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| Partial Differential Equations and Boundary Value Problems With Applications
Hardcover
Author: Mark A. Pinsky
Publisher: Waveland Pr Inc
Release Date: 2003-01-01
ISBN-10: 157766275X
ISBN-13: 9781577662754
List Price: $67.95
Average Customer Rating:
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Summaries and Customer Reviews are supplied by Amazon.com
Now available from Waveland Press, this corrected version of a classic text offers a level of rigor and completeness that rivals any book of its kind. Building on the basic techniques of separation-of-variables and Fourier series-integral methods, the book contains the solution of boundary-value problems for the heat equation, wave equation, and Laplace's equation in the standard coordinate systems--rectangular, cylindrical, and spherical. Each of the basic equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system rather than by the type of the equation, which makes the mathematics especially clear. Bessel and Legendre functions are developed in their own right, and their use is specifically indicated, where appropriate. The notion of steady-state solution and the closely related stationary solutions are developed for the heat equation and applied to the problem of heat flow in the earth. The problem of the vibrating string is also studied in detail, both from the Fourier viewpoint and the viewpoint of the explicit representation (d'Alembert's formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. Special features include more than 200 worked examples and 700 exercises, with nearly 450 answers; asymptotic methods (Laplace and stationary phase); and over 300 typographical cleanups from the previous publisher's versions!
Excellent Textbook, Wish There Were More Like This
| Customer Rating: | | As a student of mathematics, I find many textbooks that are dry and boring. This book is not. It gives examples and is written in a casual style. The exercises, that is, the problems, begin as easier yet interesting, and gradually become more difficult, but not too difficult. I really learned so much about partial differential equations and why we need to study them, too! I would have liked more illustrations, that is, pictures. There were some typos among answers to problems, but it was actually a good thing for me, forcing me to check my work. This book reminds me of Feller's books written long ago, on probability theory, which are also interesting to read. An Introduction to Probability Theory and Its Applications, Volume 2. |
Very Well Written
| Customer Rating: | This book is excellent for many reasons:
1. It is very well written and a pleasure to read.
2. The author offers motivation for the mathematics, from areas such as investing and physics.
3. Pinsky develops each concept from basics, with many worked examples.
4. The sections on employing techniques of Fourier transforms are mathematically beautiful and clear.
5. The exercises are enjoyable to solve, with many answers provided.
6. Appendices provide details and review material.
There are very few minor typographical errors, and students of mathematics can easily overlook them; perhaps in the next edition, they shall be corrected, but they are of little consequence. |
Worked examples and more!
| Customer Rating: | | This third edition, from a new publisher, has a number of attractive new features: More worked examples, more than 200 in all, more exercises with answers, more on modern developments such as asymptotic methods, correction of typographical errors,--- and loving care from the editors at Waveland Press. The result is a much nicer appearance, and high quality pedagogical improvements.-- I have taught from an earlier edition of this very nice book. Both the students and I have been happy with it. It is an important and useful topic in math [both pure and applied] , and it is especially relevant and central to the service courses offered by most math departments. Sample of topics: The Green function method, the equations of heat, and of waves, and the PDEs of Laplace and Poisson. Orthogonal functions and Fourier methods. The method of stationary phase, and the classical Sturm Liouvile problems.-- Pinsky's book is the best text for teaching these classical tools. A nice feature of the new edition is an added section on the use of Mathematica in the study of PDEs. When students need to look up one of the classical formulas in the theory of boundary value problems, I often refer to Pinsky's book which has always been on target. |
not a good book for physicists
| Customer Rating: | | THIS BOOK HAS NUMEROUS ERRORS IN THE EXAMPLES. THE PROFESSOR AND SOME STUDENTS HAVE SOLVED SOME OF THE PROBLEMS IN THE BOOK AND FOUND THAT THE CORRESPONDING ANSWER IN THE BACK IS INCORRECT. THE BOOK DOES A POOR JOB OF TEACHING THE FOURIER SERIES. WE HAVE ALREADY REACHED THE END OF THE SECOND CHAPTER AND I USE OTHER BOOKS CHECKED OUT FROM THE LIBRARY AS HELP. I WOULD THINK THAT NOT EVEN A FIRST EDITION BOOK WOULD HAVE THIS MANY ERRORS. ALSO THE PROOFS ARE WEAK. STAY AWAY FROM THIS TEXT, AND IF YOU LIKE ME USE THIS BOOK FOR A CLASS, FIND SUPPLEMATARY TEXTS TO TAKE THE PLACE OF THIS ONE |
Stay away!
| Customer Rating: | | This book has the reputation of being very weak and error-prone. If you have a choice DO NOT get this book. For a third edition, the editing is disgraceful. I don't think I would find similar errors acceptable in a first edition. For example, on page 18, various steps establish A1=0 and A2=0. The very last paragraph on that page uses both A1 and A2 multiplied to various items to derive a solution. Last time I checked, anything times zero is zero, which is what this book would get if Amazon had a "zero rating." The way in which the author "changes the rules" throughout the book leads to confusion, leaving the reader more perplexed than when she picked it up. For example, on page 104 (solving the heat equation), the author states that Lambda must be pure imaginary. If this were true, then the equation he gives cannot have boundedness. Like most folks, you may be forced to use this drek in your PDE class. If so, do your self a favor and pick it up as cheaply as possible (i.e., used) and then dump it as quick as you can once the class is over. Once someone figures out that there are very few good PDE books, he will write one.... |
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