Product Description
Excellent introductory text for students with one year of calculus. Topics include complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order nonlinear equations, linear differential equations, Laplace transforms, Bessel functions and boundary-value problems. 48 black-and-white illustrations. Exercises with solutions. Index.
... Read more

Customer Reviews (3)

Only the first half is good
The first half of this book is good.Although Dettman does occasionally skip nonobvious steps, he does a good job of introducing the reader to complex numbers, matrices, and linear algebra.The second half, though, concerning differential equations is awful.I originally got this book to teach myself these two subjects over the summer and shortly into Chapter 5 I had to give it up and switch material; the explanation is murky and the presentation confusing:it only really makes sense after you go somewhere else and learn differential equations, then come back and look at it again.

If you want to learn linear algebra, you can't go wrong with this book, although there are better choices out there.If you want to learn differential equations, this is not the book for you.

Good for reference or self study
The book is easy to read.Dettman manages to find an excellent balance between formal proof and informal explanation.The first two chapters on Complex Numbers and Linear Algebraic Equations are particularly good, and this has become the first book I usually reach for if I need to look up something about matrices.Matrix notation is used throughout the book for topics such as linear transformations and systems of equations.There are hints and answers to about half the exercises at the end of the book, making it very helpful for self study.

Excellent for Physicists
I am a physicist, and as a sophomore in college I was warned by the juniors:"Learn linear algebra!!!!They hardly teach any of it in the required math classes, and you'll die in quantum without it!!!"So I studied this book.Even without doing many of the problems I got a clear grasp of what a vector space is, why it is more than mere formalism, what a linear transformation is, the significance of bases, diagonalization, and how to work with matrices and really understand them.All of this was indispensable in studying quantum mechanics.

Of course, solving the problems will only help your understanding.I HIGHLY recommend this for any physics student who had a bad (or non-existent) linear algebra class. ... Read more

Product Description
This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject. ... Read more

Customer Reviews (6)

A valuable source
This book (the original version) has all the basics to introduce the future differential equations/dynamical systems researchers into the field. Written by authorities in the field (Hirsch and Smale,) this text offers a wide variety of topics, including linear systems, local and global stability theory for non-linear systems, and applications to physics and biology. As an added treat, the inclusion of basic linear algebra and operator theory makes this a rather self-contained work. The dedicated reader will not be disappointed - the material is well organised with sufficient level of detail, illustration, and exercises.

This is not a recipe book
I can see that this is not the book for you if you want to solve a particular differential equation.But in terms of understanding the field of dynamical systems, there is no rival.This book is a pleasure to read, for the first time I understood the importance and beauty of linear algebra.Academic Press says that this is their most successful mathematics text, and it is not hard to see why.I wish more texts were as clearly written and as beautiful to read.

A complete waste
This is not a book, it's a piece of trash!!! This so called book is a meaningless mess which wasn't even understandable for the person who had a PhD in math and was teaching our class. Do NOT bother with this nonsense. if you want to learn something just read Ordinary Differential Equations by V. I. Arnold.I would have given no star if I could!!!Just go with Arnold's and I'll be WAY better off.

Not for the average undergrad!
As a senior undergrad majoring in math and economics, this book is everything but an easy read. To all fellow undergrads who are not math superheroes (that should about 75% of us), if you happen to come across this book in an upcoming course description, it may be a good idea to look for alternative. Currently, I'm looking for another book that I may be able to use as a supplement to get me through this course with a passing grade. Up to this point in my math career, I have never come across a text as ungraspable as this one; this is unfortunate since it appears that there is a lot of knowledge and content on the pages.

Thorough and solid introduction
This is the book from which I was introduced to dynamical systems some twenty-odd years ago. It's a thorough introduction that presumes a basic knowledge of multivariate differential calculus but is pretty well self-contained as far as linear algebra is concerned. Rigorous but readable, it provides a foundational understanding of n-dimensional linear dynamical systems and their basic exponential solution.

But my opinions won't be as helpful to the Amazon math shopper as a simple listing of what's in the book. So here's the table of contents.

Chapter 1: First Examples

Chapter 2: Newton's Equation and Kepler's Law

Chapter 3: Linear Systems with Constant Coefficiants and Real Eigenvalues

Chapter 4: Linear Systems with Constant Coefficients and Complex Eigenvalues

Chapter 5: Linear Systems and Exponentials of Operators

Chapter 6: Linear Systems and Canonical Forms of Operators

Chapter 7: Contractions and Generic Properties of Operators

Chapter 8: Fundamental Theory

Chapter 9: Stability of Equilibria

Chapter 10: Differential Equations for Electric Circuits

Chapter 11: The Poincare-Bendixson Theorem

Chapter 12: Ecology

Chapter 13: Periodic Attractors

Chapter 14: Classical Mechanics

Chapter 15: Nonautonomous Equations and Differentiability of Flows

Chapter 16: Perturbation Theory and Structural Stability

Afterword

Appendix I: Elementary Facts

Appendix II: Polynomials

Appendix III: On Canonical Forms

Appendix IV: The Inverse Function Theorem

References

Answers to Selected Problems ... Read more

Product Description
The goal of this monograph is to address the issue of the global controllability of partial differential equations in the context of multiplicative (or bilinear) controls, which enter the model equations as coefficients. The mathematical models we examine include the linear and nonlinear parabolic and hyperbolic PDE's, the Schrödinger equation, and coupled hybrid nonlinear distributed parameter systems modeling the swimming phenomenon. The book offers a new, high-quality and intrinsically nonlinear methodology to approach the aforementioned highly nonlinear controllability problems. ... 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

This is the softcover reprint of the very popular hardcover edition. This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is one of its main features. Many kinds of problems are addressed. A comprehensive theory of Galerkin method and its variants, as well as that of collocation methods, are developed for the spatial discretization. These theories are then specified to two numerical subspace realizations of remarkable interest: the finite element method and the spectral method.

Product Description
Well-known authors; Includes topics and results that have previously not been covered in a book; Uses many interesting examples from science and engineering; Contains numerous homework exercises; Scientific computing is a hot and topical area ... 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
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This new edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems. ... Read more

Customer Reviews (3)

Payback in longrun; not a Cookbook.
In the graduate school, a Math professor used this book, as it talked about a bit of everything. Everything as in initial value problems (IVP) in ODE, 2 point boundary value problems ( BVP ) for ODE, finite difference schemes for boundary value elliptic PDE's and initial-boundary type hypebolic PDE's.

However, the book is written for a mathematician in mind,as the author clearly mentions in the preface. It is not for the light hearted. Book would serve as a
starting point for rigourous foundations in numerical analysis methods for solving
ODE/PDE. Excellent book over all, with numerical examples, watertight arguments,
and crisp prose, without being boring.

Informal, nice text
A very informal style of writing with lots of explanation.He doesn't skip large steps like in the old-fashioned terse style of math texts, which makes it very readable, though some readers may not like it.Not very rigorous, but he's upfront about it.

The original version from 1996 has quite a few errors, and the author maintains information on errata on his website.The most recent reprinting has corrected most of these errors.So, even though there is only a single edition, some versions have errors and some don't.So, BEWARE BUYING USED EDITIONS because they will most likely be from an earlier printing and thus have more errors.I assume the new version on amazon is the corrected version.

Excellent for a graduate course on numerical DE
This is an excellent reference and textbook for someone hoping to go beyond the introduction to numerical DE found in any of the standard numerical analysis textbooks.It is not a research monograph, but is also not easy reading.It has already become a fairly standard reference in the literature because of its complete coverage and further references to more specialized sources.I have used it as the textbook for a graduate courseon numerical differential equations.I highly recommend it for that purpose and as a reference for someone doing independent reading. ... 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
This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner. ... Read more

Product Description

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations.

From the reviews:

"The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Customer Reviews (2)

A reference book in the domain
Much literature is published on numerical methods for stochastic differential systems but most of it focuses on their use in pricing financial products. There is genuinely a lack of reference books that provide a stronger mathematical basis for the domain. Luckily, this is one of the few books that fill that gap. An excellent book, although the scope of numerical methods presented is limited.

Excellent
This book is one of the finest written on the subject and is suitable for readers in a wide variety of fields, including mathematical finance, random dynamical systems, constructive quantum field theory, and mathematical biology. It is certainly well-suited for classroom use, and it includes computer exercises what are definitely helpful for those who need to develop actual computer code to solve the relevant equations of interest. Since it emphasizes the numerical solution of stochastic differential equations, the authors do not give the details behind the theory, but references are given for the interested reader.

As preparation for the study of SDEs, the authors detail some preliminary background on probability, statistics, and stochastic processes in Part 1 of the book. Particularly well-written is the discussion on random number generators and efficient methods for generating random numbers, such as the Box-Muller and Polar Marsaglia methods. Both discrete and continuous Markov processes are discussed, and the authors review the connection between Weiner processes (Brownian motion for the physicist reader) and white noise. The measure-theory foundations of the subject are outlined briefly for the interested reader.

Part 2 begins naturally with an overview of stochastic calculus, with the Ito calculus chosen to show how to generalize ordinary calculus to the stochastic realm. The authors motivate the subject as one in which the functional form of stochastic processes was emphasized, with Ito attempting to find out just when local properties such as the drift and diffusion coefficients can characterize the stochastic process. The Ito formula is shown to be a generalization of the chain rule of ordinary calculus to the case where stochasticity is present. The authors are also careful to distinguish between "random" differential equations and "stochastic" differential equations. The former can be solved by integrating over differentiable sample paths, but in the latter one has to face the nondifferentiability of the sample paths, and hence solutions are more difficult to obtain. The authors give many examples of SDEs that can be solved explicitly, and prove existence and uniqueness theorems for strong solutions of the SDEs. And since ordinary differential equations are usually tackled by Taylor series expansions, it is perhaps not surprising that this technique would be generalized to SDEs, which the authors do in detail in this part. They also outline the differences between the Ito and Stratonovich interpretations of stochastic integrals and SDEs.

Part 3 is definitely of great interest to those who must develop mathematical models using SDEs. The authors carefully outline the reasons where Ito versus the Stratonovich formulations are used, this being largely dependent on the degree of autocorrelation in the processes at hand. The Stratonovich SDE is recommended for cases when the white noise is used as an idealization of a (smooth) real noise process. The authors also show how to approximate Markov chain problems with diffusion processes, which are the solutions of Ito SDEs. Several very interesting examples are given of the applications of stochastic differential equations; the particular ones of direct interest to me were the ones on population dynamics, protein kinetics, and genetics; option pricing, and blood clotting dynamics/cellular energetics.

After a review of discrete time approzimations in ordinary deterministic differential equations, in part 4 the authors show to solve SDEs using this approximation. The familiar Euler approximation is considered, with a simple example having an explicit solution compared with its Euler approximate solution. They also show how to use simulations when an explicit solution is lacking. The importance notions of strong and weak convergence ofthe approximate solutions are discussed in detail. Strong convergence is basically a convergence in norm (absolute value), while weak convergence is taken with respect to a collection of test functions. Both of these types of convergence reduce to the ordinary deterministic sense of convergence when the random elements are removed.

The discussion of convergence in part 4 leads to a very extensive discussion of strongly convergent approximations in part 5, and weakly convergent approximations in part 6. Stochastic Taylor expansions done with respect to the strong convergence criterion are discussed, beginning with the Euler approximation. More complicated strongly convergent stochastic approximation schemes are also considered, such as the Milstein scheme, which reduces to the Euler scheme when the diffusion coefficients only depend on time. The strong Taylor schemes of all orders are treated in detail. Since Taylor approximations make evaluations of the derivatives necessary, which is computational intensive, the authors discuss strong approximation schemes that do not require this, much like the Runge-Kutta methods in the deterministic case , but the authors are careful to point out that the Runge-Kutta analogy is problematic in the stochastic case. Several ofthese "derivative-free" schemes are considered by the authors. The authors also consider implicit strong approximation schemes for stiff SDEs, wherein numerical instabilities are problematic. Interesting applications are given for strong approximations for SDEs, such as the Duffing-Van der Pol oscillator, which is very important system in engineering mechanics and phyics, and has been subjected to an incredible amount of research.

More detailed consideration of weak Taylor approximations is given in part 6. The Euler scheme is examined first in the weak approximation, with the higher-order schemes following. Since weak convergence is more stringent than strong convergence, it should come as no surprise that fewer terms are required to obtain convergence, as compared with strong convergence at the same order. This intuition is indeed verified in the discussion, and the authors treat both explicit and implicit weak approximations, along with extrapolation and predictor-corrector methods. And most importantly, the authors give an introduction to the Girsanov methods for variance reduction of weak approximations to Ito diffusions, along with other techniques for doing the same. Those readers involved in constructive quantum field theory will value the treatment on using weak approximations to calculate functional integrals. The approximation of Lyapunov exponents for stochastic dynamical systems is also treated, along with the approximation of invariant measures. ... Read more

Product Description

This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. It also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. It also explores connections between elliptic, parabolic, and hyperbolic equations as well as the connection with Brownian motion and semigroups. This second edition features a new chapter on reaction-diffusion equations and systems.

Customer Reviews (2)

A very good choice
This is an excellent book for a PDE course with a strong vias toward
elliptic and parabolic equations. Its lack of information related to hyperbolic equations is its weakest point. However, the author is an
excellent writer and it is pleasure to read this book.

Elliptic PDE's done right
I'm no specialist in PDE's but I boldly would like to review the present book.
This book is intended(in my personal view) as a in-depth-but-not-pedantic introduction to Elliptic equations (which, if one considers the original title in german "Partielle Differentialgleichungen - Elliptische Gleichungen" makes complete sense).
As any other descent book, it doesn't aim at list down results in a encyclopedic way, but rather tour-guide the reader in the beautiful subject of Elliptic PDE's.

Motivated by Dirichlet's principle, the author introduces variational methods for Elliptic PDE's and a good deal of the regularity program for that class of equations(including non-linear equations). Most of what follows the first chapter, is a successful attempt to generalize to other elliptic equations the techniques useful in the qualitative theory of the Dirichlet problem for the Poisson equation. Some of the methods, as far as I understand them, can be generalized to Schroedinger's equation too.

The interested reader can consult also the book on analysis by Elliot Lieb and the textbook on variational methods by Prof. S. Hildebrandt(and references therein). ... Read more

Product Description
This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame (IN). Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear, however, the presented methods also apply to nonlinear problems.Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University. ... Read more

Product Description

Product Description
An ideal companion to the new 4th Edition of Nonlinear Ordinary Differential Equations by Jordan and Smith (OUP, 2007), this text contains over 500 problems and fully-worked solutions in nonlinear differential equations. With 272 figures and diagrams, subjects covered include phase diagrams in the plane, classification of equilibrium points, geometry of the phase plane, perturbation methods, forced oscillations, stability, Mathieu's equation, Liapunov methods, bifurcations and manifolds, homoclinic bifurcation, and Melnikov's method.

The problems are of variable difficulty; some are routine questions, others are longer and expand on concepts discussed in Nonlinear Ordinary Differential Equations 4th Edition, and in most cases can be adapted for coursework or self-study.

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 (1)

good!
The problem with this book is that it has several mistakes on it, algebraic mistakes especially.This is the reason because I put 4 stars only . On the other hand, it is difficult to find books like this, I mean with a huge variety of exercises includingdifficult ones. So I think that this book is good in order to prepareexams orjust develop practice. I bought only the solution book, and I like this book because it includes the questions as well. Not as happen with several books where the authors force you to buy the theory book. ... Read more

Product Description
From the reviews: "This is a book of interest to any having to work with differential equations, either as a reference or as a book to learn from. The authors have taken trouble to make the treatment self-contained. It (is) suitable required reading for a PhD student. Although the material has been developed from lectures at Stanford, it has developed into an almost systematic coverage that is much longer than could be covered in a year's lectures". Newsletter, New Zealand Mathematical Society, 1985 "Primarily addressed to graduate students this elegant book is accessible and useful to a broad spectrum of applied mathematicians". Revue Roumaine de Mathématiques Pures et Appliquées,1985 ... Read more

Product Description
Key Message: Fundamentals of Differential Equations Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software

Key Topics: Introduction, First-Order Differential Equations, Mathematical Models and Numerical Methods Involving First Order Equations, Linear Second-Order Equations, Introduction to Systems and Phase Plane Analysis, Theory of Higher-Order Linear Differential Equations, Laplace Transforms, Series Solutions of Differential Equations, Matrix Methods for Linear Systems

Market: For all readers interested in Differential Equations. ... Read more

Customer Reviews (14)

Very Very well written math book.
Anyone who has taken calculus 1 - 3 should have no problem understanding this book. This is probably one of the best well written math book out there. This book is well organized, detailed, and has many examples with step by step solutions to guide the reader.

Differential Equations Textbook
The book arrived promptly and in the condition described. I am satisfied with my purchase.

Amazing Reference
This book is a brilliant reference for anyone in engineering, natural science, mathematics, or economics. I found it to be organized in a helpful way, and the authors explain the difficult concepts of differential equations quite well. Even the often confusing "guessing method" of finding the particular solution to non-homogeneous 2nd order ODEs is done well. I highly recommend this book as a reference.

However, this is an OLD EDITION. If you are taking a class on differential equations you probably need the newest edition because some of the homework problems are different with each new edition.

Differential Equation book
This book is in excellent condition! It works perfectly for my class. Thanks! Sorry for the late review.

Decent course textbook
Although it's anything but perfect, this textbook does not deserve its current 2 1/2 star rating. It provides helpful algorithms for solving particular types of differential equations, with some proof for those who are interested, and numerous example problems. The explanations are usually concise and easy to understand, considering the difficulty of explaining some topics in differential equations. Unlike my professor, this textbook provides ample review of topics learned in Calculus, making it unnecessary for me to page through Stewart's Calculus tome.

This book does have some problems. At best, it is a useful supplement to classroom instructions, since many of the chapters are irrelevant, or deal only with applications. Sometimes its explanations are too concise, and leave the student confused. It doesn't have a table of trig identities, which is irritating when integrating trig functions in the later chapters. Furthermore, given that there are other excellent, inexpensive texts for sale, such as Ordinary Differential Equations, which are better for self-study, Fundamentals of Diffeq is overpriced. Given the nature of differential equations, the Fundamentals of Differential Equations : Solutions Manual is quite helpful. Unfortunately, it drives up the price still further.

In short, although it falls far short of Stewart's Calculus, Fundamentals of Differential equations will not automatically earn you a D. For that, you'd need to have a bad instructor. ... Read more

Customer Reviews (1)

A classic book
This is a classic PDE's book. It covers the basic topics: separation of variables, transform methods, Green functions, the method of characteristic, and variational methods. However, this is not a standard textbook. Its chapters related to the characteristic's method are extremely good, they cover a wide range of topics, and they represent almost half of the chapters in the book. Some of these topics can be founddisperse in advanced books. I believe that the treatment of first and second order hyperbolic equations presented in Chester's book is one of the most complete at elementary level. ... Read more

Product Description
Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component—modeling—to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters. Partial Differential Equations: Modeling, Analysis, Computation enables readers to deepen their understanding of a topic ubiquitous in mathematics and science and to tackle practical problems. The advent of fast computers and the development of numerical methods have enabled the modern engineer to use a large variety of packages to find numerical approximations to solutions of PDEs. Problems are usually standard and a thorough knowledge of a well-chosen subset of analytical and numerical tools and methodologies is necessary when dealing with real-life problems. When one is dealing with PDEs in practice, it becomes clear that both numerical and analytical treatments of the problem are needed.This comprehensive book is intended for graduate students in applied mathematics, engineering, and physics and may be of interest to advanced undergraduate students.Mathematicians, scientists, and engineers also will find the book useful.ContentsList of Figures; List of Tables; Notation; Preface; Chapter 1: Differential and difference equations; Chapter 2: Characterization and classification; Chapter 3: Fourier theory; Chapter 4: Distributions and fundamental solutions; Chapter 5: Approximation by finite differences; Chapter 6: The Equations of continuum mechanics and electromagnetics; Chapter 7: The art of modeling; Chapter 8: The analysis of elliptic equations; Chapter 9: Numerical methods for elliptic equations; Chapter 10: Analysis of parabolic equations; Chapter 11: Numerical methods for parabolic equations; Chapter 12: Analysis of hyperbolic equations; Chapter 13: Numerical methods for scalar hyperbolic equations; Chapter 14: Numerical methods for hyperbolic systems; Chapter 15: Perturbation methods; Chapter 16: Modeling, analyzing, and simulating problems from practice; Appendices: Useful definitions and properties; Bibliography; Index. ... Read more

Customer Reviews (1)

Good reference, bad instructional material
The book by Mattheij outlines the general forms of PDEs rather well, but falls short as an instructional resource.When completing the homework problems at the end of each set, I found myself requiring additional resources online and in other textbooks, since only the basic idea is given and developed in each section, without elaboration.
As the book wore on into Numerical Methods, the nomenclature became far more confusing to deal with and far harder to follow.
The one saving grace of this book was its application problems in the back.These were exceptionally well written and very well representative of the final projects that our class was to use.The explanations helped clear up any issues that I had with those specific scenarios. ... Read more

Product Description
Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations. ... Read more