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

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About the Author

Partial Differential Equations & Beyond Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers is one of the most widely used textbooks that Dover has ever published. Readers of the many Amazon reviews will easily find out why. Jerry, as Professor Farlow is known to the mathematical community, has written many other fine texts — on calculus, finite mathematics, modeling, and other topics.We followed up the 1993 Dover edition of the partial differential equations title in 2006 with a new edition of his An Introduction toDifferential Equations and Their Applications. Readers who wonder if mathematicians have a sense of humor might search the internet for a copy of Jerry's The Girl Who Ate Equations for Breakfast (Aardvark Press, 1998). Critical Acclaim for Partial Differential Equations for Scientists and Engineers:"This book is primarily intended for students in areas other than mathematics who are studying partial differential equations at the undergraduate level. The book is unusual in that the material is organized into 47 semi-independent lessonsrather than the more usual chapter-by-chapter approach. "An appealing feature of the book is the way in which the purpose of each lesson is clearly stated at the outset while the student will find the problems placed at the end of each lesson particularly helpful. The first appendix consists of integral transform tables whereas the second is in the form of a crossword puzzle which the diligent student should be able to complete after a thorough reading of the text. "Students (and teachers) in this area will find the book useful as the subject matter is clearly explained. The author and publishers are to be complimented for the quality of presentation of the material." — K. Morgan, University College, Swansea

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Product details

Series: Dover Books on Mathematics

Paperback: 448 pages

Publisher: Dover Publications; Reprint edition (September 1, 1993)

Language: English

ISBN-10: 048667620X

ISBN-13: 978-0486676203

Product Dimensions:

6 x 1 x 9.2 inches

Shipping Weight: 1.2 pounds (View shipping rates and policies)

Average Customer Review:

4.2 out of 5 stars

147 customer reviews

Amazon Best Sellers Rank:

#54,944 in Books (See Top 100 in Books)

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.

There are several reviews listed for this title criticizing it for leaving out proofs and developments for PDES. With that said, it is important to keep in mind that this book is not written as a comprehensive introduction to the theories in partial differential equations. It is simply an overview of techniques and methods that might be useful to engineers and some scientists. If you study or studied physics or mathematics this book will likely put you to sleep. Engineers, chemists, and other physical and social scientists that will usually never really study this subject too rigorously however, will find this a more useful and compelling read as it is designed to assist them. With that said, this book should not be listed as a required text for a math or physics course as it is not comprehensive enough for these subjects.

I needed a brief text to refresh myself on using PDEs. I still have my college textbook, but was hoping to find something a bit briefer, and somewhat more accessible, for a quick refresher on how to use them for applications. (My coursework on PDEs was a decade or so ago, and that particular skillset rusted out quite a while back.)This book fit the description of what I needed exactly, and I was very satisfied with the content. I don't think you could teach yourself DiffEQ from this book, but if you are trying to use some applied math for an application and need a bit of a refresher, this book could be what you are looking for.

A really great introductory book. It doesn't go into a whole lot of detail, but it's really good at explaining concepts. There's a lot of portions entitled something like, "An Intuitive Explanation of _____" It puts concepts into simple terms and explains them well without getting longwinded or pedantic. There's lots of analogies to real world phenomena. I would recommend reading this book and probably following it up by reading a more in depth and comprehensive book. This is definitely a great place to start though. I have the PDE book from Zachmanoglou, and it made no sense to me until I read this one.

Structured into lessons very much like Khan Academy. Very undemanding since prerequisites are provided on the fly. I had not previously studied the calculus of variations. The introductory chapter on this managed to get my interest for the first time. The presentation is as untechnical and plain as it can possibly be. Maybe someone could complain that it is not totally rigorous? However, any possible lack of rigour is amply compensated for by an elegantly simple and straight forward presentation. If like me you like to read elementary math for fun you'll love this book. Also the size and weight makes it feasible to read this on the couch and go to sleep with it over your face and still wake up alive (as opposed to Kreyzig, then you wake up dead).

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.

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