If you're in PDE's, you NEED this book
342758
It's an expensive book for sure, so before you buy it, consider checking it out at the library.

But it's well worth the investment and the time Dr. Stanoyevitch put into the book.

I took an undergrad PDE's course a few years ago, and although I learned something, I felt like I didn't really understand it.

But the problem was that I NEVER used ANY software to help visualize and understand what was going on.
You NEED something like MATLAB or Mathematica to help you understand PDE's better. Now that I'm taking a grad-level numerical analysis + PDE's course, this book came in handy. The explanations were well written, the exercises were so well thought out that I felt like I was exploring PDE's on my own rather than being guided.

So check it out to see if you like it and then buy it.
4727130
Let me start out by saying that the previous reviewer was not
refering to this book at all. If there's something this book
does NOT cover is "quantum level events in liquid forms". It
is true that the author, in the last two chapters, covers the
statistical mechanics of turbulent flow, but quantum mechanics
is "barely" mentioned (at least *I* couldn't find it).
This book was written, according to the author, with an
undergraduate level of engineering in mind, and therefore is
extremely accessible. Indeed, the first two chapters on the
ergodic foundations of statistical mechanics are extremely
easygoing (AND fairly rigorous). In chapter 3, particular
emphasis is put on low-dimensional systems, e.g. the
Henon-Heiles oscillators, and chains of oscillators, e.g. the
Fermi-Pasta-Ulam problem. Both are shown to present statistical
behavior. After also spending a whole chapter with damped
systems, the author dedicates a long discussion on the stat
mech of turbulent flow in both 2- and 3-dimensions, which is
precisely his main subject of research.
In summary, it is actually a pretty neat book on ergodic
techniques for both low-dimensional systems and fluid motion,
and I strongly encourage you to buy it if you are interested
in either of these two subjects.  The only reason I gave it 4
stars is, as the title suggests, because one could expect at
least *some* systematic discussion concerning "chaos" itself
and its relation to thermodynamics/statistical mechanics.
However, even elementary concepts such as Lyapunov instability,
KAM theorem and Kolmogorov-Sinai entropy are barely mentioned.
1133684
After a nightmarish experience with "The Finite Difference Time Domain Method for Electromagnetics: With MATLAB Simulations", I bought this book, as an attempt to understand how to create a EM simulation for my thesis work.

This book is clear and complete, evolving the topic from the basics to the most advanced topics. I shoud have bought this one and never bothered looking any other...
2154312
Readable, has a simple chapter on continuous groups that (implicitly) introduces the notion of global integrability. Discusses and uses Fuch's theorem (classification of singularities of linear ode's, basis for 'guessing' the right form of the series solution in terms of singilarities of coefficients), easy group theoretic discussion of singularities in the complex plane. Stage 2: see Arnol'd's Ordinary Differential Equations for theory, Bender and Orszag for approximation methods.
3453287
It is almost the perfect book.
It covers most of the standard topics in numerical methods.
The explanation is simple and clear.

However, one omission is topics on partial differential equations.
If the book includes the topic, than this would be the best book on numerical methods.
2493942
This is a graduate-level textbook on time-harmonic electromagnetics in the temporal frequency domain. Coming from Griffiths' Introduction to Electrodynamics this is an eye opener of how electromagnetics is done in the real world. There are sections did not understand at the time; mainly due to the prose of the particular section. In terms of practicality I can think of only one modern engineering book at this level that isn't 1000+ pages long (cough *Balanis* cough), that being Jin's Theory and Computation of Electromagnetic Fields. Due to the expense of the latter and the fact that they cover the same material more or less I would recommend this book -even for self-study.
2568232
I wanted a book to introduce me to the PDEs. As other reviewers have said, I found the author's approach very friendly to my elementary background. The "intuition" lessons and the categorization schemes he provides are much appreciated personally.

I haven't given 5 stars for 2 reasons: (1) Even if this text is highly approachable to beginners, there are points where I expected it to give more reasons and explanations about the physical meaning and the qualitative behavior of the PDEs described. I keep the 5 stars for a book which gives more on the reasons, history, derivation, and qualitative approach of the subject; (2) This was my first purchase of a Kindle thing, so I don't have an average picture of the quality of the ebooks. The thing is that this ebook has some minor typos, especially in the notation and formulas, that may produce confusion, and disrupt the reader's concentration.

All in all, I have looked at about 20 introductory books on PDEs, and this one is the only I still read.
1864650
Thorough and well written work emphasizing the applied aspects of Ordinary Differential Equations without requiring the reader or student using the book to be exposed to or steeped in Mathematical Analysis.  Excellent for students of Engineering and the Sciences, e.g., Physics.  A bit of Partial Differential Equations, limited to linear second order types (e.g., the Heat Equation), and extensions such as Nonlinear Ordinary Differential Equations and Sturm-Liouville Theory are included as optional or follow-on topics on an introductory basis for more advanced studies.

The edition I purchased, the 7th, is a expanded version of the 4th, 5th and 6th editions.  Unlike the earlier editions, e.g., the 4th, there are more mistakes, especially in the solutions in the back of the book, and occasionally in type-set equations throughout the various chapters.  For brevity, clarity and precision, I prefer the older editions, e.g., the 4th edition.

All in all, the book is well written and time honored for those intending to attain at least a junior or third year undergraduate background in Ordinary Differential Equations without requiring one to have as prerequisites in, say, introductory Complex Variables.  The book tends to be self-contained as topics are laid out in a fairly straightforward manner without referring excessively to other or more advanced works.
2239264
I am a physics PhD grad student.  I started this book during undergrad and finished in first year at grad school.

Griffiths clearly has a gift for educating.  He nails every single hard topic and explains it in the most clear way possible.  Every time you get a bit confused about something, for example why there's a negative sign in front of the derivative, Griffiths' next line will be: "you're probably a bit confused about why there's a negative sign in front of the derivative, that's because..."

I think the problems are also very helpful.  There's a solutions manual you may want to get your hands on to help you work through a bunch of problems as you learn the material.
1667292
This is an excellent both introductory and advanced book on differential equations and the calculus of variations.  Although the book was first published in the seventies, its emphasis on qualitative aspects is in agreement with more recent trends in the teaching of differential equations. In particular, the book has a chapter on Lyapunov stability and equilibria, with nice geometric proofs. Some topics, like equations with a small parameter in the highest derivative, are not often found in differential equations textbooks.

The second part, the calculus of variations, is not commontly bundled together with a differential equations course. It can be read independently if the reader is acquainted with the basic facts of the theory of differential equations. From the start, the author draws a parallel between optimization of functions of a single real variable---taught in regular calculus courses---and optimization of functionals, that is, functions whose variable is a function satisfying certain conditions. This leads the reader in a natural way to the main equations of the calculus of variations.

I was fortunate enough to attend a course taught by the author, many years ago. He was not only an excellent textbook writer, but also a masterful expositor.
103404
This is the book you want if you need to solve real compressible flow problems.  It covers all the basics plus there's tons of advanced materials. I especially like the fact that there are numerous detailed examples and coding templates.  In addition, the book contains a very extensive reference, allowing the reader to go back to the orginal papers.
2177167
This is a great book. In fact, it is the best book if like me, you don't have time to follow a teacher-led course. Stephen Chapra has authored/co-authored  several engineering texts, and this one is just as well-written as the others. My need was for a text which had the right balance of theory and practical implementation details. Since I develop water-quality & hydrodynamics software, I also was concerned with numerical methods issues. This book met my needs. Chapra has a very enjoyable style. I like his sometimes 'anecdotal' style, whereby he gives you historical or background blurbs which help view things in their proper context.
** One of the rare qualities of Chapra's books is to provide both the mathematical modeling theory, and the practical sampling and statistical tools to implement them with real data. This is so often overlooked by other authors.
I look forward to his next book on numerical methods with Matlab & Excel.
4084203
Excellent text for solving PDEs using FEM. Simple and concise explanation of methods but requires knowledge of advanced mathematics and finite element meshing. Green's theorem and closed volume and surface integral relationships.
3183227
This is one of those self published little gems, but unlike so many others, has a LOT of value if you can organize it yourself. First, there is no index, so the 150 or so worked problems flow generally from the chapters, but for specifics you'll have to create your own index if you want to use it as a reference work. Second, the Chapter titles at the beginning are very general, and don't agree with the Intro (which says, for example, that 4 is about electrical current flow (meaning "topic" 4) in circuits, whereas CHAPTER 4 is actually about strings, dynamic systems, etc.

The formulas and solutions are high quality, with few errors, and have plenty of diagrams. Despite the promotional reviews there are NOT really a lot of verbal descriptions, because the book moves at a very rapid place from example to example in order to pack at least one or two examples of each type of problem in 300 pages. The author does use the solution notation convention so later problems do refer back to previous exercises.

In summary, these are the class notes of a very bright mathematician, and show the sub steps for each technique quite clearly, as long as you know the symbols and understand the operations, which are not explained in detail. Not a lot of space is spent on inverses, which are really the toughest part of transform operators, but the problems selected solve quite clearly without the need for highly complex inversion manipulations. Some of the applications covered include solutions of PDE's, electrical applications, structural and dynamic applications, and of course equations of motion, waves, vibrating strings, etc.

For the price, a lot of good worked examples if you can get around the lack of indexing. Although there are also problems and solutions that are somewhat didactic, the book doesn't really follow a "course" format as much as topics and examples, more for the engineer who has forgotten a technique and wants to look up an example solution. From that point of view, very well done.

If there is one "best practice" in this book that I wish other, more polished texts from Wiley and Springer would follow, it is the fact that the author, while assuming you know transforms, does NOT assume you know all the intermediate steps in each problem - solution, so there are far fewer "jumps" to figure out-- the jumps are given!! For learning, maybe you need the discipline of finding intermediate steps yourself, but for real life applications and problems, you'll thank the author for including them.
3606963
In 1981, Dan published the now classical book ' Geometric Theory of Semilinear Parabolic Equations '. This book has served as a basis for this subject since its publication and has been the inspiration for so many new developments in this area as well as other infinite dimensional dynamical systems. This was the culmination of ten years of effort devoted to understanding this subject in the context of a dynamical system. Many topics and ideas in the book have not yet been fully exploited. In 1985, this book was translated into Russian.

[...]

Jack K. Hale
Regents Professor Emeritus
School of Mathematics
Georgia Institute of Technology
January 2, 2006
3357363
I read entirely this book, studying  it, with pencil and paper. I like the modern approach adopted. It treats of conservation laws, symmetries, in a new viewing of, mainly, mechanics. The chapter of Poisson brackets is very good, as is the ones about Lagrangians and Hamiltonians except pg 111- derivation of Euler-Lagrage equations. The attempt of derive this equations  using  discrete steps in the least action principle, was the unique that I found unhappy. Fortunately I know a very nice derivation found in the book "Theoretical Physics", of Kompaneyets, printed by Dover (in the MIR publication that I have, see pg 85), himself a "theoretical minimum style book" (but for advanced College level - it is much more mathematic, though very well explained (a litle dated however)).
Said this, I point some typos and errors that I found:
Page 83, last line - Since sin(pi/2)....that (both-suprime) the determinant (adds- is positive)
Page 84, first line- the Hessian are (positive-suprime, add negative). The point is therefore a (minimum-suprime adds maximum)
Page 120- in the line "the next term, mw(X+Y)", it lacks the number 1/2 before. The same apply to the formula of V (soon next)
Page 219- equations (9) and (10) have an 1/r. The correct is 1/r.
Page 221- Figure 3- in the V(r) of lower curve lacks "M". The correct is "V(r)=- GmM/r
Page 222- Figure 4- The same of figure 3.
Page 227- equation of tau- the pi is squared: pi.
Well, thats is all I have to say.
The book is not easy but worth the effort to learn something new. I think that you should have some initiation and maturity in mechanics, mainly analitical, for a good benefit. Good reading, enjoy the Theoretical minimum.
827244
I picked up this book to see if it would be useful in a numerical methods course, but I found that it was much too specific - This is a book on numerical methods for PDEs, and not a general methods text.  If you are interested in PDE models, then this might be a useful book for you- The authors do include some interesting applications.