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Partial Differential Equations for Scientists and Engineers (Dover Books on Advanced Mathematics)
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| Part No: | 048667620X |
| Manufacturer: | Dover Publications |
| MFG Part: | |
| Customer Rating: | 4.5 / 5.0 |
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- ISBN13: 9780486676203
- Condition: New
- Notes: BUY WITH CONFIDENCE, Over one million books sold! 98% Positive feedback. Compare our books, prices and service to the competition. 100% Satisfaction Guaranteed
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.
| Too Brief With Few Examples | 2010-07-01 | 2 / 5 |
| | Having gotten the dover books on ODE and Advanced Calc, I was expecting the same quality of presentation here... I was disappointed. The book offers very little explanation about each sections use or simply how to use the equations. Each section was basically a derivation, but fails to give an example of how to use it. This makes it pretty much worthless, or at least a substantial waste of time, since you cannot be sure if you are doing it right. This book may be cheap, but its really not worth it. |
| Grad student review | 2010-04-23 | 4 / 5 |
| I particularly like this book as a secondary resource to help with a more detailed/in-depth graduate course in applied mathematics that I'm currently taking. Equations are explained by appealing to ones physical intuition (ie. linear conservation equations are described well by drawing connections between the equation and phenomenon we're familiar with in the physical world).
If you're looking for a high-level PDE solving text this might not be it. For $10 however, I think it's a fantastic resourse for the price. |
| | This book is relatively easier than others and it illustrate partial differential equation in a clear way. |
| A Great Introductory Text for PDEs | 2010-03-20 | 5 / 5 |
| This text was used in my first undergraduate course in PDEs, I found it be exceedingly clear with just enough application. However, as previous reviewers have noted, the examples are far too simple and finding problems elsewhere is necessary. I was lucky enough to have a professor who also realized the shortcomings, but I digress. What is most excellent about this text though is the price, rarely do you come across such a good text at this price (well, it is a Dover). As such, the price alone makes up for problem sets.
I would definitely recommend this book to anyone who has an interest, but no experience, in PDEs. |
| an absolute gem | 2010-02-23 | 5 / 5 |
| 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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