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.
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- Reviewed in the United States on April 6, 2014
- Reviewed in the United States on January 15, 2022
Top reviews from other countries
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Nicolas IvesReviewed in Brazil on December 4, 2018
Equações Diferenciais Parciais para quem tem pressa
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Massimo Di CasolaReviewed in Italy on April 5, 2018
ottimo manuale per introduzione alle tecniche PDE
- Saurabh HegdeReviewed in India on April 4, 2016
Amazingly well written book, especially for engineers. Very ...
- Jean-René GuilbaultReviewed in Canada on July 9, 2014
Must have... can be used as a reference
