Book Description
Combining traditional material with a modern systems approach, this handbook provides a thorough introduction to differential equations, tempering its classic "pure math" approach with more practical applied aspects.
Features up-to-date coverage of key topics such as first order equations, matrix algebra, systems, and phase plane portraits. Illustrates complex concepts through extensive detailed figures. Focuses on interpreting and solving problems through optional technology projects.
For anyone interested in learning more about differential equations.
Customer Reviews:
this book should come with its own textbook.......2007-09-25
this book sucks-- plain and simple. Go and get some outlines and another textbook if you want to learn DiffE from this book. Examples are horrible, none of the problems correlate and this book just doesn't explain the in between steps. When i want to learn something, i need to see the complete though process, not spend hours trying to figure out how they got form point a to point b in the example.
Great companion to lectures........2007-04-27
The most important thing to keep in mind would be the intended audience of this book. Specifically, the concepts outlined in this text should complement the content provided by a legitimate math instructors. If I were to use this book to self-teach or something of the sorts, I'm sure I would hate this book as well. Although the examples are sometimes unclear, the summaries of techniques are the most helpful parts in the book. At the end of a section, a blue box outlining the fundamental steps in a process reveals the simplest way to approach any problem. For example, this text's summary of Variation of Parameters pretty much sums up everything about that process in a clear and concise way.
Anyways, it's not as if you have any other choice when the instructor assigns this text as a required material. If looking for a self-teach sort of book, this text is not that great. But if you're looking for a review of ODEs and whatnot, I would recommend this book.
Simply the best undergraduate text extant..........2007-04-18
and I don't "do" hyperbole.
As a math instructor (and math student), I have seen texts on everything from fundamentals of math to real analysis. This book is more practical, clear, and concise than any of them.
Students will not only learn techniques to solve differential equations, they will learn the scope and limitations of each technique. A student who truly reads and absorbs this book will walk away with not only an understanding of but also a healthy skepticism toward mathematical models. The harsh realities of mathematical modeling, such as sensitive dependence on initial conditions, are emphasized rather than downplayed. In the section on motion problems, students are treated to a discussion of how solar system models have evolved. Models must adapt to explain new data. Sometimes a model can be "tweaked" at the expense of simplicity, while some models must be scrapped altogether. Scientific ideas are not gospel, but merely a description of the world as we see it today.
Unfortunately, this text is the ONLY book I have seen which truly addresses the issues described above (and that's very sad because my undergrad degree is in chemistry). Aspiring scientists and engineers need to learn intellectual flexibility as much as they need to learn facts and formulas. This book teaches both.
If the applications in this book were not so overwhelmingly excellent, I would have started this review by exalting the proofs and derivations. They too are unusually well done. The authors do an excellent job of choosing which proofs to include, and they make them as readable as humanly possible. (I hear the bitter chuckles of innumerable math students as I type the previous sentence...)
Yes, learning to read proofs IS hard. But, trust me, this book is where you want to start. First graders think adding and subtracting whole numbers is hard. They're right; for them, it is. But imagine how much harder it would be if first graders had to work with fractions!
To paraphrase Aristotle, "learning is painful". No one can make differential equations easy (why do you think scientists and engineers get paid so well?). However, the authors of this text make it as easy and pleasant as possible.
I suspect that students who disliked this book but were able to "learn" diff. eq. merely learned enough to pass the test. Students who do not take advantage of the learning opportunity provided by this book are doing themselves a serious disservice.
Take home message- buy it and make it the central element in your studies of differential equations. You will be glad you did.
lack of examples and horrible explanations make a ghastly diffE text.......2005-10-13
Because the guy who initiated the project of writing the book is here at Rice, the rest of us are unlucky enough to have to use this book. If your class uses this book, prepare to go to class. All the time. That's because if you fall behind, the book does not do a good job of explaining things to you. Examples are generally vague and only apply to a few types of problems provided at the back of each section. A lot of the time, I'd find myself stumped on a problem, looking back, and realizing there was no example problem for me to get ideas from.
Yes there are lots of problems and that's good, in a way. But what's the point of having all those problems if the book never teaches you how to do them?
Furthermore, it is a poorly written book. Generally, reading through the book is like searching for a needle in a haystack. Literally speaking. You spend all that time figuring out what the authors talk about and once you figure it out, it was not even worth all that time.
So go to class. All the time. If the prof isnt that great, get yourself another workbook. I havent seen Schaum's but I'm pretty sure they'll do a better job on covering the topics than this text does.
Worst book in Undergrad Career.......2005-01-13
tulane uses this book exclusively for diferential equation. This is t quite possible the worst text book i have ever used. They like to say that they don't put as much emphasis on specific solution techniques as they do to solving pratical equations. this means solution methos a briefly mention then sections up section are made of problem you should be able to solve if you were to know the solution methods. some sections don't even over solving differential equations at all.
Book Description
Master differential equations and succeed in your course DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS with accompanying CD-ROM and technology! Straightfoward and readable, this mathematics text provides you with tools such as examples, explanations, definitions, and applications designed to help you succeed. The accompanying DE Tools CD-ROM makes helps you master difficult concepts through twenty-one demonstration tools such as Project Tools and Text Tools. Studying is made easy with iLrn® Tutorial, a text-specific, interactive tutorial software program that gives the practice you need to succeed.
Customer Reviews:
diffcult text for the DE student .......2007-09-24
The written derivations and examples were brief and difficult to understand. I gave up on using this book for learning DE,only use to practice problems required for assignment. After finding alternative study links, did the DE aspects become clearer. Solution manual did not bring much to the table either.
other DE books to choose from.......2007-04-18
I've run down most, if not all, of the available introductory DE books in my review of Boyce/Diprima (a book to be avoided by the way): Elementary Differential Equations and Boundary Value Problems , 8th Edition, with ODE Architect CD
ADVANCED MATHMATICS.......2006-07-25
IT'S A GREAT BOOK FOR MATH LOVERS. YET IN THE EXAMPLES THROUGHOUT THE BOOK THE AUTHOR SKIPS MANY STEPS, SO YOU HAVE TO KNOW ALGEBRA, INTEGRATION, DIRRENTATION, AND SUMS VERY WELL TO UNDERSTAND WHAT THE AUTHOR IS DOING.
Dense; Not for Self Study........2005-02-12
VCR directions. Especially how it explains variation of parameters (2.3). If you are a math whiz, this text is for you. If not, try to get a copy of Dr. Kapoor's _Differential Equations: Step by Step E-Z Math Cards_. By the way, Zill's Solutions Manuel simply omits explanations for many odd-numbered problems, so good luck.
Old, but good.......2004-12-31
This is a good introduction to DE without alot of the unnecessary textual pollution often found in math texts. It's been around awhile (I used this one some years ago) but I found it was among the simplest, clearest, and best-written math texts because its approach assumes no prior knowledge of DE. From basic equations such as the famous Bernoulli to more complicated boundary-value issues, I was able to gain a solid and more complete understanding of the multivariable calculus I had just attended as well as preparation for higher math. Although it's been awhile, I do recall some errors in this book (as another reviewer has mentioned), so be aware.
Recommended.
Book Description
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: 1) representation formulas for solutions, 2) theory for linear partial differential equations, and 3) theory for nonlinear partial differential equations.
Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and much more.
The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he emphasizes the modern interplay between functional analytic insights and calculus-type estimates within the context of Sobolev spaces. Treatment of all topics is complete and self-contained. The book's wide scope and clear exposition make it a suitable text for a graduate course in PDEs.
Customer Reviews:
A Fine Treatise on the Subject.......2007-05-02
This is a superb exposition of a difficult, yet enriching subject. This book is intended only as a beginning text (in a relative sense) and is by no means an attempt to give an exhaustive view of many topics discussed therein.
The first few chapters discuss classical solution techniques to frequently encountered PDEs such as the heat and Laplace equation. Methods of solution are discussed including Fourier transform methods and other classical methods to obtain strong solutions and/or representation formulas. The author, from this point, focuses on weak solution techniques for second order PDEs and systems in addition to conservation laws and other nonlinear PDEs. There is also a self-contained chapter on Sobolev spaces that proves to be fairly useful.
There is a necessary mathematical maturity needed to fully benefit from this text. The reader should be relatively comfortable with standard topics from classical analysis. It would help if the reader has seen Lebesgue spaces and is familiar with basic functional analysis and operator theory although many of these topics are reviewed in the apendices.
While this book is dense and difficult at times, it has a prominent place on my bookshelf.
Solid opening, weak ending........2007-03-04
If you are just getting started in learning PDEs and want to see all the classical problems/solutions (Poisson, Laplace, Heat, and Wave Equations), then this book might be a little advanced for you, but it is solid in this content if you have a solid background in analysis (probably best to have at least one high-level analysis class that covers all the multivariable calculus material as you will find that your ability to identify and use Green's Theorems will make life much easier as you get started). This is considered "Part I" of the book.
Once you have covered all the nice problems that don't exist in practice, you are ready to move onto general linear PDE theory in Part II of the book. I would recommend you complete a course in measure theory before you start in on chapter 5, which covers Sobolev spaces. I would then recommend that you complete a course in functional analysis before starting chapter 6 or 7 (chapters 5-7 are Part II of this book). This is not necessary as you will have access to a fairly complete appendix of functional analysis results in this book, but once you understand functional analysis and measure theory, then you will be able to grasp the idea of an elliptic (or in chapter 7, parabolic or hyperbolic) operator acting on a function space (the function space being a Sobolev space) more easily and these ideas won't seem so abstract. Overall, the second part of this book is great if you have a lot of the prerequisites I just suggested because many of the proofs can easily be made to be three to five times longer as many steps that link ideas in functional analysis are skipped. The proofs on higher regularity will be hard to understand your first time through, so I wouldn't worry about it too much. Read through the chapters and then read through the regularity stuff again. If you just want to get the basic ideas you can skip either the parabolic or hyperbolic section in chapter 7 because the techniques in solving either type of problem are fairly similar.
Once you are done with the linear PDE theory and are ready to start chapter 8, I recommend putting the book down and getting a different one. Evans gets fairly abstract in the nonlinear part of the book (Part III). I would recommend getting "Navier-Stokes Equations: Theory and Numerical Analysis" by Temam as it is a great source for nonlinear PDE theory and has more results and better proofs than Evans on this subject. I just feel like the Evans book is a great book to learn from for your first two semesters of PDEs at a graduate level, but after that it is time to change texts.
The best book in PDE.......2007-01-12
If you want to learn PDE you have to study this book... as simple as that.
Review of Book that i bought........2006-08-05
Partial Differential Equations (Graduate Studies in Mathematics, V. 19) GSM/19 (Graduate Studies in Mathematics)
The Book i bought was in good condition and was sent in time. The price of the book was also very reasonable and the packing was very good.
I have good words for Amazon about my first purchase.
The best book for an introduction to PDE's for a graduated student.......2006-06-07
If you're looking for a book to learn PDE's at a basic level, please don't buy this book. In the other hand, if you have already worked on this subject it's not surprising why the book doesn't include some topics or techniques. The appendix is for remembering basic facts while you are reading, so if you don't acknowledge this subjects, you have to study them before (you can't ask a book to have an appendix that covers all the related theories you need).There are several books which cover very well the classical theory and the linear cases in the weak sense. As one of the reviews says, this is an excellent book for a GRADUATED COURSE so it is assumed you have a basic background on the subject and you know what you should know about other subjects such as analysis. The book has the basic tools for THE NON-LINEAR CASES which can't be seen in a basic course. If you don't believe me, try to find a book which cover the same content in such an easy way.
Book Description
Incorporating a modeling approach throughout, this exciting text emphasizes concepts and shows that the study of differential equations is a beautiful application of the ideas and techniques of calculus to everyday life. By taking advantage of readily available technology, the authors eliminate most of the specialized techniques for deriving formulas for solutions found in traditional texts and replace them with topics that focus on the formulation of differential equations and the interpretations of their solutions. Students will generally attack a given equation from three different points of view to obtain an understanding of the solutions: qualitative, numeric, and analytic. Since many of the most important differential equations are nonlinear, students learn that numerical and qualitative techniques are more effective than analytic techniques in this setting. Overall, students discover how to identify and work effectively with the mathematics in everyday life, and they learn how to express the fundamental principles that govern many phenomena in the language of differential equations.
Customer Reviews:
Unique, Impressive.......2007-07-11
Great for learning. Poor for reference.
This book is unique. Most differential equations textbooks simply provide formulae for different types of problems, but you don't really see the big picture. This book lets you see the big picture, but omits many of the most useful formulae that you may need in your career. This for that. It would be nice to see a book with the best of both worlds, but if you simply want to learn and understand the topic, this book is the way to go. Also, there is a good emphasis on qualitative and numerical techniques. Students often feel like they get less out of a mathematics class when qualitative and numerical techniques are emphasised over more analytic approaches. However, those of us who have worked in the "real world" know that the qualitative and numerical techniques are probably even more important. I have worked as a research statistician and my research areas emphasise computing. When I'm presented with real problems and real data (which, in my career, usually comes in large, unmanageable quantities), do I usually pull out my notebook and tackle the problem in a very precise manner, working out an exact solution? No, quite often I cannot realistically do that. Now I'll admit that I don't use much from this particular field on the job, but it still applies. Moving on, I must also mention that the book does a very good job at explaining these qualitative and numerical techniques in addition to things that are more analytic, although it sometimes a little too verbose.
Regarding applications, the book covers a lot of fields and does put a big emphasis on applications. Physics, biology (especially population growth models), and electrical/computer engineering receive the most treatment. Overall, I would say that the book does an excellent job at including plenty of applications and choosing meaningful ones.
I don't have much to say about the exercices. Most aren't too contrived and they mixed up the difficulty fairly well. However, I would have liked to see more "hard" problems.
In summary, I'd recommend that you pick up a different book if you need a reference for work or research, but pick this one up if you actually want to learn and UNDERSTAND the basics of differential equations.
ODE.......2007-02-07
So i really hate this book... it give maybe one example of certain concepts and they are not even that descriptive. i might just be use to my other math books... but coming from a girl who is a math major, i would stay away!!!
for weak students........2005-12-08
the main objections i have to this book, are similar to others here:
1) much too expensive for what you get.
2) much too verbose for what is being said.
the masterful book by hurewicz from the 1950's covers the same ideas of dynamical systems and geometrically oriented o.d.e,'s but in succint, clear, deep, and well organized prose.
and i bought a copy of hurewicz for 5 bucks last week.\
even the vaunted exam ples of this book, such as the tacoma narrows bridge disaster, is cribbed from other books like braun.
but to ask a poor student to lay out 130 dollars for an inflated ripoff of better, shorter, cheaper books, is morally wrong, and as a professor i will do a lot to avoid it.
Poorly Organized, Slow, Insufficient Depth.......2005-09-23
I don't like this book; it's like most undergraduate differential equations books. It moves slowly yet doesn't explain things in enough depth.
The order in which topics are presented is chaotic; one moment one is using an analytic technique and then the next moment the book switches into discussion of qualitative methods; the reader never gets a feeling of mastering one or the other. It's hard to skip around in the book because it's hard to sort out which material builds on previous material.
The book presents diffeq as a chaotic, hodge-podge subject, which might be accurate, but this leaves the reader confused and without an overall picture of what diffeq is.
Relative to the volume and cost of this text, you will learn very little from it. Among the "big" undergrad texts I prefer Boyce and DiPrima, although only slightly. The best introductory books on differential equations are from the Springer-Verlag series, in my opinion: check out the text by Braun or the other one by Hubbard...both are listed in my reviews.
Fun to read!!.......2005-09-02
Normally I get the homework from the professor and that is usually the only time I crack open any textbook. However, with this book I was able to enjoy the authors' humor and clear description of the material. It is true that the answers in the back of the book are not very helpful, but I think I think the book is written well enough to help you get to the right answer. Furthermore, the CD that comes with the book is not compatable with Mac OS X, but if your University has access to Maple, Mathematica, or Matlab there is no real loss in not being able to use the CD. I would disagree with one of the book reviews that graphical solutions are not important to science majors. Analytical solutions are extremelly important to science and that is why this book is heavy on the graphical solutions, and as a physicist I find these problems and examples the most useful.
Book Description
This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications. The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the book. For mathematicians and those in the field of computer science.
Customer Reviews:
Could be better.......2005-11-20
I don't think this is a good book for learning from, but if you know the material, it is a good reference.
Differential equation text.......2005-09-26
The textbook was in good condition and i recieved within a week
Pretty good.......2004-04-26
Not a bad book at all. Physical applications well explained, theory OK but not as good in my opinion. Unfortunately, contains a fair number of typos, and the book is physically weak (the binding of mine is splitting after only 4 months of use) for a book of this price. Still, pretty good overall.
A good differential equations textbook.......2003-08-12
I think the strength of this textbook is the amount of material it encompasses: this book is used in two separate courses in my school--introduction to DE and engineering analysis. I didn't appreciate the textbook so much until I completed my differential equations course and then looked back at the sections on mechanical vibrations to review for my physics course. I then realized that the explanations and derivations were extremely satisfying, much more than your average introductory physics text. Also, the emphasis on the qualitative aspects of DEs, such as slope fields and phase portraits, aid in the coneptual understanding of the otherwise rigorous computation aspects of the topic. My only complaint is that the proofs could've been done in a more understandable manner.
NO!!!!!!!.......2003-07-17
On the whole I wasn't satisfied with the book. In all fairness I did take DE as a summer class. Maybe that's why I don't have fond memories of this book. I'm not an engineering major. I'm not physics major. I found the books almost constant reliance on engineering and physics to introduce concepts to be very disappointing. I think the book lacks balance. Also I found some of the examples lacking. I found better explanations of identical topics in my calculus book (Larson) and in my linear algebra book (Kolman). An engineer that I know tried to use the book to review some stuff and found it fairly useless. Dover makes some good cheap DE book.
Book Description
This revision of the market-leading book maintains its classic strengths: contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. Like its predecessors, 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. Sound and Accurate Exposition of Theory--special attention is made to methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace development of the discipline and identify outstanding individual contributions.
Customer Reviews:
Differential Equations with BVP.......2007-09-25
Good book, and covers a well range. JustAsk is a feature they have for an extra cost. While I think it is better then the pearson prentice hall books and online content it still skips steps with eigen values and vectors.
obfuscatory.......2007-06-27
The book tries to make things simple and fails miserably. The round-about explainations are confusing. The maladroit, verbose language obfuscates what they are trying to impart. (It's curious that the 5th edition I looked at is often clearer than this 8th edition, and it's shorter too.) What ahould be simple and direct is convolved (no pun intended) into meandering examples unworthy of the name, the point of which often a mystery even to those who are very experienced with ODEs, and obfuscatory verbosity. I'm baffled as to how they book's author (or anyone) thought this might be a useful style. If you are a Professor, then please be nice to the kids and don't use this. If you are a student, I strongly recommend you buy an additional textbook; it would amaze me to see anyone learn ODEs from this; it should be at least possible, albeit difficult, to learn the subject from a textbook alone.
Great text for ODE's class.......2007-06-01
I used this text in my ordinary differential equations class and found it to be very helpfull. This text had good coverage of material for an upper class undergraduate or first year graduate course. Each subject was introduced in a clear manner with a detailed outline of the derivation of the method being used. I had another text while I was taking this course and the authors of that text would give you a theorem and then the method or formula to solve your given problem with no connection between the two. This book was very best in allowing you to gain a deeper understanding of what you were doing. The authors did clearly state the theorems, but did lack in proof in most cases. They did gave an outline to proof most of the time, which was helpful in working my own proof. Overall this text is a good one and I would strongly recommend it.
Dont be fooled........2007-04-17
Those of you that believe those 5 star reviews are true, forget it. After passing a course of differential equations throughout a grueling semester I can certainly attest to the latter.
This book has horrid if not completely non-existent examples and even the solutions manual is nearly worthless. If you've spent more than a semester without calculus you might as well forget trying to use this book in a formal course.
Perhaps if you're a "bright" student you could make use of this book, though still it is absolutely no testament to professional teaching methodology. If you intend to learn the subject for any moderate application, look elsewhere. This book has no practical application examples worth any salt. This book is not for engineers; most certainly it's best application being for theoretical mathematicians.
If your instructor requires this book, and you're an engineer, you'd better start hoping he's a darn good instructor.
this book is a disgrace to mathematics.......2007-03-27
If I didn't have better things to live for, I would dedicate my life to hating this book. It's TERRIBLE! Visual learners shudder and linguists are baffled left and right. The examples don't match up AT ALL with the exercises and the book is not succinct at all, whatsoever. There is no elegance. This book is a disservice to mathematics. PLEASE, if your instructor requires this book, CHANGE INSTRUCTORS.
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
Customer Reviews:
A new version of a classic book.......2007-02-21
I bought a copy of this new book and I have its old version with Hirsch and Smale as its only authors. Main differences between these books are some new chapters covering chaos and the exercises. Old version has better chapters dealing with linear algebra. I find this new version hard to read and it leaves many details to be filled by the reader. I would say that the new version is still a good choice for a second course in ODE or supplementary text for a graduate course. I gave it four stars.
Excellent Book.......2006-05-05
This is a great introduction to the next stage of differential equations after a first course. Devaney is a master of presenation, and makes everything seem easy. It is not as encyclopedic as some other books on this material, such as Arnold and Perko, but it is easier to read and still covers the most important advanced material.
good, not ideal.......2005-12-08
the two books by hirsch smale, one with devaney, seem like good books, but I am not crazy about either, at least from the few pages one can search online here.
the latter book with devaney just seems a dumbed down version of the earlier book by the two more famous authors. i expected that earlier book to be far better, but found to my regret that the two books actually share almost the same first page, and the main difference noticeable in the early going is that the 2 author work is poorly written, and the 3 author one is not written much better.
it is clearer but seems to be talking down to the reader in an annoying way. so neither is the absolute pleasure to read that the wonderfully written text of arnol'd is, or the classic of hurewicz. i would skip these books and get arnold and hurewicz instead.
New Edition.......2004-02-26
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 to a 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.
Customer Reviews:
A very good textbook, just not quite right for me.......2007-01-13
As an instructor at a small college, I am called upon to teach nearly every course in the mathematics curriculum. Therefore, I spend a great deal of time trolling for textbooks, as I never know from one year to the next what I will be teaching. I examined this book for possible adoption as a text for a single semester course in differential equations. My conclusion was that it is acceptable, but since it contains enough material for a two semester sequence, it must be assigned a rank lower than those that cover only a single semester.
However, I do strongly approve of the pedagogical approach taken by the authors. Their use of blue highlighting for the important formulas is eye-catching and effective. As I scanned through the book it was sometimes easier to determine the topic of a section by looking for the equations that were in blue. The exposition made the material easy to follow and the many worked and varied examples make the coverage complete.
I was also pleased to see the occasional theorem with proof. While courses in differential equations are largely, "give the technique(s), here is how to use it", it is still an upper division math course and an occasional proof is certainly reasonable and effective. The authors also include a short set of technical writing exercises at the end of the chapters and there are plenty of exercises with answers to the odd-numbered ones included in an appendix. While I don't think that I would ever make use of the technical writing exercises, I am sure that there are others who would take advantage of the opportunity.
In conclusion, even though I was impressed with this book, I doubt that I would adopt it. The differences between differential equation texts tend to be rather small, so the fact that this book is suitable for a two-semester sequence is enough for me to continue to look elsewhere.
Fundamentals of Differential Equations, Sixth Edition.......2006-11-12
the book was in perfect condition just like the seller said so.
so poorly written.......2006-06-28
Wow, the examples are absolutely putrid. I am so disgusted with this book, universities are probably given some seriously cut rate deals on this book to use it. One simple example of the poor quality of this book is the following:
page 513
"...diagonal matrices, which are square matrices with only zero (0) entries off the main diagonal (that is, a(ij)=0 if i does not equal j); and column vectors, which are nx1 matrices. For example:
A=
(3,4,1
2,6,5
0,1,4)
B=
(3,0,0
0,0,0
0,0,7)...
Then A is a square matrix, B is a diagonal maxtrix....."
WAIT BACK UP! I thought if you were a diagonal matrix then you had zeros for all numbers except for the diagonal....remember if you have i rows and j columns in a square matrix then the only time i=j is along the diagonal and didn't the book already says that a(ij)=0 if i doesn't equal j? So why does B(2,2) have a 0? Is it because not all values in the diagonal can be 0 or is it because there is a typo? I don't know but if I pull out my linear algebra book or perhaps surf the web I can find out...but isn't that a waste of my time trying to make sure these people are just using poor notation or pressed the wrong key? I think so. I certainly would never use this book again nor would I ever use it as a reference. I actually went and picked up another book for diff eq that I use along side this terrible book, and the only reason I keep this diff eq book by nagle is so I can refer back to the table of contents for topics when my teacher says which chapters the test are on.
Pretty Standard Textbook.......2005-05-27
I just finished a class that used this textbook, and I had no real problems with it. I've seen some really poor reviews on this book which I think are unwarranted. This may not be the best book around, but it is certainly not the worst. Put simply, this is an average textbook. It is neither outstanding, nor terrible. I did find the wording awkward in places. For example, Theorem 1 regarding existence and uniqueness is stated as,
===============================================================
"Given the initial value problem,
dy/dx = f(x,y), y(xo) = yo,
assume that f and the partial derivative of f with respect to y are continuous functions in a rectangle
R = { (x,y): a
< x
< b, c
< y
that contains the point (xo, yo). Then the initial value problem has a unique solution phi(x) in some interval x0-delta
< x
< x0 + delta, where delta is a positive number."
================================================================
Using the phrase "assume that..." seems to completely de-emphasize the salient point which is that,
================================================================
IF f and the partial derivative of f with respect to y are continuous functions in a rectangle...
THEN the initial value problem has a unique solution phi(x) in some interval....
================================================================
But this is a fairly minor complaint, and mostly just a matter of personal taste. I am grateful that I had a good instructor though, as he was able to pull out the important points that were not obvious from the text.
On the plus side, the book has an excellent Student's Solutions Manual by Victor Maymeskul. For the most part, all the odd numbered problems were thoroughly worked and explained. I would highly recommend getting the solutions manual.
Bottom line, if this is a textbook for a class, don't worry about it. The book will be just fine, and a good instructor will be able to use it effectively. If you want a book for self study, this may not be the best at clearly explaining concepts, but at least with the solution manual you will have lots of practice problems you can work and check. For self-study, you might check out "Ordinary Differential Equations" by Morris Tenenbaum and Harry Pollard. I have not used it extensively, but it seems to be quite clearly written, and has generally received good reviews.
An excellent text.......2004-06-23
I used the fifth edition of this textbook for my differential equations class, and since then I have continued to use it. The examples do a thorough job of explaining new concepts, as long as the reader is comfortable with working along and filling in the extra steps (Actually, in my opinion, this should be the standard method for learning from a textbook).
Since my first differential equations class, I have encountered some difficulty understanding partial differential equations, particularly heat equations and vibrations of a spring. The textbook I use for my intermediate engineering math course that I am covering this material for does a sloppy and incoherent job. However, using this book as a reference I was able to break down the process to "discovering" partial differential equations and am on my way to understanding at least heat equations and vibrating strings rather well. This book also clearly facilitates the reasoning behind fourier series and transforms.
I highly recommend this book. Although I didn't have much choice in selecting it for my courses, its use after the end of the intended course certainly exemplifies its value.
Average customer rating:
- very nice conceptual overview
- Not for the practitioner
- Trash
- Excellent Introduction, Sparse on Details
- A Good Introductory Survey
|
Scientific Computing
Michael T. Heath
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ASIN: 0072399104 |
Book Description
Heath 2/e, presents a broad overview of numerical methods for solving all the major problems in scientific computing, including linear and nonlinear equations, least squares, eigenvalues, optimization, interpolation, integration, ordinary and partial differential equations, fast Fourier transforms, and random number generators. The treatment is comprehensive yet concise, software-oriented yet compatible with a variety of software packages and programming languages. The book features more than 160 examples, 500 review questions, 240 exercises, and 200 computer problems. Changes for the second edition include: expanded motivational discussions and examples; formal statements of all major algorithms; expanded discussions of existence, uniqueness, and conditioning for each type of problem so that students can recognize "good" and "bad" problem formulations and understand the corresponding quality of results produced; and expanded coverage of several topics, particularly eigenvalues and constrained optimization. The book contains a wealth of material and can be used in a variety of one- or two-term courses in computer science, mathematics, or engineering. Its comprehensiveness and modern perspective, as well as the software pointers provided, also make it a highly useful reference for practicing professionals who need to solve computational problems.
Customer Reviews:
very nice conceptual overview.......2006-07-22
Wow, people seem to be really split on this book. I had Mike Heath for numerical analysis/scientific computing and he was an excellent instructor, one of the best lecturers I've ever had. (As a consequence, I have a hard time separating the book and the class, so judge accordingly.) The book is based on his lecture notes, though he added some material and didn't cover every topic in the book. Just reading the book is useful to give you an overview of the point behind different methods. The goal of the class for which this book was written is actually quite conceptual. It was to give scientists (that's me: a stats researcher who makes heavy use of numerical computation) and CS people in areas other than scientific computing a leg up. It was only a first class for people in scientific computing, the rough equivalent of intro Physics or intro Probability/Stats for people in those respective majors. However, you *won't* be prepared to "roll your own" from this book. In fact, at the beginning of the semester Heath was very careful to note that if you have the opportunity to use a library function for most numerical programming, you are nuts to roll your own. Why? Numerical algorithms are usually extremely complicated and the authors of the code often spend years developing careful expertise on them. Frequently the formulas used to elucidate a given method are NOT the ones used to implement it. You need error traps, tricks to handle ill-scaling and other special cases, etc. These are things that someone who has a one-semester, superficial understanding of a topic simply won't have. So consider the book on the goals it set: it is an overview of a field. If you want to learn more about any one topic, you have to dig deeper and consult references and other works, but this is a good place to start. For this, the book serves admirably.
Not for the practitioner.......2005-11-17
If you are interested in Scientific computing from the viewpoint of the end user that is the guy who uses the method to solve practical engineering problems then this book is lacking.
Not enough methods in this book to constitute an introductory survey of the field. Every chapter gets heavy dose mathematical treatment, apparently Heath loves his math but for the rest of us it doesnt translate into know-how. Know how to solve equations using computational techniques. Very few derivations to back his mathematical swagger, very few examples (if any) and fewer numerical schemes to solve problems. Many of the chapters receive cursory treatment such as PDE's get about 70 pages of print. Far too little to do anyone any good.
He does talk about interesting issues such as conditioning and error analysis and computer precision and memory issues but it is done from such a superficial viewpoint that one cannot use anything to improve ones code. Not recommended if you want to learn numerical methods even if you have an excellent professor to learn from. His chapter on FFT's was even more abstruse and there was hardly any methods with which to solve PDE's.
I had this for a graduate course in Numerical Methods but ended up using Hoffman's excellent book on Numerical Methods.
Trash.......2005-10-14
If you want to have a solid understanding of numerical computation, this book is definitely the last choice. Many theorems are given without any proof or even intuitions behind them in this book. Even when a proof is provided, it's often far from rigorous. The organization of chapters is the worst I have ever seen, revelant materials are scattered over several different locations rather than put together. Take the SVD for example, it is mentioned in the end of chapter 3, but reappears in chapter 4, which is very confusing. If you are new to this area, please don't read this book. It gives you many many facts without explanations, which I think is not a good way to learn new things. David S. Watkins' Fundamentals of Matrix Computations is a lot better and easier to understand. It also emcompasses many detailed treatments of various theorems. If you have bought Heath's book, don't be sad, at least it can serve as a coaster.
Excellent Introduction, Sparse on Details.......2004-11-20
While sparse on the details of many of the algorithms and theorems mentioned, as an introduction it covers a broad range of material-enough for two semesters of study. The writing is lucid, and when a proof of a theorem is given, it is easy to follow and explained in english afterward. Rationale is given for everything, which is a great benefit to a student not familiar with the nuances of sophisticated linear algebra.
A Good Introductory Survey.......2002-11-05
This book excels at presenting a reader with little to no knowledge in computer science and a mild mathematical background (knowledge of differential equations as a prerequisite) with the fundamental concepts regarding scientific computing. The presentation of pseudo-code algorithms helps smooth the transition from analytical (pencil and paper) thinking to numerical thinking. The algorithms are presented in a manner such tha anyone with access to dozens of possible environments can apply them, though they are by no means complete, thus requiring some thought into the processes. The material covered is 110% of what an engineer will want to know, 90% of what an applied mathematician will want to know, and 45% of what a numerical analyist will want to know. In all, a great book to begin a foray into numerical computing.
Average customer rating:
- Great introduction to mathematical economics!
- A must read text book for any economics undergrad student
- A must read for graduate students in economics
- not so good
- The best math textbook for economist
|
Fundamental Methods of Mathematical Economics
Alpha C Chiang
Manufacturer: McGraw-Hill/Irwin
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ASIN: 0070108137 |
Book Description
The best-selling, best known text in Mathematical Economics course, Chiang teaches the basic mathematical methods indispensable for understanding current economic literature. the book's patient explanations are written in an informal, non-intimidating style. To underscore the relevance of mathematics to economics, the author allows the economist's analytical needs to motivate the study of related mathematical techniques; he then illustrates these techniques with appropriate economics models. Graphic illustrations often visually reinforce algebraic results. Many exercise problems serve as drills and help bolster student confidence. These major types of economic analysis are covered: statics, comparative statics, optimization problems, dynamics, and mathematical programming. These mathematical methods are introduced: matrix algebra, differential and integral calculus, differential equations, difference equations, and convex sets.
Customer Reviews:
Great introduction to mathematical economics!.......2007-07-18
I enjoy Chiang's writing style. I've been reading up on mathematical methods in preparation for a masters econ program, and feel very comfortable with the material thanks to this textbook. The international edition is a good bargain.
A must read text book for any economics undergrad student.......2006-04-02
I found it extremely easy to read and at the same time rigorous enough to settle the bases. The author knows very deeply the economics students needs of mathematical methods and achieves a precise and complete explanation of all notions I needed to know for my undergrad course. I strongly recommend it during the first or second year.
A must read for graduate students in economics.......2006-02-26
Alpha Chiang's text should serve as the foundation for all quantitive analysis done in economic theory. It is an invaluable teaching tool for graduate students in economics and will help them better understand the mathematical techniques that have become so necessary for economic modeling.
I am not a highly quantitative person myself, but I found Chiang's book comprehensible and a useful reference guide in my gradaute economics classes. Along with Hal Varian's "Microeconomic Theory" and Jan Kmenta's "Econometrics", I would say that Chiang's "Fundamentals of Mathematical Economics" should serve as sacred literature for any prospective graduate student in economics.
not so good.......2005-10-14
the text carries to excess the concept of "keeping the presentation as simple as possible". but in general you cannot understand or solve problems with a fifth grader's ability to abstract them.
especially the relunctance to use matrix notation makes some topics actually harder to understand once they become more complicated.
furthermore I find the structure quite confusing since the text amounts to a monotous blabla - clear definitions might be helpful and some rigor would keep the reader conscious instead of drifting off. after all the text is not so bad but I think we deserve something better. blume might be better.
The best math textbook for economist.......2005-09-30
That is why it used everywhere, in nearly all economic departments. I strongly recommend you buy this book. It really helped me in my undergrad, and it is helping in my graduate courses. If you want to buy another book to accompany this, get Simon and Blume book. One person (probably little masochistic) was saying that Chiang has so many examples, blah, blah, blah. Look, not everyone is a math genius, undergraduate student's need Chiang, it's even useful for graduates. Math is used quite too excessively in economics...showing off?
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