Book Description

This unique, self-contained reference presents a systematic study of current developments in stochastic differential delay equations driven by nonlinear integrators;detailing various exponential stabilities for stochastic differential equations and large-scale systems. ... Read more

Book Description

Designed for use by sophomore engineering or junior physical science majors, this text is suitable for an introductory course in linear algebra and differential equations or a course in differential equations with a linear algebra prerequisite. This text contains detailed coverage of applied topics and includes theorems specifically applicable to engineering students. There is a new chapter on "Stability and the Phase Plane", approximately 300 new problems added throughout and several BASIC programs on numerical solutions of differential equations are included. ... Read more

Reviews (9)

I disagree with the other reviewers....
I think the other reviewers all looked at this book from the perspective of an engineering major who wasn't interested in learning the topics but just wanted to get through a required course without having to put in the effort to understand the material. This book does an excellent job of tying together the two topics at hand. Yes, like any good math book, there are lots of proofs. Of course, I'm reading this from the perspective of a graduate student in geochemistry with a bachelors degree in math from several years ago. It's a great reference/review book for me. So, I'd just like to counter the other reviewers by saying if you're looking for a book with a good concise theory based introduction to Differential Equations and Linear Algebra, this is the best one I've seen.
One final note -- I think this web form is screwy, I can't correct the repeated sentence above...

just about worst math book i have used
I used this for a introductory differential equations course. All the reviewers are dead on. This book will make you hate math with a passion such as you have never known.

Avoid it like a cold
I had to buy it for an engineering math course. It is truly aweful. It has proof after proof and theorem after theorem with very few examples. Very abstract explanations. I do not know if anyone could learn anything from this book except to buy a different book if you really want to learn linear algebra. I just purchased a different Linear algebra book so I can understand the material. Take the advice of someone who has used the text and do your self a favor. Do not buy this book not even as a joke.

Extremely poor !! Very Very bad !!!
This book just show very easy example and give extremely hard(even impossible) exercises to solve, the solutions are very short or practically nonexistant . This book is written in a very unprofessionnal manner , the author does not care about who reads his book and assume that everybody is a genious , if you're a teacher and want to adopt this in your college you'll run in a lot of complaints from your students .
I really had a nigthmare studting this book, all i learnt from this book is to hate it!!!
This book should be burned and removed from circulation !!!!

Elementary! My Dear Watson!
This book is titled ELEMENTARY Differential Equations with Linear Algebra. The information in the book figures you've know a good deal about differentials and if you don't, you'll be lost. The book seems to skim over things quickly, give very easy samples and difficult questions. Not only this, but the author brings the information across to the reader in a boring and at times abstract detail. I found myself thoroughly disgusted about differentials applications altogher after briefly going through this book. If I could give this book a -1, I would.

Getting back to the title, the only thing elementary about this textbook is the preface. If you have this book for your course in college, you may want to skip this book and just xerox the questions. There really aren't many per chapter. END ... Read more

Book Description

Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students provides sophisticated numerical methods for the fast and accurate solution of a variety of equations, including ordinary differential equations, delay equations, integral equations, functional equations, and some partial differential equations, as well as boundary value problems. It introduces many modeling techniques and methods for analyzing the resulting equations. Instructors, students, and researchers will all benefit from this book, which demonstrates how to use software tools to simulate and study sets of equations that arise in a variety of applications. Instructors will learn how to use computer software in their differential equations and modeling classes, while students will learn how to create animations of their equations that can be displayed on the World Wide Web. Researchers will be introduced to useful tricks that will allow them to take full advantage of XPPAUT's capabilities. In addition, readers will learn several concepts from the field of dynamical systems, including chaos theory, how systems depend on parameters, and how simple physical systems can lead to complicated behavior.

XPPAUT is a tool for simulating, animating, and analyzing dynamical systems that evolved from tools developed by the author for studying nonlinear oscillations. XPPAUT offers several advantages over MATLAB, Maple, and Mathematica, including the following:

1) a faster way to numerically solve differential equations and do numerical integration;
2) more flexibility with integration, including interactive integration that allows the user to see the progress of the solution as it is computed;
3) an interface with AUTO, a continuation package;
4) simpler syntax for setting up differentiation equations; and
5) free downloading of the source code

Audience
This book will be most useful to researchers and modelers who want to simulate and analyze a system, and to students as an adjunct to a class in modeling or differential equations. ... Read more

Book Description

This book differs from others on Chaos Theory in that it focuses on its applications for understanding complex phenomena. The emphasis is on the interpretation of the equations rather than on the details of the mathematical derivations. The presentation is interdisciplinary in its approach to real-life problems: it integrates nonlinear dynamics, nonequilibrium thermodynamics, information theory, and fractal geometry. An effort has been made to present the material ina reader-friendly manner, and examples are chosen from real life situations. Recent findings on the diagnostics and control of chaos are presented, and suggestions are made for setting up a simple laboratory. Included is a list of topics for further discussion that may serve not only for personal practice or homework, but also as themes for theses, dissertations, and research proposals.

Key Features
*Includes laboratory experiments Includes applications and case studies related to cell differentiation, EKGs, and immunology
* Presents interdisciplinary applications of chaos theory to complex systems
* Emphasizes the meaning of mathematical equations rather than their derivations
* Features reader friendly presentation with many illustrations and interpretations
* Deals with real life, dissipative systemsIntegrates mathematical theory throughout the text ... Read more

Reviews (3)

Soft but scientific introduction to chaos theory
This is more like a historical perspective of the development of the concepts of chaos theory than a deep coverage of chaos theory. Emphasis is on introducing the concepts for allowing interested people to get into advanced theoretical developments (and practical too). However there are some scientific prerequisites (physics, dynamical systems...).

Writing is very good, intuitive, does not assume any particular mathematical background or practice with tools for simulating chaotic systems. Exposition is rather short because of a scientific writing style, it's not about scientific popularization (don't feel this is pedantic, writing is concise and not meant to be crowded with examples). In its approach, i think it's the smoothest scientific introductory book on the subject. For example Schroeder's (Fractals chaos and power laws) is overly mathematical as an introduction. Williams' (chaos theory tamed) on the other hand has a similar approach to this one but it is longer, more general and with less emphasis on the applied side of chaos theory (the analytic side). From an economical point of view, William's is cheaper while covers more about chaos theory, but this volume is scientifically better and more useful than Williams', which is too "generalistic".

In summary : a very good self-contained and short introduction to chaos theory. But for a first book on chaos theory go to Williams, it's easier to read.

Recommended only if you don't need it!!
The book has some fine features. But it doesn't explain anything. So, if you already know about chaos and want to read a brief review then probably it is ok (but read ahead). If you don't know about chaos you'll get lost.

The book is too expensive for what it offers!!.

Cogently Written
Not a bad survey. Well written and easy enough for any layman to understand. This is a survey that puts the author's uniqique synthesis of some rather broad and difficult fields into words and he does a good job of it. After reading this book you will not only have a good handle on what chaos is or isn't but how it has emerged from seemingly dipsarate fields of science. ... Read more

Book Description

The essential point in computational physics is not the use of machines, but the systematic application of numerical techniques in place of, and in addition to, analytical methods, in order to render accessible to computation as large a part of physical reality as possible.The various available techniques, disparate as they may seem, are traced back to only three main methodological sources; finite difference calculus, linear algebra, and stochastics. Each algorithm is carefully introduced and every computational tool is explained in terms of fundamental numerical techniques. Examples from statistical mechanics, quantum mechanics, and hydrodynamics are employed to bridge the gap between basic methodology and modern research.This second edition of Franz Vesely's renowned textbook takes into account the new vistas that have opened up recently in this rapidly evolving field. Furthermore, web-based sample programs augment the text. ... Read more

Reviews (1)

Review from Measurement and Control Volume 37/1 Feb 04
....provides a good working knowledge of the techniques used to solve problems in hydrodynamics, quantum mechanics, and statistical mechanics. To get the most out of the book, the reader should be familiar with vector notation (div, grad and curl), matrix algebra, the theory of ordinary and partial differential equations, and Monte-Carlo simultation techniques. The 2nd edition of Franz Vesely's book includes recent developments in lattice-gas cellular models for hydrodynamics such as the Lattice Boltzmann method. This is an advance on the Frisch, Hasslacher and Pomeau model. The conclusion is that any book attempting to contemporise the field of computational physics will always be worth the expenditure; it not only reaffirms background theory, but also points the way to new ideas and fresh applications. Review by Paul Barker ... Read more

Book Description

This book presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; and methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics. ... Read more

Reviews (1)

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 course on numerical differential equations. I highly recommend it for that purpose and as a reference for someone doing independent reading. ... Read more

Book Description

Beginning Partial Differential Equations provides a challenging yet accessible introduction to partial differential equations for advanced undergraduate and beginning graduate students. Features include:
* A discussion of first order equations and the method of characteristics for quasi-linear first order PDEs
* Canonical forms of second order PDEs
* Characteristics and the Cauchy problem
* A proof of the Cauchy-Kowalevski theorem for linear systems
* A self-contained development of tools from Fourier analysis
* Connections between the mathematics and physical interpretations of PDEs
* Numerous exercises, many with solutions provided
* Experimental, computer-based exercises designed to develop lines of inquiry.

The treatment of second order PDEs focuses on well-posed problems, properties and behavior of solutions, existence and uniqueness of solutions, and techniques for writing representations of solutions. Techniques include the use of characteristics, Fourier methods, and, for the Dirichlet problem, Green's function and conformal mappings. Also included are the Kirchhoff/Poisson solution of the wave equation, Huygens's principle, and Lebesgue's example of a Dirichlet problem with no solution. ... Read more

Book Description

Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms. By means of these extremality results, the authors prove the existence of extremal solutions between appropriate upper and lower solutions of first and second order discontinuous implicit and explicit ordinary and functional differential equations. They then study the dependence of these extremal solutions on the data.The authors begin by developing an existence theory for an abstract operator equation in ordered spaces and offer new tools for dealing with different kinds of discontinuous implicit and explicit differential equation problems. They present a unified approach to the existence of extremal solutions of quasilinear elliptic and parabolic problems and extend the upper and lower solution method to elliptic and parabolic inclusion of hemivariation type using variational and nonvariational methods.Nonlinear Differential Equations in Ordered Spaces includes research that appears for the first time in book form and is designed as a source book for pure and applied mathematicians. Its self-contained presentation along with numerous worked examples and complete, detailed proofs also make it accessible to researchers in engineering as well as advanced students in these fields. ... Read more

Book Description

Book Description

This book provides readers with a solid introduction to differential equations and their applications emphasizing analytical, qualitative, and numerical methods. Numerical methods are presented early in the text, including a discussion of error estimates for the Euler, Heun, and Runge-Kutta methods. Systems and the phase plane are also introduced early, first in the context of pairs first-order equations, and then in the context of second-order linear equations.Other chapter topics include the Laplace transform, linear first-order systems, geometry of autonomous systems in the plane, nonlinear systems in applications, diffusion problems and Fourier series, and further topics in PDEs. ... Read more

Reviews (1)

Extraordinary Introduction to DE
Dr. Hollis here gives us a book that explains, in plain terms, the very esoteric subject of differential equations.

The subject should not be esoteric. The limit is encountered in every man's life. Here, we finally see it in action. This is the author's forte. He knows his subject completely.

Hollis has a simple, yet very adventurous plan: Mathematics without appeal to the physical world can not appeal to the average man. In this, he succeeds beyond all expectations.

The Mathematica examples are astounding. Have you ever seen a ticking watch flick, or wondered about the bright moon sailing across the sky, or watched in horror as a raw egg fled from your hand to the floor and wondered: "What happened?" This is the book for you. His explanation of Runge-Kutta is the best I've seen.

The only weakness I perceive is in the section on Laplace transforms. Laplace transforms should require only a mechanical mathematician and some knowledge. Given that Laplace transforms are a fundamental tool, I would have expanded this chapter. The average engineer needs a sound basis. The classroom teacher can decide for himself what his students need.

The last chapters should appeal to those who want to "push the envelope". The equations lay down very neatly and precisely what can and can not be done.

Writing: Very clear. Lot's of examples help the average to excellent student.
Overall: Outstanding. A great learning tool.

Looking forward to the third edition. ... Read more

Book Description

Utilizing MATLAB's computational and graphical tools right from the start, this analysis of differential equations helps users probe a variety of mathematical models, encouraging them to develop problem-solving skills and independent judgment as they derive mathematical models, select approaches to their analysis, and find answers to the original physical questions. Providing immediate graphic and numeric support, it demonstrates how physical problems motivate the central ideas and techniques of differential equations, showing how they model physical phenomena by examining ideas from four perspectives: geometric, analytic, numeric, and physical.Introduces qualitative analysis and numerical methods for scalar equations and systems early on, without sacrificing coverage of the most important traditional analytical methods. Fully integrates MATLAB into the text and exercises, and uses mathematical models of physical problems throughout to emphasize the interplay between the physical problem and the analytic, graphical, and numeric information available from the differential equation model. Seamlessly integrates over 1,400 exercises, open-ended chapter projects, and motivational 'Thought Questions'.For scientists and engineers. ... Read more

Reviews (2)

great explainations
this book has very little illustrations and graphics to show what the mathmatical models are doing, yet it's still a great learning tool.in some instances, the book can give you an example and jump right to a conclusion, which can be confusing, so you will need someone to explain the middle ground to you unless you are very very fluent in algebra and calculus.however, most of the time, the explainations and instructions are very clearly written (in comparison with most math texts). I'm not using MATLAB, so i don't know how well the book teaches and utilizes the software.

No MATLAB syntax
If you're looking for a book to learn how to model differential equations with MATLAB, don't buy this book. No examples in MATLAB are given, only references to what commands in 'DELAB' (The author's MATLABinterface) can be used to solve problems. I purchased and returned thisbook. ... Read more

Book Description

Symmetry methods have long been recognized to be of great importance for the study of the differential equations arising in mathematics, physics, engineering, and many other disciplines. The purpose of this book is to provide a solid introduction to those applications of Lie groups to differential equations that have proved to be useful in practice, including determination of symmetry groups, integration of ordinary differential equations, construction of group-invariant solutions to partial differential equations, symmetries and conservation laws, generalized symmetries, and symmetry methods in Hamiltonian systems. The computational methods are presented so that graduate students and researchers in other fields can readily learn to use them.

Following an exposition of the applications, the book develops the underlying theory. Many of the topics are presented in a novel way, with an emphasis on explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter.

This second edition contains a new section on formal symmetries and the calculus of pseudodifferential operators, simpler proofs of some theorems, new exercises, and a substantially updated bibliography. ... Read more

Reviews (1)

This book fulfils a great lack
Application of symmetries and Lie groups to differential equations (primarily PDE's) is a hot issue in contemporary Mathematics and Physics. Unfortunately, only few textbooks are available on this area.

The book is one of the best attempts to put this topic into an ordered, easy to studying form, despite of its being a rapidly developing and thus hard to teaching issue. It survived two editions, and I am sure this is not the last.

I am also sure that anyone who is involved in the area, will need to read this book, or have already read it. ... Read more

Book Description

This is the third of three volumes on partial differential equations. It is devoted to nonlinear PDE. There are treatments of a number of equations of classical continuum mechanics, including relativistic versions. There are also treatments of various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. Analytical tools introduced in this volume include the theory of L^p Sobolev spaces, H lder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is addressed to graduate students in mathematics and to professional mathematicians, with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis and complex analysis. ... Read more

Reviews (2)

Difficult topics treated in a comprehensive manner.
One of the most important and subtle features of mathematics is the great difference existing between linearity and non-linearity. One always tries to linearize whenever possible, because linear problems are easier to solve, but unfortunately the world is not linear, and we have to learn how to deal with non-linear problems.

This volume discusses thoroughly some very important cases of non-linear PDE's which are important in mathematical physics or that possess intrinsic theoretical interest.

The contents are: Function space and operator theory for nonlinear analysis; nonlinear elliptic equations; nonlinear parabolic equations; nonlinear hyperbolic equations; Euler and Navier-Stokes equations for incompressible fluids; Einstein's equations.

A little bit more advanced and speciallized than the other two volumes, but still useful for a broad community. A graduate student with a solid background will find it perfectly acquaintable. Includes lots of excercises and references.

Please read my other reviews (just click on my name above).

Navier-Stokes, and Einstein's eqtn
This final volume, of a set of three, discusses what *little* is generally known about the extraordinarily diverse set of non-linear PDE. The first chapter of the text presents function spaces and operator theory for non-linear analysis. That chapter presents a number of analytical techniques including L^p sobolev spaces, imbedding theorems, Holder and Zygmund spaces, pseudo and para differential operators and more. Three following chapters discuss nonlinear elliptic, parabolic and hyperbolic PDE. Those chapters present many interesting results such as the Nash imbedding theorem, minimal surfaces, Nash -Moser inequalities, fixed point theorems, non-linear Trotter products, quasi-linear parabolic and hyperbolic, compressible fluids, Cauchy -Kowalewski theorem,. Riemann invariants and entropy flux, and strings. The final two chapters cover incompressible fluids and Einstein's equations. Both chapters are ideal for physicists in need of a reference detailing rigorous existence proofs, and formulations.

As with other volumes in this seriers, the writing in this text is for the professional mathematician or advanced graduate student. Having said that, these volumes make an ideal set for someone who seeks to have a definitive and up to date account of what is known about PDE in general ... Read more

Book Description

The book treats differential forms and uses them to study some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely the Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames of E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. Everything is then put together in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces. ... Read more

Book Description

This revised and updated Second Edition of Green's Functions and Boundary Value Problems maintains a careful balance between sound mathematics and meaningful applications. Central to the text is a down-to-earth approach that shows the reader how to use differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics.

Ivar Stakgold incorporates developments that have altered the field of applied mathematics in recent decades—particularly in areas of modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods. This modernized text, however, retains the many features that made its predecessor one of the most successful graduate-level texts of its kind, including:

• A unique blend of topics
• A balanced discussion of theory and applications
• 44 illustrations and numerous practical examples that supplement the text
• Chapter introductions and clear explanations of basic concepts
• Plentiful exercises, many of which are new to this edition

Green's Functions and Boundary Value Problems is an ideal text for a modern course in applied mathematics designed for students in the physical sciences, engineering, and mathematics. It is also an excellent reference for practicing professionals in these areas. ... Read more

Reviews (2)

Systematic, not a 'cookbook'
Actually, I preferred the first (2 volume) edition of this work and used the first volume along with Whittaker and Watson to teach first semester math methods to physics and engineering students. This book provides the most readable, systematic approach to boundary-value problems, based on Weyl's lemma. Not to be compared with the usual cookbooks on math methods because it shows you how to construct nonstandard orthogonal expansions, not merely the usual Fourier, Bessel and Legendre variety. Also very good on Dirac's delta funaction. For second semester, for years I also used Bender and Orszag.

G is called 'the Green function' and not 'the Green's function' (one does not say 'the Bessel's function').

This is one of the best books on applicable PDE's
This is a classic text. The authors not only knows much more than is in the book but also has a clear idea about the applied side of math. A close competitor is Sobolev's book on PDE's. ... Read more

Book Description

Several distinctive aspects make Dynamical Systems unique, including:otreating the subject from a mathematical perspective with the proofs of most of the results includedoproviding a careful review of background materialsointroducing ideas through examples and at a level accessible to a beginning graduate studentofocusing on multidimensional systems of real variablesThe book treats the dynamics of both iteration of functions and solutions of ordinary differential equations. Many concepts are first introduced for iteration of functions where the geometry is simpler, but results are interpreted for differential equations. The dynamical systems approach of the book concentrates on properties of the whole system or subsets of the system rather than individual solutions. The more local theory discussed deals with characterizing types of solutions under various hypothesis, and later chapters address more global aspects. ... Read more