Book Description
Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations. Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial differential equations, nonhomogeneous problems, Green's functions for time-independent problems, infinite domain problems, Green's functions for wave and heat equations, the method of characteristics for linear and quasi-linear wave equations and a brief introduction to Laplace transform solution of partial differential equations. For scientists and engineers.
Customer Reviews:
Great Math Book!.......2007-09-19
I am a pure math student, so I get easily frustrated with applied math books that offer intuitive proofs instead of the mathematical details. Haberman is a great author, not just in the sense that the book offers an easy and interesting reading, but both intuition and a lot of the technical details are provided for each topic. I can only say this about very few of my applied math books, so I am very happy with my purchase. I would recommend this book to anyone who wants precision and more clarity of thought into the subject.
No worked examples.......2007-04-22
While the presentation of the book was very understandable (especially compared to some other partial differential equation textbooks), there are few worked examples in the book. For those who want worked examples, just type in the google key words "haberman site:.edu". If this book could include some of those worked examples, it would be much better.
The book also uses slightly different notation from that of many other books.
Pretty good.......2005-11-27
Pretty good book to learn from. Well laid out. Some areas could be clearer, but will use often!
Absolutely no sense.......2005-09-27
I wouldn't listen to the other reviews. Coming from a student who's done very well so far in all his other engineering courses, nothing in this book makes any sense at all. They jump into topics you've never even heard of, and expect you to know everything right off the bat. There aren't many examples, most of it's derivation, and the book takes a tone that you are a genious and will understand everything without a concrete explanation. I wouldn't get this if its not a required text, if I were you.
Smooth transition to advanced topics!.......2005-08-22
Most books on PDEs either address very basic, introductory concepts or tackle advanced topics requiring Measure theory. In addition, they focus mainly on theoretical concepts and do not provide adequate worked examples. Haberman's text is immensely useful both in bridging the gap between elementary and advanced books as well as in providing many, many completely worked problems. Indeed once you have had a basic course in PDEs you could use this text to teach yourself graduate-level topics such as Green's functions.
I do not try to convey the impression that this is a mere cookbook - "here's a problem, let's look up the solution". To the contrary. Haberman provides the motivation for each kind of mathematical treatment and interprets his results, pointing out their important consequences. His presentation of Gibbs' phenomenon is the most clear and comprehensive I have yet come across.
I heartily recommend this book especially to Math and Physics seniors who hope to continue on to graduate school in either of these subjects. In either case, it is expected of you to be adept at Green's functions and Haberman's book lays the groundwork for this topic.
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Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications (Stochastic Modelling and Applied Probability)
Guy Fayolle ,
Roudolf Iasnogorodski , and
Vadim Malyshev
Manufacturer: Springer
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ASIN: 3540650474 |
Book Description
This monograph aims at promoting original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes are of interest in several areas of mathematical research and are encountered in pure probabilistic problems, as well as in applications involving queuing theory. Using Riemann surfaces and boundary value problems, the authors propose completely new approaches to solve functional equations of two complex variables. These methods can also be employed to characterize the transient behavior of random walks in the quarter plane.
Book Description
One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics.
This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications.
Key features include:
* Applications to a wide variety of physical problems in numerous interdisciplinary areas
* Over 900 worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry
* Historical comments on partial differential equations
* Solutions and hints to selected exercises
* A comprehensive bibliography—comprised of many standard texts and reference books, as well as a set of selected classic and recent papers—for readers interested in learning more about the modern treatment of the subject
Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarily serve as a textbook for the first two courses in PDEs, or in a course on advanced engineering mathematics. The book may also be used as a reference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering. Readers will gain a solid mathematical background in PDEs, sufficient to start interdisciplinary collaborative research in a variety of fields.
Also by L. Debnath:
Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition, ISBN 0-8176-4323-0.
Customer Reviews:
Aimed at the Person who needs to do Real Work.......2007-04-05
Partial Differential equations are really the first time that the science or entineering student begins to see that math can really represent real life situations that are more complex than the almost trivial examples he has studied up until now.
This book, now in its fourth edition reflects comments made by users: students, faculty and researchers as well as covering the major new discoveries of methods for the solution of partial differential equations in the years since the last edition. The book is aimed at the advanced undergraduate or beginning graduate student, and it should be useful as a research reference for professionals in mathematics, science, engineering and the other applied sciences. In addition other fields of study from the social sciented to financial analysis have begin to use more advanced mathematics in their calculations.
The intent in this book is to provide the working physicist/engineer or whatever with the tools he needs to perform his work. In a few places this has meant a slight slacking of the rigor normally required by the pure mathematician in favor of producing solutions that give the user the answers he needs.
Book Description
This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. This expanded second edition contains new chapters on additive Schwarz preconditioners and adaptive meshes. New exercises have also been added throughout. The book will be useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory, and numerical analysis, while building upon and applying basic techniques of real variable theory. Different course paths can be chosen, allowing the book to be used for courses designed for students with different interests.
Customer Reviews:
A book for experienced people only........2006-12-20
This book certainly has a lot of information in it, but it is not lucid at all. This book is a hard read. The presentation is not done very well, and a lot of details get put off to the literature. I would actually recommend the FEM book by Braess instead. Only use this book as a reference.
a nice introductory book.......2000-04-06
This book is a very nice introductory book on the subject. It has a very nice presentation of the fundamental issues on finite element theory, such as interpolation theory on Sobolev spaces and variational formulations of elliptic problems. Also, it covers some advanced and more specific subjets such as multigrid methods and mixed methods for fluid mechanics, where it reviews some of the most used techniques to solve the saddle-point problems such as Augmented Lagrangian techniques and penalty methods.
Also, at the end of the book there is a very well written chapter focused on Interpolation operators, where there is a very nice (and very easy to read) presentation of the Sccot-Zhang interpolation operator, and some of the principal results on approximation.
Resuming, it is a very recomendable book in the subjet, specially recomendable for mathematics students interested on finite elements, and researchers in the field.
Book Description
This well-known advanced undergraduate- and graduate-level text uses a few basic concepts to solve and develop complete answers to linear homogeneous partial differential equations such as the problems of the vibrating string, the vibrating membrane, and heat conduction. With problems and solutions. 31 illustrations.
Customer Reviews:
You could do a whole lot worse........2003-09-12
This is a beautifully written book! This is a great place to start and perhaps end one's study of boundary and eigenvalue problems. The first chapter even provides one of the best treatments of first variation I have seen in print. The vibrating string, heat conduction, PDEs, Fourier series,special functions, self-adjoint operators, it is all there and written in an easy to understand format. Some may find the notation a little dated but that is little price to pay for such a treasure of knowledge. Read and enjoy.
A treatise for starting a career.......2000-06-27
I bought Sagan's book while a senior, and used it for a text while a second year professional and a third year graduate student in mathematics. The course led to a series of courses in theoretical mechanics, and untimately, a doctorate in control theory. The course taught from this book, and the following course in mechanics provided a strong foundation for a career. I continue to have my students read Sagan's book.
Physical problems treated with mathematical rigor........2000-05-19
This text includes material usually covered in mathematical physics courses, but its approach is somewhat different, and better, than most of the classics. The point is that the author felt not content with just explaining how to employ the most common mathematical methods to solve physical problems. He, on one hand, presents full motivation from the physical point of view, while on the other hand keeping high-level mathematical rigor. Believe me: this is not usual in mathematical physics books. By doing so, the author has produced a text valuable for both physicists and mathematicians.
Its contents are: Hamilton's principle and the theory of the first variation, representation of some physical phenomena by partial differential equations, theorems related to partial differential equations and their solutions, fourier series, self-adjoint boundary value problems, Legendre polynomials and Bessel functions, characterization of eigenvalues by a variational principle, spherical harmonics, the nonhomogeneous boundary value problem.
Includes excercises for most sections and references for each chapter. Suitable for third year undergraduates and on.
A high-class, beautifully written text.......1998-07-19
The problem with books on mathematical methods for physics is that they look more like a collection of recipes than like a coherent text. This was not true of the older classics, like Sommerfeld's "Partial Differential Equations of Physics". Fortunately, there is this beautiful book by Hans Sagan, now on Dover catalogue, to follow that tradition. A highlight is his treatment of the Sturm-Liouville problem. Having previously introduced variational methods, he shows that there is a "Lagrangian" whose "Euler-Lagrange equations" are just the Sturm-Liouville equations. In so doing, he has all the arsenal of approximation methods of variational calculus at his disposal to apply in the so-called special functions. As a beautiful example he estimates the position of the zeros of Bessel functions. The reader will find many other mathematical gems in this fine text.
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Systems of Conservation Laws 2: Geometric Structures, Oscillations, and Initial-Boundary Value Problems
Denis Serre
Manufacturer: Cambridge University Press
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Systems of Conservation Laws 1: Hyperbolicity, Entropies, Shock Waves
ASIN: 0521633303 |
Book Description
Systems of conservation laws arise naturally in physics and chemistry. Continuing where the previous volume left off, the author considers the maximum principle from the viewpoints of both viscous approximation and numerical schemes. Convergence is studied through compensated compactness. The author applies this tool to the description of large amplitude wave propagation. Small waves are studied through geometrical optics. Special structures are presented in chapters on rich and Temple systems. Finally, Serre explains why the initial-boundary value problem is far from trivial, with descriptions of the Kreiss-Lopatinski condition for well-posedness, with applications to shock wave stability, and certain problems in boundary layer theory. Throughout the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.
Book Description
KEY BENEFIT Emphasizing physical interpretations of mathematical solutions, this book introduces applied mathematics and presents partial differential equations.
KEY TOPICS Leading readers from simple exercises through increasingly powerful mathematical techniques, this book discusses hear flow and vibrating strings and membranes, for a better understand of the relationship between mathematics and physical problems. It also emphasizes problem solving and provides a thorough approach to solutions. The third edition of , Elementary Applied Partial Differential Equations; With Fourier Series and Boundary Value Problems has been revised to include a new chapter covering dispersive waves. It also includes new sections covering fluid flow past a circular cylinder; reflection and refraction of light and sound waves; the finite element method; partial differential equations with spherical geometry; eigenvalue problems with a continuous and discrete spectrum; and first-order nonlinear partial differential equations. An essential reference for any technical or mathematics professional.
Customer Reviews:
Outstandingly clear, although somewhat overly idealized........2006-11-18
This is an amazingly clear book that makes the subject of Partial Differential Equations seem very easy; it does so by exploring idealized problems and their solutions in a context where the student can master the various techniques and methods. The result is that the field of PDE's seems more unified than it does in most presentations. There is rich and clear discussion, and the book thoroughly explores the motivation behind the various techniques. Its only possible flaw is that it doesn't prepare the student for the "real world", although it does provide a quick path towards obtaining the necessary background to read books that engage in more "ugly" mathematics.
This book seems oriented towards an undergraduate course in PDE's and would be excellent in that role. However, I still found it immensely useful in my graduate courses as a reference and as a place to quickly master techniques I had skipped or forgotten. This book is exceptionally well-suited to self-study, with a healthy dose of exercises with answers in the back. An advanced student will find this book very easy to move through, in stark contrast to other PDE texts like the Weinberger. This book is well-complemented by the "Applied Mathematics" book by Logan; where the books overlap, Logan's book provides a more practical and less idealized (although more difficult) approach and is a natural next step after this book. Students moving in a more theoretical direction might look to the book on PDE's by Evans as a logical next step.
ok that it's not rigorous IMO, it's just an intro.......2004-04-12
I don't mind that this book isn't very rigorous; after all it's just an intro. This book may be better for a physics or engineering student for that reason, and the rigour can come later if you're in math. I had this text for an intro PDEs course that had many students from physics or engineering, so I totally believe that this is the right book for them. Maybe if math students want more rigour they could learn the proofs of everything. This book is a pretty good 1-stop text for everything you'd want to do in undergrad PDEs. There are enough examples and problems to make things clear. It's definitely a keeper if you're going to carry on with PDEs.
Comprehensive, detailed, easy to read -- a good PDE text.......2004-02-11
This PDE text by Haberman covers the ideas about separation of variables, Sturm-Liouville problem, finite difference numerical method, Green's function, Fourier transform, Laplace transform, and the method of characteristics. It presents the materials in quite plain, detailed manner. To me, the best part of this book relative to another books is that of Green's function. I've read Arfken, Farlow, and Strauss's texts, but have never got a satisfactory understanding.
The Strauss's one is the worst. To a beginner or non-mathematician, it is impossible to accept that kind of crazy things. The Farlow's one doesn't pay enough effort on this topic. It just goes through in a few pages. The Arfken's one (Mathematical Methods For Physicists) gives a concise presentation in quite physical way, but not for beginner. It is more like a summary.
Haberman introduces Green's function in his book with two chapters and in a quite different manner. He doesn't, like most physicists do, introduce it by Poisson's equation, but by heat equation and Fourier series; the ordinary definition of Green's function with delta function is given later. Though I think this is not a good idea and the presentation is not good, I do agree that it is much easier for beginners to understand. He makes no haste going into the three-dimensional case. Instead, he works on one-dimensional cases, then two and three-dimensional cases systematically. The point is, I think this won't make it too mathematical like the Strauss's one or too physical so that it is too constricted. In addition, he derives Green's functions in deductive way, instead of only taking a look at the physical suggestions. This makes the results convincible and gives readers a more comprehensive understanding.
Perhaps the most annoying thing of this book is that it is too wordy. However, this may be another advantage-the text is hard not to understand!
Someone says that Haberman hardly works on subjects other than heat equations. That kind of comment is misleading. He does work on wave and Laplace's equations. He just use heat equation as a main thread.
If you're learning PDE for physics or engineering or other applications, this book is quite suitable for self-studying. If you only want to study the most basic ideas about PDE, then Farlow's may be a light choice. If you want to study more, you can read Haberman's text.
Feedback from using book in a course.......2003-03-24
This book is below my expectations as a good introductory book. It doesn't have enough examples, and the examples are too straightforward in some cases. Too much attention is sometimes paid to development of the proofs, which can be left out if this book is as the title suggests : "elementary", because it's more useful to show the reader how to solve the problems. In terms of the organisation of the book, it's a bit confusing (this is especially obvious if you compare this book with Farlow). I think an excellent book can be produced if this book is merged with Farlow and with plenty examples thrown in. i'm not sure how this book was selected as a required text for my math course in Boundary Value Problems because i'd hope that there are better books out there in this 21st century.
An Applied Math Text for PDEs.......2002-11-04
Haberman's book clearly explains how to solve various kinds of PDEs and does provide insight into the meaning of the techniques and solutions. It is a good applied math text and those who are looking to use the techniques for other pursuits will find the book useful. It is not a math text, and may lack "rigor" for those who want it.
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Boundary Value Problems for Elliptic Systems
J. T. Wloka ,
B. Rowley , and
B. Lawruk
Manufacturer: Cambridge University Press
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ASIN: 0521430119 |
Book Description
The theory of boundary value problems for elliptic systems of partial differential equations has many applications in mathematics and the physical sciences. The aim of this book is to "algebraize" the index theory by means of pseudo-differential operators and new methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. Because many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises. This book is ideal for use in graduate level courses on partial differential equations, elliptic systems, pseudo-differential operators, and matrix analysis.
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Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains, Volume 69 (North-Holland Mathematical Library)
Michail Borsuk , and
Vladimir Kondratiev
Manufacturer: Elsevier Science
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ASIN: 0444521097 |
Book Description
The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.
Key features:
* New the Hardy Friedrichs Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.
* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.
* The question about the influence of the coefficients smoothness on the regularity of solutions.
* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.
* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.
* The behaviour of weak solutions near conical point for the Dirichlet problem for m Laplacian.
* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.
* The question about the influence of the coefficients smoothness on the regularity of solutions.
* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.
* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.
* The behaviour of weak solutions near conical point for the Dirichlet problem for m - Laplacian.
* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.
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Elliptic Boundary Value Problems with Indefinite Weights, Variational Formulations of the Principal Eigenvalue, and Applications (Research Notes in Mathematics Series)
Fethi Belgacem
Manufacturer: Chapman & Hall/CRC
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Binding: Paperback
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ASIN: 0582315972 |
Book Description
Elliptic Boundary Value Problems With Indefinite Weights presents a unified approach to the methodologies dealing with eigenvalue problems involving indefinite weights. The principal eigenvalue for such problems is characterized for various boundary conditions. Such characterizations are used, in particular, to formulate criteria for the persistence and extinctions of populations, and applications of the formulations obtained can be quite extensive.
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