Read more

Book Description

Thirty years in the making, this revised text by three of the world's leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.

The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field's Medal for his work in dynamical systems.

* Developed by award-winning researchers and authors
* Provides a rigorous yet accessible introduction to differential equations and dynamical systems
* Includes bifurcation theory throughout
* Contains numerous explorations for students to embark upon

NEW IN THIS EDITION
* New contemporary material and updated applications
* Revisions throughout the text, including simplification of many theorem hypotheses
* Many new figures and illustrations
* Simplified treatment of linear algebra
* Detailed discussion of the chaotic behavior in the Lorenz attractor, the Shil'nikov systems, and the double scroll attractor
* Increased coverage of discrete dynamical systems ... Read more

Reviews (1)

New Edition
You should be aware that there are two similar books with similar titles by the same authors. The old edition is a hardcover all green book by Hirsch and Smale called:

"Differential Equations, Dynamical Systems and Linear Algebra"

The second with the lorenz attractors in yellow on the cover is by Hirsch, Smale and Devaney and is called:

"Differential Equations, Dynamical Systems and an Introduction to Chaos"

Now, that may be obvious to you, but it is important to note that because those are VERY different books (which I have both of right here). The 'old' one is a more theoretical text that mainly addresses linear systems and is organized more like a math monograph than a contemporary (i.e. with pictures and examples) textbook. It is difficult for most people. The newer version is COMPLETELY different and is written for a more diverse audience. It starts with linear systems but then goes into nonlinear systems and discrete systems. It is somewhat similar in character to Strogatz's Nonlinear Dynamics and Chaos. If you do not have a very strong abstract theoretical type of math background I would not recommend you start learning about differential equations from the "old" edition. You will find it very difficult. If you are used an general abstract presentation of results you should be fine. For the NEW edition the level is very different. I would guess that courses in multi-variable calc, elementary diff eq, and linear algebra (if you understood them) would be sufficient preparation. Both books are excellent, just be clear on what you are looking for. ... Read more

Book Description

The Fourth Edition of the best-selling text on the basic concepts, theory, methods, and applications of ordinary differential equations retains the clear, detailed style of the first three editions. Includes new material on matrix methods, numerical methods, the Laplace transform, and an appendix on polynomial equations. Stresses fundamental methods, and features traditional applications and brief introductions to the underlying theory. ... Read more

Reviews (4)

Not perfect but a very good intro to ODEs.
Although this text has its problems, its an overall strong introducton to ODEs. Just exactly like another reviewer said, Some techniques (such as the operator method) are not given enough attention, while others are given a little too much attention. The applied sections can get a little flaky as well (Why the author does not use metric units is beyond me)

That being said, it is a very clearly written book. It is rarely (if ever) confusing, and the examples are generally good. His language and notation is not difficult to understand, and the plainly written style is a plus for any beginner to differential equations. I used this in my ODE class and this book alone is enough I would say. If it were a little more balanced with the methods and had a more robust applied sections I would give it five instead of four stars.

A nice book for beginner
I rated this five stars for several reasons:
1. English isn't my native language. But when studied ODE in
sophomore life, I could read this book thoroughly without
any difficulty. It's style is clear, plain.
2. For a beginner to ODE, I thought an "introduction" is most
important. This book undoubtedly provides an introduction
to ODE and more to make you aspire to study other deeper
books.
3. "An example speaks more than thouand words of
explanation."
Besides giving you complete and good explanation, the book
also has wonderful examples to them. Read the explanations
and examples, then do execises.
I found that I had more clear concepts about ODE than others.
Thank you, Mr. Ross. ^_^

A good book on ODE
I used this book when I was an undergrad student...as far as I can remember it is an easy to read book. The exercises are well chosen and helps to reinforce the basic principles quite well. In other words, whatever is discussed in that book is discussed well. However, some very important techniques in solving ODE's are left out such as the operator methods which could been easily integrated into the text. Instead, methods such as variation of parameters and undetermined coefficients are discussed at length. Furthermore, more emphasis should have been given to the Laplace transform. That is the reason why the book was given 4 stars. Overall, Ross' book is a good introduction to ODE and the interested undergraduate student would most likely enjoy reading it.

UC functions
My idea for finding a particular solution for linear differential equation by using UC function is too long and unnessary .The varition of parameters is enough for finding a particular solution. ... Read more

Book Description

Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie's striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail.
* This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory
* Includes a concise and self contained introduction to differential equations
* Easy to follow and comprehensive introduction to Lie group analysis
* The methods described in this book have many applications
The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems. ... Read more

Reviews (1)

Sharing my joy
It is wonderfull to find in this book that the need for the theory flows directly from ordinary problems in diferential equations, in one or more variables. The text is adorned with good physical examples and many otherwise mysterious things fit in place. ... Read more

Book Description

"A good book for a nice price!" Monatshefte fr Mathematik ". . . for lecture courses that cover the classical theory of nonlinear differential equations associated with Poincar and Lyapunov and introduce the student to the ideas of bifurcation theory and chaos this is an ideal text . . . " Mathematika "The pedagogical style is excellent, consisting typically of an insightful overview followed by theorems, illustrative examples and exercises" Choice ... Read more

Reviews (3)

Springer dropped the ball
Over all, Verhulst does a ressonable job of conveying the central ideas of the topic. I found it to be slow going for a couple of reasons: First, it's clearly a translation and Springer should have done a better proofreading job ... many of the sentence constructions are unusual for English which is, at the very least, distracting. Second, there are substantial gaps in some of the arguments ... maybe ok for a book at this level, but it often creates considerable frustration.

In contrast, the book by Jordan and Smith (Nonlinear Ordinary Differential Equations) has few flaws and, in my view, should be read first.

This book is not even reasonable
This book was not written for an student of ODE, he was written to the author himself!

This book was used in a course of PhD here in Brazil and the results were very negative. I strongly don't recomend this book... Avoid it...

This book takes you by hand through dynamical systems theory
What I like more of this work is tha the autor explains all theconcepts he is using, so it is ideal for people who is a naturalscientist but not necesarilly knows all the formalism of modern mathematics. It is not hard to read and covers the basics for study recent research papers. END ... Read more

Book Description

Boundary Value Problems, Fourth Edition, continues to be the leading text on boundary value problems and Fourier series. The author, David Powers, has written a thorough, theoretical overview of solving partial differential equations by the methods of separation of variables. The text is comprised of five comprehensive parts which include: a prerequisite summary of ordinary differential equations, Fourier series, and solving linear partial differential equations by separation of variable methods, by Laplace transform methods, and by numerical methods. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering problems.

* New section on Error Functions in Chapter 2
* New section on Applications of Legendre Polynomials in Chapter 5
* Provides the most comprehensive treatment ofThe Potential Equation
* Detailed coverage of Laplace Transform
* Presents Numerical Models in Chapter 7
* Addition ofabout 75 new exercises, including problems from current engineering literature with authentic parameter values ... Read more

Reviews (3)

Okay book written at a low level.
This book is good for a first course in PDE's at the undergradute level. It teaches you very little theory and most of the problems seem to be little more than a slight change in examples. The book seems to be more aimed for engineering majors than math majors. My suggestion is if you need it for a class buy it, if you are looking for a book for reference or to learn PDE's by yourself check out something else.

excellant graduate level work
Used as a text in my Boundary Value Problems class at Prairie View A&M University. I found the text very readable and the numerous problems challenging, but not too difficult at all. Powers has written an excellant work for anyone who wishes to learn the heat equation, and wave equation. His worked out answers to selected problems is very helpful for the student. This book is a keeper to be used for reference after the class.

An easy to read thorough treatment on all aspect of DE's...
I originally purchased this text to help with my study for an undergraduate course in Partial Differential Equations and Waves. From start to finish, this book always presents the material in an easy to read and easy to understand manner.

Generally, the book gives a really good understanding on the topics of solving ordinary differential equations, and then the various types of partial differential equations, such as the heat equation, where the solution methods involved can be confusing at times. The book also has a large selection of worked examples and wide ranging practise problems.

The book has the effect where even if the reader is only armed with basic undergraduate calculus, it gives them a very good understanding of the material in a short time. ... Read more

Book Description

This volume provides an introduction to the properties offunctional differential equations and their applications in diversefields such as immunology, nuclear power generation, heat transfer,signal processing, medicine and economics. In particular, it dealswith problems and methods relating to systems having a memory(hereditary systems). The book contains eight chapters. Chapter 1 explains where functionaldifferential equations come from and what sort of problems arise inapplications. Chapter 2 gives a broad introduction to the basicprinciple involved and deals with systems having discrete anddistributed delay. Chapters 3-5 are devoted to stability problems forretarded, neutral and stochastic functional differential equations.Problems of optimal control and estimation are considered in Chapters6-8. For applied mathematicians, engineers, and physicists whose workinvolves mathematical modeling of hereditary systems. This volume canalso be recommended as a supplementary text for graduate students whowish to become better acquainted with the properties and applicationsof functional differential equations. ... Read more

Book Description

The present book builds upon the earlier work of J. Hale, "Theory of Functional Differential Equations" published in 1977. The authors have attempted to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a completely new presentation of linear systems (Chapter 6-9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global attractors was thoroughly revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (Chapters 1,2,3,9,10). Chapter 12 is also entirely new and contains a guide to active topics of research. In the sections on supplementary remarks, the authors have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. ... Read more

Book Description

This book integrates both classical and modern treatments of difference equations. It contains the most updated and comprehensive material, yet the presentation is simple enough for the book to be used by advanced undergraduate and beginning graduate students. This third edition includes more proofs, more graphs, and more applications. The author has also updated the contents by adding a new chapter on Higher Order Scalar Difference Equations, and also recent results on local and global stability of one-dimensional maps, a new section on the various notions of asymptoticity of solutions, a detailed proof of Levin-May Theorem, and the latest results on the LPA flour-beetle model. ... Read more

Reviews (8)

An Introduction to Difference Equation
El texto An Introduction to Difference Equations del profesor Dr. Saber N. Elaydi ha sido utilizado en reiteradas ocasiones, en el curso Ecuaciones en Diferencias Finitas, dictado por el profesor Dr. Julio López, de la UniversidadLa Frontera de Chile, curso del cual, este semestre soy alumno.

El texto del profesor Elaydi, es un libro que explica de forma amena, clara y precisa, distintos tópicos de Ecuaciones en Diferencias. Comenzando el estudio de los primeros conceptos a tópicos avanzados del tema, destaco dentro de sus muchas cualidades el gran número de ejemplos y aplicaciones expuestas en distintas áreas de las ciencias, además de gran cantidad de ejercicios propuestos, lo que permite al alumno practicar e internalizar las definiciones, proposiciones y teoremas estudiados.Me parece, sin lugar a duda, el texto más claro e interesante que he leído sobre el tema. Cabe destacar que este texto contiene tópicos, que en otros no son tratados. Otra importante cualidad del texto es, que aunque se tiene sólo ediciones en ingles, el profesor Elaydi, ha escrito su libro de tal manera, que no es un impedimento para los hispano parlantes, tenerlo como libro guía en nuestros cursos.

Alex R. Sepúlveda C.
Alumno de Ingeniería Matemática
Universidad de La Frontera
Chile.

One of the Very Best Introductions on Difference Equations.
Among the few introductory texts to difference equations this book is oneof the very best ones. It has many features that the other texts don'thave, e.g., stability theory, the Z-transform method (including a study ofVolterra systems), and asymptotic behavior of solutions of differenceequations (including Levinson's lemma) are studied extensively. It alsocontains very nice examples that primarily arise in applications in avariety of disciplines, including neural networks, feedback control,biology, Markov chains, economics, and heat transfer. Unfortunately, amongdifferential and difference equations, students usually only learn aboutdifferential equations, although many problems they encounter later can besolved using difference equations. Hence it is very useful for students tostudy difference equations (or even, dynamic equations, which canaccomodate differential and difference equations at the same time), and forsuch an undergraduate or beginning graduate course, Saber's book can beused as a textbook. It is particularly useful for such a purpose since itcontains many exercises and also many programs for the calculator TI-85.Although the first edition did contain several misprints, the secondedition has eliminated most of them. Saber's superb writing style makesreading this book very enjoyable.

Exceptional: the defintive book on difference equations
This book is a must read by all those mathematicians, scientists and engineers who like to understand difference equations and discrete dynamics. It contains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations. Ithas an extensive number of applications in a variety of fields from neuralnetwork to host-parasitoid systems. The most enjoyable part of the book isthe new chapter on continued fractions and orthogonal polynomials and thetotally revised chapter on asymptotics. The chapter on stability theory isby far the best exposition on the subject; it updates most of the materialin the popular LaSalle book. I enjoyed very much the lucid and transparentwriting style of Elaydi which many math books lack. I am planning to usethis textbook in my undergraduate course on differnce equations anddynamical systems in the Fall of 2000. There are some minor misprints anderrors that I was able to decipher. The author may need to considerpublishing a solutiion manual since some of the problems in the book arequite challenging. It is also desirable if the author post an errata on hisweb page and/or on amazon.com.

Needs an errata
A very readable text, but I noticed several annoying misprints, mostly involving references to equations, examples, and theorems within the text.

Recommended, but caveat reader.

a wonderful book that fits several levels
This is the best book on modern difference equations. It contains a wide range of material on difference equations and may be very interesting in applications in Physics, Biology, economics and other many subjects. It iseasy and readable for those who want a quick overlook on the subject. Atthe same time it is very deep and goes to high level and leads to manyresearch problems for those who wish that. I am so impressed by this bookthat I am going to translate it into Arabic through the Arabic Organizationfor Education, Culture and Science. Shortly , this is a wonderful book andI strongly recommended it to every scientist who is working and interestedin discrete models ... Read more