Fundamentals of Differential Equations, Sixth Edition

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.

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?

Spectral Methods: Fundamentals om Single Domains (SCIENTIFIC COMPUTATION)

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Spectral Methods: Fundamentals om Single Domains (SCIENTIFIC COMPUTATION)
Canuto
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Accessories:

ASIN: 3540307257

Book Description

Since the publication of "Spectral Methods in Fluid Dynamics", spectral methods, particularly in their multidomain version, have become firmly established as a mainstream tool for scientific and engineering computation. While retaining the tight integration between the theoretical and practical aspects of spectral methods that was the hallmark of the earlier book, Canuto et al. now incorporate the many improvements in the algorithms and the theory of spectral methods that have been made since 1988. The initial treatment Fundamentals in Single Domains discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in smooth, global basis functions. The first half of the book provides the algorithmic details of orthogonal expansions, transform methods, spectral discretization of differential equations plus their boundary conditions, and solution of the discretized equations by direct and iterative methods. The second half furnishes a comprehensive discussion of the mathematical theory of spectral methods on single domains, including approximation theory, stability and convergence, and illustrative applications of the theory to model boundary-value problems. Both the algorithmic and theoretical discussions cover spectral methods on tensor-product domains, triangles and tetrahedra. All chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is greatly expanded as are the set of numerical examples that illustrate the key properties of the various types of spectral approximations and the solution algorithms.

A companion book "Evolution to Complex Geometries and Applications to Fluid Dynamics" contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries and provides detailed discussions of spectral algorithms for fluid dynamics in simple and complex geometries.

Partial Differential Equations in Mechanics 1: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation

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Joe Walker in Jackson, MS

Partial Differential Equations in Mechanics 1: Fundamentals, Laplace's Equation, Diffusion Equation, Wave Equation
A. P. S. Selvadurai
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540672834

Book Description

This two-volume work mainly addresses undergraduate and graduate students in the engineering sciences and applied mathematics. Hence it focuses on partial differential equations with a strong emphasis on illustrating important applications in mechanics. The presentation considers the general derivation of partial differential equations and the formulation of consistent boundary and initial conditions required to develop well-posed mathematical statements of problems in mechanics. The worked examples within the text and problem sets at the end of each chapter highlight engineering applications. The mathematical developments include a complete discussion of uniqueness theorems and, where relevant, a discussion of maximum and miniumum principles. The primary aim of these volumes is to guide the student to pose and model engineering problems, in a mathematically correct manner, within the context of the theory of partial differential equations in mechanics.

Customer Reviews:

Joe Walker in Jackson, MS.......2002-07-12

I bought this text book because I was trying to solve the biharmonic equation for the bending of thin plates or slabs using the separation of variables technique. What I found in Section 8.11.13 on page 339 is exactly what I was looking for. I liked Partial Diffential Equations in Mechanics 2 so well that I also ordered Partial Differential Equations in Mechanics 1 as well. I like it equally well. I have not examined other sections as thoroughly as Section 8.11 in PDE Mechanics 2. But I can tell you that this is an excellent reference to have if you plan on solving PDEs.

I have also bought the following titles in reference to the bending of thin plates or slabs:

Book Description

This graduate level text explains the fundamentals of the theory of dynamical systems. After reading it you will have a good enough understanding of the area to study the extensive literature on dynamical systems. The book is self contained, as all the essential definitions and proofs are supplied, as are useful references: all the reader needs is a knowledge of basic mathematical analysis, algebra and topology. However, the first chapter contains an explanation of some of the methods of differential topology an understanding of which is essential to the theory of dynamical systems. A clear introduction to the field, which is equally useful for postgraduates in the natural sciences, engineering and economics.

Solving Nonlinear Equations with Newton's Method (Fundamentals of Algorithms)

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Nice introduction

Solving Nonlinear Equations with Newton's Method (Fundamentals of Algorithms)
C. T. Kelley
Manufacturer: Society for Industrial Mathematics
ProductGroup: Book
Binding: Paperback

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ASIN: 0898715466

Book Description

This brief book on Newtonâ€™s method is a user-oriented guide to algorithms and implementation. In just over 100 pages, it shows, via algorithms in pseudocode, in MATLAB, and with several examples, how one can choose an appropriate Newton-type method for a given problem, diagnose problems, and write an efficient solver or apply one written by others. Solving Nonlinear Equations with Newton's Method contains trouble-shooting guides to the major algorithms, their most common failure modes, and the likely causes of failure. It also includes many worked-out examples (available on the SIAM website) in pseudocode and a collection of MATLAB codes, allowing readers to experiment with the algorithms easily and implement them in other languages.

Customer Reviews:

Nice introduction.......2004-03-31

This is a concise and practical introduction to some Newton method scheme, which can be read in a day or two if the reader has some background in numerical methods. The book sketches the main idea behind the methods and clearly explains the pros and cons of each method.

Book Description

A coherent unification of Newtonian and Lagrangian dynamics. Formulates and solves equations of motions with an emphasis on solutions of linear mechanical systems. Numerous examples, ranging from simple to complex, expose readers to a variety of nuances that arise in a broad range of extremely useful models. The 12 appendices provide underlying theoretical and mathematical support for the text thus streamlining the main presentation as well as enhancing its structure.

Customer Reviews:

Mechanics Coach.......2007-03-19

When it comes to learning a subject, sometimes you can choose a subject and you get it, like music. You can get behind a piano and some people just get it; on the other hand, some people need to be showed every step to make a improvement. It takes more effort and more than likely, your in the latter category and require a book like Applied Dynamics. I really had difficulties with seeing the Mechanics, and for good fortune, I purchased the book. The book is accurate and shows you how to do basic dynamical problems in a logical manner. I use this book a a reference now!

Learning Dynamics: One of the best textbooks .......2005-12-24

I am a graduate student in Mechanical Engineering Department at Texas A&M University, College Station. To keep my knowledge and concepts of dynamics up to date, I have been referring to this book and I find it is one of the most well-written textbook, with thoroughly worked out examples and clear explanations. I have enjoyed reading this book. The way in which author has clarified and applied the Indirect Approach(Lagrangian/Hamilton Formulations) for the equations of motion formulation is very illustrative and clear of all ambiguities. This is a great favour of author since this approach is particularly powerful and extremely important for complicated electro-mechanical systems in particular and all dynamical systems in general.

Finally, I respectfully disagree with Mr.Daine (from Boston, MA) to have made such ignorant and un-educated remarks about such a brilliant piece of work. I believe Mr.Daine has been looking for some short-cut type, particular problem solving textbook that will never lay the foundations but solve some limited problems of immediate interest, never illustrating the complete framework. In other words, telling the truth, but not the whole truth. That is how any subject, with dynamics no exception, becomes obscure and horrible to students. But this book is all about laying the foundations and making you enjoy the process of learning, while never straying away from the main objective of all engineering analysis: Design. Hence it is a great book.

Muddy and loquacious.......2005-12-18

I used this text for an undergraduate dynamics class. I treat my textbooks as references and get the concepts from lectures.

This textbook is the most worthless I've ever purchased. The author drones for pages at a time before reaching a concept, and although he seems to find himself very entertaining, I'd be much happier with something clear and concise.

The example problems in the text are very unsatisfying. They are convoluted and never quite seem to be completely finished.

I found myself referencing Ogata and leaving this one on the shelf.

Best Dynamics book I've found.......2004-05-08

I was trying to learn dynamics on my own and looked through the local university library at several texts, trying to find one that would illuminate the Lagrangian method. They all cover it, but usually in ways I couldn't easily figure out from the text. Finally I stumbled on this fabulous book by James Williams of MIT. I immediately purchased my own copy and have been happily referring to it often.

Prof. Williams really takes pains to explain every step. It is obviously the result of many years of teaching, because he really knows how to convey the material to those who have not yet mastered it. (It seems to me math & physics texts are often written with maximum brevity to impress colleagues who already understand it all!). There are many examples, all worked out in detail. And many additional problems for practice.

There is also an interesting section on the history of science at the start -- some may find this out of place, but I think its great.

One more note I found interesting and unusual about this book. On page 179 Prof. Williams introduces the "indirect" methods of analyzing dynamics: the Lagrangian & Hamiltonian approaches. He writes "We shall take Hamilton's principle as the fundamental law for deriving the equations of motion of dynamic systems... While this perspecitve is not unique, it is unconventional, since many writers designate Newton's laws as the fundamental principles of mechanical dynamics... Indeed, many writers begin with Newton's laws and then proceed to 'derive' Hamilton's principle, a process we feel is philosophically and technically inappropriate." In other words, he doesn't try to justify the Hamiltonian methods, he just takes them as facts of nature as fundamental as F = m a. I admire this approach, but at the same time I crave some additional insight into why these methods work so well -- it is astonishing magic to see the answers pop out. Perhaps those insights are in the text -- I've yet to read it all.

(...)

Dyanmics Applied at its Best.......2002-08-05

This applied dynamics book is the most well-written dynamics text book I've ever read. In addition to explaining ALL the steps that are normally left to the reader to supply, it gives credit to the originators of all major concepts. Dr. Williams explains why there are direct and indirect methods for calculating the equations of motions. Most people I polled had never seen it as well explained. (It seems rather simple now, and we wonder why no one else has taken the time to really get down on the student's thinking level.) I collect physics/math books. This is the best I've seen.

Fundamentals of Algebraic Microlocal Analysis (Pure and Applied Mathematics)

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Fundamentals of Algebraic Microlocal Analysis (Pure and Applied Mathematics)
Goro Kato , and Daniele C Struppa
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover

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Book Description

"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."

Fundamentals of Differential Equations and Boundary Value Problems (3rd Edition)

Average customer rating:

Excellent introduction to differential equations
So far it's not that bad
could be worse
hmmm
This book is'nt great, but surely it's adequate

Fundamentals of Differential Equations and Boundary Value Problems (3rd Edition)
Kent R. Nagle , Edward B. Saff , and David Arthur Snider
Manufacturer: Addison Wesley
ProductGroup: Book
Binding: Hardcover

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ASIN: 020133867X

Customer Reviews:

Excellent introduction to differential equations.......2007-02-23

This is an excellent introduction to differential equations for both math and physical science majors. It is at the level of most first and second year calculus courses, which is to say focussed on conveying methods rather than dissecting logical structure. I believe this is the extent of the training most physical scientists seek, and is a good place to start for math majors. The exposition is clear and important results are well delineated. Helpful review sections are included for topics the reader may need to brush up on, like linear algebra. The chapters are arranged in a natural progression, moving from lower to higher order DEs and then into systems of DEs. Of course, the other important topics are present too--Laplace transforms, series solutions, phase plane analysis, and basic PDEs. One additional virtue of this book is its utilization of physical problems to motivate the material. I found this appealing, some math majors really do not. Most of the problems have an analagous worked example in the text and don't require great fits of inspiration. That said, one's fortitude will be tested by a Dirichlet boundary value problem in cylindrical coordinates. Overall, I suggest this is the place to start once the basic mechanics of calculus have been learned (though vector calculus is not required). Physical science majors shouldn't have to look beyond this for their ODE needs and third year math majors can learn this in parallel with the fundamentals of analysis.

PS Don't expect to find Fourier transforms here, though there is plenty on Fourier series.

So far it's not that bad.......2004-09-22

I am midway through our semester and I have to say that so far
I am impressed with this textbook. It is not heavily bogged down in proofs...sorry math majors...but shows you how
to solve the problems in each chapter. I can't really complain but if your a math major who loves proofs, then look elsewhere. If your like me and just want to learn how to solve the problems, this is a good start. I also recommend "Ordinary Differential Equations" by Pollard/Tenenbaum. Good luck.

could be worse.......2003-01-22

Granted, the semester is young, but so far this book's not too bad. Especially considering last semester I had to endure part of the McCallum/Hughes-Hallet series of calculus books for Multivariable/Vector Calculus. In comparison, this book has far more practice problems where you just work out the equations, rather than having to contend with applications and word problems while still wrestling with the concepts. While the examples are a little convoluted, at least they draw parallels to the problems, something the McCallum et al. series does not. In short, this may not be the best math book, but it could be a lot worse.

hmmm.......2001-02-22

It appears I'm the only person not from ithaca to review this book. I assume they're using this text at Cornell, or ithaca college, but I used this text at Texas A&M. Perhaps it was the instructor, but i didn't think that this book was that bad. Some of the proofs and explainations and examples were pretty lousy, but the assignment problems were pretty diverse, and i thought most of the explainations and examples were adequate. What i'm trying to say is that this text isn't that bad....

This book is'nt great, but surely it's adequate.......2000-07-22

This is the required text for a math class I am currently taking. While the book is not spectacular, it is written at an elementary level and it is not mired in proofs, so one can learn the material simply by opening the book and reading. A definite strength of this book is that it covers a wide range of problems, from ordinary DE's to some PDE's. But it also includes whole chapters on applications to mechanical and electrical systems(circuits), as well as numerical methods and Laplace Transformations. The book is clearly written as an introductory text, but it covers a broad range of material applicable to higher level courses.

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