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Partial Differential Equations for Scientists and Engineers (Dover Books on Mathematics), by Stanley J. Farlow
PDF Ebook Partial Differential Equations for Scientists and Engineers (Dover Books on Mathematics), by Stanley J. Farlow
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Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.
This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing the mathematical model) and how to solve the equation (along with initial and boundary conditions). Written for advanced undergraduate and graduate students, as well as professionals working in the applied sciences, this clearly written book offers realistic, practical coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, and numerical and approximate methods. Each chapter contains a selection of relevant problems (answers are provided) and suggestions for further reading.
- Sales Rank: #19086 in Books
- Published on: 1993-09-01
- Released on: 1993-09-01
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 6.00" w x 1.00" l, 1.27 pounds
- Binding: Paperback
- 448 pages
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
Most helpful customer reviews
85 of 86 people found the following review helpful.
an absolute gem
By arpard fazakas
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.
63 of 67 people found the following review helpful.
A rare gem
By Atul Sharma
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.
0 of 0 people found the following review helpful.
The best book for starting with PDEs
By Amazon Customer
This is an excellent book for anyone who is just starting with PDEs and does not want to go into deep details.
But it is not a book of numerical methods, although there is a chapter, but it does not cover that much.
I like the explanation of the physics behind the equations and the simplicity.
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