Customer Reviews

Partial Differential Equations for Scientists and Engineers (Dover Books on Mathematics)

5 star:		(39)
4 star:		(11)
3 star:		(5)
2 star:		(4)
1 star:		(0)

 

 

We all had to go through the drudgery of PDE's in undergraduate courses and except if you're a math major your knowledge of the methods of solution will probably stop at separation of variables, Laplace transform and D'Alembert. This book is an excellent review of a host of methods for solution but what is more important is the physical interpretation of the PDE's the author insists on. Most of the physical examples are drawn from the fields of heat and mechanics but they can be easily applied to electromagnetic and semiconductor charge transport problems. Every aspiring senior in an engineering discipline should study this book for his own good.

Unbeatable as far as breadth. Covers a lot of ground, conceptually it's extremely well organized, and the explanations are very easy to follow. This text is ideal for self-study.

The two major shortcomings are (1) slight lack of depth and (2) the exercises, which are far too few and far too simple.

Partial differential equations can be obscure, and are often not dealt with at all at the undergraduate level. Assuming only a reasonable familiarity with calculus and ordinary differential equations, this book is extraordinarily clear and even enjoyable. Divided into neat, digestible segments suitable for self-study, I found it a very useful introduction to PDE's, covering a very broad range of topics and examples. My only suggestion for improvement would be a more up-to-date review of numeric methods using a computer algebra system. Nonetheless, even this section (examples intended to be worked by hand) is very clear and makes alternate texts much easier to absorb. I would recommend it to anyone wishing to be more comfortable with PDEs.

If you'd like to teach yourself the subject of partial differential equations, and you have a decent background in calculus and ordinary differential equations, this book is perfect. It is composed of 47 chapters each of which is only a few pages long and covers an important topic, with exercises. The author is very good at explaining potentially complicated ideas in simple terms. It's all very practical, with no theorems or proofs. At the end of each chapter is suggested reading for exploring the topic in more detail. An auto-didact couldn't ask for more. I had so much fun going through this book!

One of the reviewers mentioned that the answers to the exercises had a lot of errors, and I agree. I've listed the ones I found below, with the caveat that maybe a "typo" reflects my faulty understanding. You can decide for yourself. Other than this, I can't find anything to criticize in this marvelous book.

Some specific comments:

Table 13-2: although the separation of variables method is listed as being inapplicable to nonhomogeneous boundary conditions, in fact it can be used to solve Dirichlet problems on a rectangle with one non-homogeneous boundary.

Lesson 32 p. 251: Laplacian in spherical coordinates fourth term should be cot(phi), not cot(theta).

Lesson 39 p. 320: step 2 of implicit algorithm for heat problem: u11 and u16 should be zero, not 1, so first and fourth equations equal zero, not 1, and final result is u22 and u25 are 0.2, not 0.6, and u23 and u24 are 0.6, not 0.8. These results are closer to the results given by the analytic solution u=pi/4 times sum n odd sin(n pi x)/n times exp(-n^2 pi^2 t).

Lesson 41 p. 338: step 3, the coefficients of the new canonical form are computed from equations (41.3), not (41.5).

Lesson 44 p. 359: J(y)=1.28, not 0.46.

Lesson 45: p. 369 problem 2: I believe new function z(t)=(1-t)y(t), not (1-x)y(t).
Problem 5: A=.004, not .06, and B=.097, not .04. The values given in the book do not satisfy the boundary condition u(x,1)=0. The correct values can be calculated from the analytic solution u(x,y)=((cosh(pi y)-1)/pi^2 - (cosh(pi)-1)/(pi^2 sinh(pi))sinh(pi y))sin(pi x).

Lesson 47 p. 385: I think gamma=t/((x-t)^2 + y^2), not 2t/(...). This gives results for u^2+v^2 close to those listed in (47.6), whereas using the result for gamma given in the book gives u^2+v^2=3.95 and 23.9.
Page 386: phi(u,v) and phi(x,y)=0.53 ln(u^2+v^2)+1, not 0.57 ln etc.

Answers to Problems:

8.1: u(x,t)=4/pi exp(1/2(x-t/2)) etc, not 4/pi exp(-1/2(x-t/2)) etc. Also in the sum there should be a term exp(-n^2 pi^2 t).

9.3: sum should be from n=1 to infinity, not n=0 to infinity.

9.5: T subscript n (t) = (-1)^(n+1) etc, not (-1)^n.

12.3: denominator should be sqrt(4 alpha^2 t + 1), not sqrt(4 alpha^2 + 1).

13.3: alpha should be 1.

20.5: both terms should include 8h, not 4h.

24.2: given solution doesn't satisfy initial conditions. I believe u(x,t) should be 1/2((x+ct)+(x-ct)).

25.2: the exponents of e should be minus and plus (n^2 pi^2 alpha^2 - b)t, respectively, not minus and plus (n^2 pi^2 alpha^2)t.

25.6: second equation should equal 6 pi + 1 for n=3, not 8 pi + 1.

28.4: log term for u(x,t) = ln(abs(1-t/x)), not -ln(t+1).

35.5: calculation for a subscript n can be taken further to get (-1)^((n-1)/2) times(2n+1)/2^n for n odd, zero for n even.

37.3: u i,j = 1/4 (etc etc) not 1/2 (etc etc).

37.4: denominator is 2(h^2-2), not 2(h-2).

39.2: u i,1 = 1, not zero.

41.3: I got u epsilon epsilon + u nu nu +(nu^2/(2 sqrt(2)) u nu = 1/2 exp(-nu^2/4), but this is so different from the book that it may be my bad.

45.2: should be (z'/(1-x) + z/(1-x)^2)^2, not z'/(1-x) + z/(1-x)^2.

Appendix 3: 3-d spherical Laplacian all thetas should be phi's and vice versa.

I used this book in an undergraduate course, and since I couldn't see the board during lectures, I relied on only the book and it was very easy to read and understand. The major drawback of this book, and I don't know if this accounts for it's abnormally low price, is that there seem to be far more errors in the solutions than most books have. About 100 pages into the book, I had encountered so many errors, that thereafter whenever my solutions were different from the solutions in the book, I wondered first if the book was wrong, not if I had done something wrong.

As the title implies, this book is not intended to mathematicians, although it could finely serve as additional text for them, too. On the other hand it is excellent as an itroductory overview of the types of PDE's met and the methods used for their solution. There are references to more advanced texts for the interested, excercises in each chapter and, most importantly, nice, qualitative remarks on the properties of mathematical tools (like Fourier and Laplace transform) which help the reader to comprehend them.

I can't say it presented much detail. Lots of derivation was missing and sometime it just seem like they're not adding enough-For example, the section on Duhamel's Principle was lacking. Though it does a good job on explaining how this principle can make some problem much easier to solve, it does not have enough examples to fully understand. Also, like most reviewrs pointed out, there's not enough problems~Usually four or five problems on each section. Lastly, beware of the several mistakes on the answer on the back of the book. My professor had to give us several of the correct solutions. Overall, its a good book for engineering major, and for those who just been introduce to partial differential equation. However, its so much of a "cook book" that I'm not sure whether anyone can really understand.

I teach an intro course in PDE regularly and, although I don't use this as the main textbook, it is required reading for the course. Given its approach, its mathematical rigor is not quite right for the course that I teach, and it could use more interesting exercises. That said, it is indispensable for its physical and visual insights. It's brief and to-the-point and a cursory reading gives a wonderful introduction to the various topics and ideas of PDEs. The book is well written, and the informal writing matches the approach. And - the price is right!

This is a very well written textbook. However, it would help if you have some background in Fourier series and DFS (Discrete Fourier Series). It is important that you understand that in a linear system you can use superposition. These are linear differential equations that are talked about in this book so the idea of superposition is used a great deal in the process of solving PDE's. This is not really explained forcefully enough in the text. If you have these as background the text should be a breeze. I really like the idea of 47 short lessons. He is right. You can do about one lesson a day. Therefore, you should be able to finish the entire book in about 47 days. I have found that most math textbooks are written in a puzzle format so that you must have a paper and pencil handy to figure out exactly what the author is saying. While this is still true of this textbook, in most lessons the author works through a specific example instead of giving general equations like many math texts do. In one lesson, the solution is found graphically. It took me a while to understand what he was trying to do. The first 300 pages of the book are on analytical solutions and then the rest of the book is on numerical solutions. He also has a chapter on the benefits of each method, analytical versus numerical. I think the numerical methods are more useful as they are more general, and will solve more types of PDE's. I really studied this book as background for a book on the finite element method and I believe I accomplished what I wanted.

the subject of PDE's looks vague and scary for most students, even for those with math background.This book is probably the best education, self-study material available for the subject.It covers all the important aspects with very clear explanations .I bought it as a secondary book for my PDE course based on the amazon's reviews and it was really a very nice experience. Worth more than... and highly recommended