Product Description
It has been 13 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books has used the functional analytic method of presenting semimartingales and stochastic integration. Thus a 2nd edition seems worthwhile and timely, though we will no longer call it"a new approach."

The new edition has several significant changes, most prominently the addition of exercises for solution. These are intended to supplement the text, but lemmas needed in a proof are never relegated to the exercises! Many of the exercises have been tested by graduate students at Purdue and Cornell Universities. Chap. 3 has been nearly completely redone, with a new, more intuitive and simultaneously elementary proof of the fundamental Doob-Meyer decomposition theorem, the more general version of the Girsanov theorem due to Lenglart, the Kazamaki-Novikov criteria for exponential local martingales to be martingales, and a modern treatment of compensators. Chap. 4 treats sigma martingales (important in finance theory) and gives a more comprehensive treatment of martingale representation, including both the Jacod-Yor theory and Emery's examples of martingales that actually have martingale representation (thus going beyond the standard cases of Brownian motion and the compensated Poisson process). New topics added include an introduction to the theory of the expansion of filtrations, and an elementary treatment of the Burkholder-Gundy-Fefferman martingale inequalities. Last, there are of course small changes throughout the book. ... Read more

Customer Reviews (2)

Received a cheaper knock-off printing
This review is about the material quality of the printing in the copy I received. This is not about the content.

I have access to a copy of this second edition (third corrected printing, 2005) in my office. It is the usual Springer high quality hardcover: it has a matte cover with texture, beautifully bound; the paper inside is high-quality, very soft and slightly off-white; and the printing of the text is very sharp. The version I received from Amazon claimed to be exactly the same, but was very different:
- The hardcover was shiny, did not have texture, and had a natural tendency to bend strongly outwards;
- The paper inside is whiter, horribly white;
- The text printing looks like a photocopy of the original.
It looks and feels like a cheap knock-off photocopy done in a backyard. They didn't even bother changing the information about the printing including the 'Printed in Germany' and 'Printed on acid-free paper'.

When I pay a lot of money for a hardcover edition I want the real thing, not a cheap knock-off. I returned mine.

Very good textbook
This book covers EXACTLY what the title promises. The approach to stochastic integration is a bit different from other books I have read, but very intuitive, general and understandable.
The proofs of the theorems are generally quite easy to understand, but do not lack rigor at all - quite the opposite.
The prerequisites in probability theory are quite modest, however some understanding of measure theory (at least on an intuitive level) is helpful. Some knowledge of stochastic processes (such as maertingales...) also facilitates the reading of the book.

Overall, it is quite amazing how Prof. Protter manages to explain deep subjects rigorously, yet very understandably!

The book contains a "normal" amount of typos, but almost all are harmless - they do not affect the understanding at all.
The only draw-back to the serious researcher might be the large number of French language references. ... Read more

Product Description
This text is designed for engineers, scientists, and mathematicians with a background in elementary ordinary differential equations and calculus. ... Read more

Customer Reviews (14)

Outstandingly clear, although somewhat overly idealized.
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
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
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
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
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. ... Read more

Product Description

For combined differential equations and linear algebra courses teaching students who have successfully completed three semesters of calculus.

This complete introduction to both differential equations and linear algebra presents a carefully balanced and sound integration of the two topics. It promotes in-depth understanding rather than rote memorization, enabling students to fully comprehend abstract concepts and leave the course with a solid foundation in linear algebra. Flexible in format, it explains concepts clearly and logically with an abundance of examples and illustrations, without sacrificing level or rigor. A vast array of problems supports the material, with varying levels from which students/instructors can choose.

Customer Reviews (22)

Cheaper than Bookstore
It was cheaper than getting it at the bookstore, and with free Amazon prime for .edu students, it got here in two days. What more is there to say?

good product
i use this book for the school textbook. I think the reading the book is very confusing. make sure to get the manual too. the manual helped me a lot more than the book.

Totally horrifying .
This book is written in Greeks and none of the examples explained the topic well.
And also, there are numerous mistakes in the answer booklet.

It's my first time frustrating with Math, why? because of this book.
The answer key made me really mad ! for real

Used book that looked new!
The book came at a good speed. Got it about 2 weeks after i ordered it. Book was nearly in perfect shape. Pages had small pencil marks but otherwise very good shape. Recommend this seller.

Good text with fairly easy examples
I took a class using this book my freshman year while also taking a 400 level Math class at the same time. Needless to say, I didn't have a lot of time to focus solely on the homework for this class. The book was clear and gave adequate examples. I feel that most people probable have complained about this book because they didn't give the lessons and examples a thorough reading/understanding, as is a common cause of dislike of a text. This was a great book for an intro class to linear algebra. My one reason for giving this book a 4 rather than a 5 is that the problems weren't challenging enough. I thought that most questions could be answered after only a thought or two, rather than careful contemplation and study. ... Read more

Product Description
Partial differential equations (PDEs) play an important role in the natural sciences and technology, because they describe the way systems (natural and other) behave. The inherent suitability of PDEs to characterizing the nature, motion, and evolution of systems, has led to their wide-ranging use in numerical models that are developed in order to analyze systems that are not otherwise easily studied. Numerical Solutions for Partial Differential Equations contains all the details necessary for the reader to understand the principles and applications of advanced numerical methods for solving PDEs. In addition, it shows how the modern computer system algebra Mathematica® can be used for the analytic investigation of such numerical properties as stability, approximation, and dispersion. ... Read more

Product Description
Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This is a practical and mathematically well informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included. ... Read more

Customer Reviews (1)

Its a handbook for numerical solutions of ODE & DAE.
This book is excellent.The concepts about stiff, initial value problems, boundary value problems and differential-Algebraic equations (DAE) is treated with relative deep.

The numerical methods for many cases is covered.

The bad is that don't show the code.The code is in a web (NETLIB) and is writed in Fortran Language.

Is very expensive! ... Read more

Product Description

Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations. Written to a multi-disciplinary audience, it sets each area of science in his historical context and then guides the reader towards questions of current interest.

Product Description

This book is designed as an advanced undergraduate or a first-year graduate

course for students from various disciplines like applied mathematics,

physics, engineering.

The main purpose is on the one hand to train the students to appreciate the

interplay between theory and modelling in problems arising in the applied

sciences; on the other hand to give them a solid theoretical background for

numerical methods, such as finite elements.

Accordingly, this textbook is divided into two parts.

The first one has a rather elementary character with the goal of

developing and studying basic problems from the macro-areas of diffusion,

propagation and transport, waves and vibrations. Ideas and connections with

concrete aspects are emphasized whenever possible, in order to provide

intuition and feeling for the subject.

For this part, a knowledge of advanced calculus and ordinary differential

equations is required. Also, the repeated use of the method of separation of

variables assumes some basic results from the theory of Fourier series,

which are summarized in an appendix.

The main topic of the second part is the

development of Hilbert space methods for the variational formulation and

analysis of linear boundary and initial-boundary value problems\emph{. }%

Given the abstract nature of these chapters, an effort has been made to

provide intuition and motivation for the various concepts and results.

The understanding of these topics requires some basic knowledge of Lebesgue

measure and integration, summarized in another appendix.

At the end of each chapter, a number of exercises at different level of

complexity is included. The most demanding problems are supplied with

answers or hints.

The exposition if flexible enough to allow substantial changes without

compromising the comprehension and to facilitate a selection of topics for a

one or two semester course.

Customer Reviews (1)

a valuable new addition for students and Professionals
Sandro Salsa's book: "Partial Differential Equations in Action: From modelling to Theory" is true to it's title. It guides the reader
from the modeling stage to the theory, i.e. it is written from
the point of view of an applied mathematician who wishes
to understand the phenomenon that gives risethe PDE but who also
seeks to gain an analytical understanding of the PDE before proceeding
to it's numerical implementation. The book is written at a level
suitable for both an advanced undergraduate or first year graduate
school class at most American Institutions.
Salsa's light but incisive touch in writing about PDE's is reminiscent,
for those familiar with Gilbert Strang's books,
with Strang's way of entertaining while at the same
time challenging the reader. The book is unique
in many ways. For instance the use of Fourier series in treating
the diffusion equation is, in of itself standard, but Salsa's
use of the energy method to show that the Fourier series
solution is the unique solution is a nice illustration
of how the book alternates between the practical and
the more qualitative or technical aspects of the subject.
For students of mathematical finance and mathematical
biology, as well as for students of mathematical physics
the treatment of random walks and their relations to
Brownian motion and to the diffusion equation is the
best I've ever seen. For students of mathematical
finance there is a nice section on the Black-Scholes equation
and a use of the maximum principle to show that
call option prices are increasing with increasing
volatility. For studentin applied physics the
sections on the wave equation and on hyperbolic
problems are some of the best I've found available.

In later Chapters more advanced material introducing the
student to the use of Sobolev spaces in solving Elliptic
equations and evolution equations is carried out
in a highly efficient and very clear fashion.

In summary, I highly recommend this book.
Indeed, I think it is destined to become a classic. ... Read more

Product Description
Ledder's innovative, student-centered approach reflects recent research on successful learning by emphasizing connections between new and familiar concepts and by engaging students in a dialogue with the material. Though streamlined, the text is also flexible enough to support a variety of teaching goals, in part through optional topics that give instructors considerable freedom in customizing their courses. Linear algebra is presented in self-contained sections to accommodate both courses that have a linear algebra prerequisite and those that do not. Throughout the text, a wide variety of examples from the physical, life and social sciences, among other areas, are employed to enhance student learning. In-depth Model Problems drawn from everyday experience highlight the key concepts or methods in each section. Other innovative features of the text include Instant Exercises that allow students to quickly test new skills and Case Studies that further explore the powerful problem-solving capability of differential equations. Readers will learn not only how to solve differential equations, but also how to apply their knowledge to areas in mathematics and beyond. ... Read more

Customer Reviews (1)

Okay for review, TERRIBLE for learning
While Ledder tries an innovative approach to teaching differential equations in his book, the attempt fails miserably. The book goes into detail explaining things at the conceptual level, but it leaves much of the technical math explanation to the reader in "instant exercises" and then does not actually cover examples that help solve the vast majority of the highly technical problems seen in the end of each chapter and on any exams you will take with your professor (the section on partial differential equations is most guilty of this). Furthermore, the material it does cover on its own is usually done in vague, unclear terms (with a couple notable exceptions involving linear systems). The modeling bits are somewhat interesting, but this book is not very useful in terms of learning to solve and manipulate the differential equations yourself. Unless you plan on learning all of the material in class, this book will have very little use for you. ... Read more

Product Description
Identifies significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. This book contains a chapter on Lewy's example of a linear equation without solutions. ... Read more

Customer Reviews (3)

Review on Partial Differential Equations by Fritz John
I required this book for one of my post graduate course module studies. My professor is following this book. In my opinion, this contains the latest research findings and is one of the best books in this subject.

Very impressive
I'm very impressed by John's book on PDE's. Very complete, top down approach to the subject, while remaining lucid and concrete. It's the work of a master.

Excellent summary of the most important PDEs!
I studied this book from cover to cover, and I found its explanations lucid and complete.F. John's writing style makes excellent reading, and the details he supplies are complete enough that anyone with only abackground in undergraduate multivariable calculus can understand thearguments.Like any good mathematics textbook, this one leaves the readerto work out his/her own steps at some points, but Dr. John always makes itclear which elements areneeded.This book will always have a place onthe shelf in my office. ... Read more

Product Description
This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems.Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles.In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems. ... Read more

Customer Reviews (2)

Very good graduate ODEs text, with some flaws
Perko's book is one of the best books that gives an advanced introduction to dynamical systems from the point of differential equations.Many other good books tread the same ground, without emphasizing the connection to ODEs.Perko's text is particularly strong in several respects.First, the dynamical systems it considers are almost always expressed in terms of underlying differential equations.Second, it gives proofs or outlines of proofs of most major theorems used in this field.Third, it covers the most important topics, including: local theory of hyperbolic equilibria, invariant manifolds, Hamiltonian systems, flows on R^2, stability theory, and elementary bifurcations.Also reviewed are the results from linear systems theory, in a particularly well-written and easy to follow introductory chapter.Another great feature of this book is its solid coverage of center manifold theory, which is an important and somewhat difficult topic.

There are a couple of problems with this book.The proofs to some of the major theorems are occasionally abstruse or poorly derived.Perko seems to bend over backwards to give analytical proofs, when algebraic or topological proofs might be easier.Many of the problems reuse the same elementary example equations.This is OK insofar as it allows the reader to see how different techniques can be used to analyze the same systems, but it limits the reader's exposure to the full variety of interesting dynamical systems that can arise in practice.The author also tends to emphasize polynomial vector fields, which is a potential limitation.Occasionally the problems are significantly more difficult than the examples worked in the text.

Overall, Perko's text is a very solid introduction to advanced ODEs and continuous dynamics.It is especially well-suited for scientists and engineers who want a readable introduction to the qualitative theory of ODEs.

A Book on Advanced Dynamical Systems
This book is a useful textbook for advanced courses on differential equations and dynamical systems for senior undergraduate students or first year graduate students.

The book presents a systematic study of thequalitative and geometric theory of nonlinear differential equations anddynamical systems.

The book has a sketch of the proof of theHartman-Grobman Theorem which was useful for my second undergraduate courseon dynamical systems and nonlinear differential equations.

I liked thebook and I am quite sure it will become a classic textbook on this veryuseful branch of Math that has so many old and new applications in Physics,Economics and Finance. ... Read more

Product Description
Publisher: John Wiley And Sons, Inc.Publication date: 1923Subjects: NATURAL SCIENCESMathematicsFundamental and general consideration of mathematicsNotes: This is an OCR reprint. There may be numerous typos or missing text. There are no illustrations or indexes.When you buy the General Books edition of this book you get free trial access to Million-Books.com where you can select from more than a million books for free. You can also preview the book there. ... Read more

Product Description
An essential aid for those in math, science, andengineering.The 39 comprehensive chapters of this book cover thefield from separable equations to second order equations, systems ofequations, and non-linear equations.A particularly large number ofapplications are included.Problem-solving strategies and methods ofattack are included at the beginning of every chapter for each topiccovered. ... Read more

Customer Reviews (6)

Good
This is a classical and in a great shape book.
Service was outstanding.
It is difficult to comment when a good service is received.
Just keep the big spirit

I doubt that there's a better supplemental DE book out there
I used this book for an introductory differential equations course.With the help of this book, I was completely prepared for everything the professor threw at us and more.

Some of the problems are simple and should help to reinforce the basic concepts learned from another book.Learn the fundamentals from some other book (or even a professor), and refine your thought processes using this one.There are some basic explanations of concepts and problem types, but most of the space is devoted to problems and solutions, as you may have guessed.If I had trouble with a problem from another book, I could almost always find a similar one in the REA book.A few problems are extremely difficult or involved, but the book leads you through every step of every problem.I was blown away by the depth of a few problems, but following the reasoning in this book really helped me to develop a better "feel" for the subject.

Yes, the font looks like something from your mother's typewriter, but the book is very sensibly organized into a (huge) number of chapters that should more than cover any intro-level DE course.My test reviews consisted of working problems from this book and doing little else, and I've never felt more confident going into exams.

If you're willing to put in the time, this book is probably one of the best course-related resources you could ever spend your money on.It would also be a good reference for someone who occasionally wants help with troublesome problem types.

Excellent
This is an excellent supplement to any Differential Equations class.It starts out with easy and straight forward problems and progressively gets to the more advanced problems.All steps are worked out in an easy to understand way.Most importantly this book shows the algebraic steps in obtaining solutions, which is ussually where students have trouble.This book is a must have for any science major.

An Excellent Resource!
If you are studying DEs, get this book! It beats the usual text books that only contain solutions to selected problems, namely the ones that the professor does not assign or examine you on. This book is comprehensive and contains stratagies for attacking the various problems you will encounter in undergraduate DE courses. It even contains problems and solutions to Partial Differential Equations, Fourier Series and Boundary Value Problems, not just ODEs!

Great - after learning hoe to work with - its a life saver
The book is very good, but the student have to spend some time knowing thesystem of the book. it is not strait foward . ... Read more

Product Description

Partial Differential Equations and Boundary Value Problems with Maple presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple's animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations.  Maple files can be found on the books website.

Customer Reviews (2)

Maple files unavailable : it's a shame !
pretty good stuff but where is the code???

Typing all the code is error prone and boring !

Good but where is the code?
This is a nice, neat book that in a plodding, slow way gives lots and lots of examples of how Maple can solve PDEs.It is a bit unusual in that the first chapter, after a review of ODEs, goes right to Sturm-Liouville systems and Green's functions.Both allow for a nice and systematic treatment of PDEs in the subsequent chapters.I have typed up the code in this SLs chapter and it works just fine -- I used Maple 9.

The book should complement, not replace, a regular textbook by say Haberman.Haberman's explanations of theory are much better -- but nothing helps more than having a CAS do all the intense busy work that can be required for even a simple problem.The best is a combo of good systematic and thorough theory with many worked examples using automation.

For these purposes the book would get 5 stars, except that there is no website with the code, as the book indicates there should be somewhere.Going to the publishers site there is a dead link.Perhaps these things will be remedied soon.The long and short of it: it's a good book, but you will have to type in the code for each example.This can, of course, have didactic pluses, but, none-the-less, the author says there's a website and there isn't and there is no CD.

... Read more

Product Description
The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. ... Read more

Customer Reviews (2)

Great PDE book
I like this book.Right from the beginning, Taylor uses concepts from smooth manifold theory to obtain results in a coordinate free fashion (on a Riemannian/Lorenz manifold) when possible.At the same time, he will go to coordinates when necessary, or even revert to R^n when stronger results are possible there.As an added "bonus" the book contains surprisingly few errors, or at least I found less than usual, so maybe I'm getting slow!

I didn't find this to be an introductory (as in first year of grad school) level book.The proofs are often given in less detail than those found in the standard introductory graduate texts.Reading and understanding this text requires knowledge of Real Analysis and smooth manifolds/differential geometry at the introductory graduate level.Fourier transforms and distributions are built up from scratch, but the treatment is quick and probably assumes you have some previous knowledge.Note that my opinion is formed after using this book for self-study, so you can probably relax the prerequisites slightly if this book is used as part of a course.

Another point worth mentioning is that the exercises are often quite easier than verifying the individual proofs in the chapter.

Why not 5 stars?I found the book and chapter introductions to be quite uninspiring and not very useful.He essentially lists off the material that will be covered with no thought to motivation.I like to read something about why one particular approach is necessary or better or just different than another approach.Simply listing off concepts to be covered has little meaning if one has no idea what those concepts mean!The discussion of results is also rather sparse, sort of like Rudin.

Complete, accurate and well-written.
The author accomplished the goal of presenting this broad and many-faceted subject in a thorough and comprehensive manner. Beginning from the fundamentals of ODE theory to the most sophisticated methods for solving important PDE's of mathematical physics, this series of three volumescomprises all what a modern analyst must know about the topic and muchmore.

The contents of volume 1 are: Basic theory of ODE;Laplace andwave equations; Fourier analysis, distributions, and constant-coefficientlinear PDE; Sobolev spaces; linear elliptic equations; linear evolutionequations. Appendices: Outline of functional analysis; manifolds, vectorbundles, and Lie groups.

Originally intended for graduate students andworking mathematicians, most of the material is suitable for advancedundergraduate courses. Includes excercises for each section and extensivereferences. ... Read more

Product Description
This is a thoroughly updated and expanded 4th edition of the classic text Nonlinear Ordinary Differential Equations by Dominic Jordan and Peter Smith. Including numerous worked examples and diagrams, further exercises have been incorporated into the text and answers are provided at the back of the book. Topics include phase plane analysis, nonlinear damping, small parameter expansions and singular perturbations, stability, Liapunov methods, Poincare sequences, homoclinic bifurcation and Liapunov exponents.

Over 500 end-of-chapter problems are also included and as an additional resource fully-worked solutions to these are provided in the accompanying text Nonlinear Ordinary Differential Equations: Problems and Solutions, (OUP, 2007).

Both texts cover a wide variety of applications while keeping mathematical prequisites to a minimum making these an ideal resource for students and lecturers in engineering, mathematics and the sciences. ... Read more

Customer Reviews (5)

Great book!
I am taking a Nonlinear Dynamics course in grad school and this is the text book. Although it is very hard for any text book to be absolutely complete (without being extremely large) I think J&S do a good job at covering many aspects. There are several examples for each concept and good explanations. It will earn a place in my shelf of references.

An Unique Resource
Jordan and Smith have done an excellent job in describing and providing techniques to solve non-linear differential equations.Non-linear ordinary differential equations are stiff and can be solved numerically, but numerical solutions do not provide physical parametric insight.Consequently, it is often necessary to find a closed analytical solution.When faced with this challenge in my personal research, I looked around for books that would help me solve the non-linear forced differential equation that science had presented to me.Even in a good research university library, I could not find any that beat Jordan and Smith's work.I did find summary presentations in the specialized literature of physics, but those works referenced Jordan and Smith for futher details.Together, Jordan and Smith's textbook and sourcbook provide a wealth of practical information for solving non-linear equations along with lots of good examples.I feel fortunate that I found their work and have successfully solved my equations following their advice.Their work even helped me to visualize and interpret my results.I heartily recommend the two books to anyone faced with the need to solve nonlinear ordinary differential equations using techniques (for example, averaging methods, perturbation methods, Fourier expansion methods, liapunov methods, chaos, etc.# that lie beyond those studied in college for solving linear differential equations.Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers #Oxford Texts in Applied and Engineering Mathematics#Nonlinear Ordinary Differential Equations: Problems and Solutions: A Sourcebook for Scientists and Engineers #Oxford Texts in Applied & Engineering Mathematics)

Not an instructive textbook
I am in an introductory graduate level math course using this textbook. I agree with the other reviewer who criticizes its lack of rigor, numerous typos, and overabundance of examples. The text is not well-written, so the authors wander among seemingly related topics within each chapter without giving much explanation of their background or intuitive insight into the physical phenomena they describe. Moreover, the examples have not been very instructive for me. They often leave out several steps (for example, many assume that you already have an analytic solution for a differential equation, thus I sometimes find myself needing to use Mathematica to derive one). The problems are loosely related to the examples, but there is enough of a disconnect between the two so that I have trouble doing the homework assignments. I find myself referring to other (more elementary) texts on differential equations for better insight into the problems.

I strongly discourage the use of this book and am looking forward to when the class ends.

very non-rigorous approach with a sizeable number of typos
(I am referring to the paperpack 3rd edition)

The text serves as an ok introduction to nonlinear ODEs.I would not recommend it for any kind of rigorous course, since the approach is very nonrigorous.There are no theorems, and no attempt at analysis, so you must take everything at the author's word.The book is mainly a large collection of examples.The difficulty of the problems depends on how rigorous you want the answers to be, and there are a lot of answers in the appendix (but without any comments about how they were derived).

Personally, the book irritates me, but I can see its usefulness.One of the main causes of irritation was the unusually high number of typos, at the rate of one per page in some chapters (and in the problems and their solutions too).I find this quite significant.This is the third edition, and there is no excuse for so many errors.I have never encountered a published book with this kind of error rate.

I do not have much experience with similar books, so I can't rate this text in context very well.It is similar to, say, Marion and Thornton's Classical Dynamics, except with less physics (of course) and more on difficult nonlinear ODEs, and with more typos.

Approachable introduction to nonlinear ODE's
Certainly worth the price. Very approachable. I haven't reviewed many similar books -- this text is good enough that I haven't felt the need.

Covers: solution, characterization, and stability analysis, including bifurcation and chaos.

The new 3rd edition is much better andsignificantly longer than the earlier editions. ... Read more

Product Description
An Introduction to Partial Differential Equations with MATLAB is a textbook that features MATLAB to aid with problem solving. It includes carefully explained central ideas of the subject, derivations of equations, and historical accounts. It also contains a computational chapter that focuses on the use of finite differences-the numerical method most widely used by engineers. MATLAB is integrated throughout the book in chapter projects that present the problem to be solved along with instructions on how to use the MATLAB software. The MATLAB routines used in the book are provided for download from the Internet. Prerequisites for the book are courses in calculus and differential equations. ... Read more

Customer Reviews (3)

Too many typos for me.
The book is more of a pure PDE book and definitely is independent of Matlab.

After reading the first 5 chapters I have come across so many typo errors that I have lost count!

There are many interesting exercises but not enough detailed solutions showing how to solve them step by step.

Overall I would not recommend buying this book.

Good and Clear
I used this book for the first time this past semester. It is well written, although a bit informal for my taste (although the students seemed to like it). There are numerous exercises, although sometimes too many of the plug-and-chug variety, and I wish there were a few more of the highly challenging problems. The order of topics is exactly the way I like it, except that Chapter 5 is a little out of place. However, in a course like this I think it may be impossible to find a natural place for the method of characteristics. Most texts put it first, which doesn't seem right for a course that emphasizes Fourier methods. For our course, I interchanged Chapters 5 and 6. The MATLAB is not heavily integrated. That is a good thing, for a couple of reasons. It means that the mathematics, and not MATLAB, is the main focus, and it allows the text to be used with or without it. We did use MATLAB and it worked well.Overall, this was a good basic introduction to the subject. It steers a course between mathematical rigor on the one hand, and computation, physical intuition and applications on the other, and it does so quite well. I could envision its being used for a higher level course for scientists and engineers, though not for a course with a more theoretical bent.

Very well written with excellent explanations.
First, I have to say that I'm biased because I'm a former student of Prof. Coleman's (Multivariable Calc and ODE's). But I was happy to see that he had written a PDE book and I bought it so that I could relearn PDE's, since the PDE course I had wasn't so great. I haven't been disappointed. I've read most of the first six chapters so far - the book is easy to read and the explanations are clear. There are tons of homework problems and applications. However, I don't have access to MATLAB so I can't really comment on that aspect of the book. ... Read more

Product Description

Combining traditional material with a modern systems approach, this handbook provides a thorough introduction to differential equations, tempering its classic "pure math" approach with more practical applied aspects. Features up-to-date coverage of key topics such as first order equations, matrix algebra, systems, and phase plane portraits. Illustrates complex concepts through extensive detailed figures. Focuses on interpreting and solving problems through optional technology projects. For anyone interested in learning more about differential equations.

Customer Reviews (3)

Maybe not so good....
My son found this book to be largely unhelpful in his second course on differential equations where this was the course textbook.He frequently found himself going to the internet looking for better descriptions of the material.I ended up buying him a couple of better rated books on Diff. EQ. to get him back on track.

Diff Eq book
The book was in fairly decent shape and it was shipped promptly to my house. I recommend this seller.

Great Book for ODE's
I used this book for a course in ODE's. The edition that was available for purchase at our school's bookstore also included a book by the authors for using MatLab for solving ODE's, The combination of the two were great. The book is logically structured and generally easy to read. The authors use many examples from a variety of fields. The MatLab book was a phenomenal help: it's the best intro to MatLab that I've found, and was very useful in helping to solve problems. My only beef with the book is that since this is a first edition, there are several errors in the odd numbered solutions at the end of the book, which caused many sleepless nights. ... Read more