Reviews (4)

Excellent Book!
This book explains differential equations in a mathematical context rather than simply a "plug and chug" approach. What is particularly good is the section on partial differential equations and their applications. I have used the second edition extensively in my work, and the third edition is even better. The authors are to be congratulated for their clarity in writing.

Good primer, but that's about it.
I was expecting more. The notebooks on CD-ROM were not particularly helpful. All I could do with them was to run the authors's examples. Could not modify them to do my own.

Unless you are a complete novice in the field of differential equations, don't buy this book!

A very useful book
Abell and Braselton strike a nice balance between the analytical solution of differential equations by hand, and numerical solution by computer. Mathematica is used to simplify some of the details, but they teach how to do everything by hand, including programming runge-kutta solution methods, fourier series, and other topics that lazier authors might have skipped over.

Every chapter starts with basic definitions and builds to useful solution techniques. The book is packed with fully worked examples. My edition is a few years old and talks about the "newly released" Mathematica 3.0, but everything applies just as well to version 4.2.

Great. Great. Great.
What a great book! I read it at once. I'm a biologist, not a mathematician, but I can ensure that everyone that have access to the Mathematica (TM) program can learn very much about a such not easy subject, also if he/she is a novice about the differential equations. I think this book is a "must have" and I hope to see soon the third Edition. This edition cover Mathematica (TM) 3, but I used it with Mathematica (TM) 4 and I can say it was very good as well. Very nice the CD-ROM enclosed. A great book, thanks to the authors. ... Read more

Book Description

K. Ohkitani presents a mathematically challenging account of the effect of non-linear dynamics on the formation of singularities, precisely for graduate students and researchers. Turbulence and, in particular, the formation of vortices, has long been a subject of study by mathematicians, physicists and engineers, using experimental, analytical and numerical methods. Recent observations suggest vorticity is likely to be spatially localized, forming a structure. ... Read more

Book 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

Reviews (5)

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

Solid and basic book
This book is a classical in the subject. It will provide you with solid information even if you are an absolut beginner with proficiency only in undergraduate algebra, calculus. ... Read more

Book Description

Boiled-down essentials of the top-selling Schaum's Outline series, for the student with limited time

What could be better than the bestselling Schaum's Outline series? For students looking for a quick nuts-and-bolts overview, it would have to be Schaum's Easy Outline series. Every book in this series is a pared-down, simplified, and tightly focused version of its bigger predecessor. With an emphasis on clarity and brevity, each new title features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form. Graphic elements such as sidebars, reader-alert icons, and boxed highlights feature selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials.

Book Description

This title presents new ideas on the visualization of differential equations with user-configurable tools. The authors use the widely-used computer algebra system, Mathematica, to provide an integrated environment for programming, visualizing graphics, and running commentary for learning and working with differential equations. ... Read more

Reviews (1)

A remarkable achievment in visualization
This is one of those math books that you can leave on the coffee table for guests to browse--the color pictures are beautiful. For the mathematician or student, the book will give you a new perspective on differential equations. (Note - If you can't find a hardcopy, VisualDSolve is now available as an e-book, with the Mathematica code, from Wolfram Research at http://store.wolfram.com/view/book/D0706.str.) ... Read more

Book Description

In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented. A main tool is the theory of Grbner bases, which is reexamined here from the point of view of geometric deformations. Perturbation techniques have a long tradition in analysis; Grbner deformations of left ideals in the Weyl algebra are the algebraic analogue to classical perturbation techniques. The algorithmic methods introduced here are particularly useful for studying the systems of multidimensional hypergeometric PDEs introduced by Gelfand, Kapranov and Zelevinsky. The Grbner deformation of these GKZ hypergeometric systems reduces problems concerning hypergeometric functions to questions about commutative monomial ideals, and leads to an unexpected interplay between analysis and combinatorics. This book contains a number of original research results on holonomic systems and hypergeometric functions, and raises many open problems for future research in this area. ... Read more

Book Description

Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of which was published as Volume 5 of the Encyclopaedia of Mathematical Sciences, have given a masterly exposition of these two theories, with penetrating insight. ... Read more

Book Description

The subject of dynamic equations on time scales continues to be a rapidly growing area of research. Behind the main motivation for the subject lies the key concept that dynamic equations on time scales is a way of unifying and extending continuous and discrete analysis.This work goes beyond an earlier introductory text "Dynamic Equations on Time Scales: An Introduction with Applications" (ISBN 0-8176-4225-0) and is designed for a second course in dynamic equations at the graduate level. Key features of the book: excellent introductory material on the calculus of time scales and dynamic equations * numerous examples and exercises * covers the following topics: the exponential function on time scales, boundary value problems, positive solutions, upper and lower solutions of dynamic equations, integration theory on time scales, disconjugacy and higher order dynamic equations, delta, nabla, and alpha dynamic equations on time scales * unified and systematic exposition of the above topics with good transitions from chapter to chapter * useful for a second course in dynamic equations at the graduate level, with directions suggested for future research * comprehensivebibliography and index * useful as a comprehensive resource for pure and applied mathematicians Contributors: R. Agarwal, E. Akin-Bohner, D. Anderson, F. Merdivenci Atici, R. Avery, M. Bohner, J. Bullock, J. Davis, O. Dosly, P. Eloe, L. Erbe, G. Guseinov, J. Henderson, S. Hilger, R. Hilscher, B. Kaymak¿alan, K. Messer, D. O'Regan, A. Peterson, H. Tran, W. Yin ... Read more

Book Description

High-order numerical methods provide an efficient approach to simulating many physical problems. This book considers the range of mathematical, engineering, and computer science topics that form the foundation of high-order numerical methods for the simulation of incompressible fluid flows in complex domains. Introductory chapters present high-order spatial and temporal discretizations for one-dimensional problems. These are extended to multiple space dimensions with a detailed discussion of tensor-product forms, multi-domain methods, and preconditioners for iterative solution techniques. Numerous discretizations of the steady and unsteady Stokes and Navier-Stokes equations are presented, with particular sttention given to enforcement of imcompressibility. Advanced discretizations. implementation issues, and parallel and vector performance are considered in the closing sections.Numerous examples are provided throughout to illustrate the capabilities of high-order methods in actual applications. ... Read more

Book Description

Book Description

This is a two volume introduction to the computational solution of differential equations using a unified approach organized around the adaptive finite element method. It presents a synthesis of mathematical modeling, analysis, and computation. The goal is to provide the student with theoretical and practical tools useful for addressing the basic questions of computational mathematical modeling in science and engineering: How can we model physical phenomena using differential equations? What are the properties of solutions of differential equations?How do we compute solutions in practice? How do we estimate and control the accuracy of computed solutions? The first volume begins by developing the basic issues at an elementary level in the context of a set of model problems in ordinary differential equations. The authors then widen the scope to cover the basic classes of linear partial differential equations modeling elasticity, heat flow, wave propagation and convection-diffusion-absorption problems. The book concludes with a chapter on the abstract framework of the finite element method for differential equations.Volume 2, to be published in early 1997, extends the scope to nonlinear differential equations and systems of equations modeling a variety of phenomena such as reaction-diffusion, fluid flow, many-body dynamics and reaches the frontiers of research. It also addresses practical implementation issues in detail. These volumes are ideal for undergraduates studying numerical analysis or differential equations. This is a new edition of a 1988 text of 275 pages by C. Johnson. ... Read more

Reviews (3)

Best of EDP in !!!
This book is excelent because there's reviews of calculus, linear algebra and all sort of classical numerical methods needed to understand the finite element method. Moreover, the authors try and succed in giving a clear explanation of many applications of the method.

Well, a must of numerical analysis that every scientific searchers and engineers must own !!!

An excellent book
Great book to learn the fundamentals of finite element methods (FEM). The authors combine both rigour and simplicity in their presentation of the FEM as a means of numerically solving a wide variety of partial differential equations. Highly recommended for engineers--especially those who have been taught FEM using the traditional "structural mechanics" approach.

Amazing
Excellent approach for numerical and computational issues. Perfect for creating solid programs that work and it also explains every detail in a great way. ... Read more

Book Description

This book presents the classical theory from a systems point of view, including physical and biological systems. Besides making system theory the unifying take, the book offers an abundance of applications, examples, and problems including many intended for use with MATLAB. Differential Equations with Applications is designed for engineers and scientists. It presents systems of ordinary differential equations and combines classical techniques, applications, and computer solutions. A valuable reference book on differential equations for both engineers and scientists.

Book Description

The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community. ... Read more

Reviews (1)

A Classic and a Current
While Newton (arguably) founded the subject, Euler (pronounced 'oiler') developed all the methods used today in Differential Calculus. Not only was Leonhard Euler the greatest Mathematician of his day (he actually wrote over a quarter of the tracts from the 18th century!), but he wrote in a humbling and readable manner such that anyone with a foundation may approach his proofs. And this text is no different; simply a book any mathematician should own. Truly one of the milestones of Calculus. ... Read more

Book Description

Stochastic processes with jumps and random measures are gaining importance as drivers in applications like financial mathematics and signal processing.This book develops stochastic integration theory for both integrators (semimartingales) and random measures from a common point of view. Using some novel predictable controlling devices, the author furnishes the theory of stochastic differential equations driven by them, as well as their stability and numerical approximation theories. Highlights feature DCT and Egoroff's Theorem, as well as comprehensive analogs to results from ordinary integration theory, for instance, previsible envelopes and an algorithm computing stochastic integrals of c`agl`ad integrands pathwise. ... Read more

Reviews (1)

A treatise sacrificing clarity for technicality.
If you think you know about Markov processes with jumps, Levy processes and even the Poisson process, read this book and you will change your mind: the author presents notions familiar to many students in such a complicated way that you will not recognize these objects anymore!
The author, known for his work on stochastic integration and semimartingale theory, wants to go into the very details of the concepts of integrability and measurability from the start but seems to have failed to transmit his knowledge tothe readers. Random variables are called "universally measurable functions",
notations are complicated and non-standard, no examples are given and the order of presentation is anti-pedagogical: the Poisson process, which is the simplest example of a jump process, is defined on page 270 (!), well AFTER Levy processes (page 239). One could think that simplicity has been sacrificed for generality, but this is not always the case: for example, the corrollary 5.6.11 stating the relation between PDEs and Markovian flows driven by Levy processes is quite weak: it only gives results for bounded C^2 initial conditions while many others are known in this context. For those interested in stochastic integration for jump processes, I recommend Gikhman and Skorokhod, Jacod and Shiryaev (more complete) or Protter's book (much simpler). The last point which surprized me a lot is that the author was trained as a physicist: nothing could be more unbelievable given the Bourbaki style of this book! ... Read more

Book Description

Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student in applied mathematics and engineering, this text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation. Prerequisites suggested for using this book in a course might include at least one semester of partial differential equations and some programming capability. The author stresses the use of technology throughout the text, allowing the student to utilize it as much as possible. The use of graphics for both illustration and analysis is emphasized, and algebraic manipulators are used when convenient.

This is the second volume of a two-part book. ... Read more

Book Description

Here is an elementary development of the Sinc-Galerkin method with the focal point being ordinary and partial differential equations.This is the first book to explain this powerful computational method for treating differential equations.These methods are an alternative to finite difference and finite element schemes, and are especially adaptable to problems with singular solutions.The text is written to facilitate easy implementation of the theory into operating numerical code.

The authors' use of differential equations as a backdrop for the presentation of the material allows them to present a number of the applications of the sinc method.Many of these applications are useful in numerical processes of interest quite independent of differential equations.Specifically, numerical interpolation and quadrature, while fundamental to the Galerkin development, are useful in their own right.

The intimate connection between collocation and Galerkin for the sinc basis is exposed via sinc-interpolation.The quadrature rules define a class of numerical integration methods that complement better known techniques, which in the case of singular integrands, often require modification.The sinc methodology of the text is illustrated on such applications as initial data recovery, heat diffusion, advective-diffusive transport, and Burgers' equation, to illustrate the numerical implementation of the theory discussed.

Engineers may find sinc methods a very competitive approach to the more common boundary element or finite element methods.Further, workers in the signal processing community may find this particular approach a refreshingly different view of the use of sinc functions.

Sinc approximation is a relatively new numerical technique.This book provides a much needed elementary level explanation.It has been used for graduate numerical classes at Montana State University and Texas Tech University. ... Read more

Book Description

The aim of the book is to present the state of the art of the theory of symmetric (Hermitian) matrix Riccati equations and to contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach. The book is intended to make available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background. ... Read more

Book Description

Designed to prepare readers to better understand the current literature in research journals, this book explains the basics of classical PDEs and a wide variety of more modern methods—especially the use of functional analysis—which has characterized much of the recent development of PDEs. It gives equal treatment to elliptic, hyperbolic, and parabolic theory, and features an abundance of applications to equations that are important in physics and engineering—both on the basic and more advanced level. Provides worked, figures and illustrations, and extensive references to other literature.First-Order Equations. Principles for Higher-Order Equations. The Wave Equation. The Laplace Equation. The Heat Equation. Linear Functional Analysis. Differential Calculus Methods. Linear Elliptic Theory. Two Additional Methods. Systems of Conservation Laws. Linear and Nonlinear Diffusion. Linear and Nonlinear Waves. Nonlinear Elliptic Equations. Appendix on Physics.For anyone using PDEs in physics and engineering applications. ... Read more