by Stanley J. Farlow
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Product Description
Highly useful text for students, professionals working in the applied sciences shows how to formulate and solve partial differential equations. Realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems and numerical and approximate methods. Problems and solutions. Suggestions for further reading. 1982 edition.
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Average Customer Review:
1 of 1 people found the following review helpful:
 an absolute gem, 2010-02-23
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.
0 of 0 people found the following review helpful:
One of the best, 2010-01-17
I bought the book about 2 years ago. I have to say this is by far the best book on the topic that can accompany with any other "text book".
The topics are well explained and can be understood by people from decent backgrounds. I have had friends who had never taken ODE before and said they understood the topic very well from this book. Another big point is that the books lays a good amount of foundation and uses a build up procedure to come to showing you various methods.
I have used this and Colton for primarily learning the subject and used Strauss more as an "Excercise Book".
The main issue I have is that it lack problems. To learn mathematics, you have to do mathematics. So where are practice problems? This is the only concern.
The coverage on Numerical method is very shallow. But this is expected due the vastness of this topic. It is normal to look at books specialized in that topic
0 of 0 people found the following review helpful:
Physically Meaningful Introduction, 2009-12-07
This book is a rarity because Farlow actually succeeds in explaining how to model physical problems using PDE's. This is a volume for engineers rather than mathematicians, so expect clarity rather than pages of ugly and worthless abstractions. It's not exhaustive, but, given the price, you wouldn't be justified in demanding a detailed treatment of all the intricacies of a subject as vast as PDE's. As a pedagogical tool, Farlow stresses the physical origin of PDE's , so many problems include units and very insightful diagrams. For example, unlike many other authors, Farlow reveals the intuitive meaning of the LaPlacian, which is a noteworthy distinction reminiscent of the writing of Tristan Needham, the author of Visual Complex Analysis. If your primary interest is real understanding rather than an adeptness at manipulating meaningless symbols, this book contains all the physical motivations necessary to advance your ambitions.
0 of 0 people found the following review helpful:
good reference, 2009-09-21
It is well organized and the information is easy to understand. However, the lack of detailed examples will leave you needing a pure math based reference if your PDE and ODE solving skills are rusty.
0 of 0 people found the following review helpful:
Impressive Value, 2009-08-18
Once again, Dover comes across as the students best friend. Not only is their line of textbooks astoundingly cheaper, but they lose nothing in value. This text is no different. Not only does is get ideas and tough topics across with crisp, clear examples but their chapter breakdowns are excellent. Instead of filling your head with lots of extra theorems and corollaries this book pushes application and solid examples. Not only is it best for the engineer, but it's a great starting text. When I need to remember an advanced PDE method, I often start here. If you want more in depth and theorems and analysis, then simply move to a deeper book but this one gets the ball rolling. It's a must-have (and a very economic one at that) for anyone dealing with DiffEqs as an engineer and any mathematician.
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