Book Description

The book is suitable for readers with a background in basic finite element and finite difference methods for partial differential equations who wants gentle introductions to advanced topics like parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to *compute* solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment, so to take advantage of these examples some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through discretization methods, algorithms, software design, verification, and computational examples. ... Read more

Book Description

This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations.It is a more modern, comprehensive treatment intended for students who need more than the purely numerical solutions provided by programs like the MATLAB PDE Toolbox, and those obtained by the method of separation of variables, which is usually the only theoretical approach found in the majority of elementary textbooks.

This will fill a need in the market for a more modern text for future working engineers, and one that students can read and understand much more easily than those currently on the market.

* Includes new and important materials necessary to meet current demands made by diverse applications
* Very detailed solutions to odd numbered problems to help students
* Instructor's Manual Available ... Read more

Book Description

This is an introduction to advanced analysis at the beginning graduate level that blends a modern presentation with concrete examples and applications, in particular in the areas of calculus of variations and partial differential equations. The book does not strive for abstraction for its own sake, but tries rather to impart a working knowledge of the key methods of contemporary analysis, in particular those that are also relevant for application in physics. It provides a streamlined and quick introduction to the fundamental concepts of Banach space and Lebesgue integration theory and the basic notions of the calculus of variations, including Sobolev space theory.The new edition contains additional material on the qualitative behavior of solutions of ordinary differential equations, some further details on Lp and Sobolev functions, partitions of unity and a brief introduction to abstract measure theory. ... Read more

Book Description

Concise, first-rate introduction for undergraduates includes, among other topics, a survey of first order equations, discussions of complex-valued solutions, linear differential operators, inverse operators and variation of parameters method, the Laplace transform, Picard’s existence theorem, and an exploration of various interpretations of systems of equations. Numerous clearly stated theorems and proofs, examples, and problems followed by solutions.
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Reviews (2)

Not for beginners
I am currently taking Diff EQ and this book is not helpful at all. It shows very few examples and skips too many steps. I am very frustrated with this book and would not recommend it to people taking this course for the first time

Best Concise Book on D.E.
There are other short books on ordinary differential equations. This may be the best. It's title is quite on target. This book is short and it covers the important topics of D.E. Bear is one of the best writers in analysis (his other books are on real analysis). It pays off here. Especially at this price, every student taking O.D.E. should have this book. ... Read more

Book Description

Similarities, differences, advantages and limitations of perturbation techniques are pointed out concisely. The techniques are described by means of examples that consist mainly of algebraic and ordinary differential equations. Each chapter contains a number of exercises. ... Read more

Book Description

This is a book on nonlinear dynamical systems and their bifurcations under parameter variation. It provides a reader with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems. Special attention is given to efficient numerical implementations of the developed techniques. Several examples from recent research papers are used as illustrations. The book is designed for advanced undergraduate or graduate students in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first edition, while updating the context to incorporate recent theoretical developments, in particular, new and improved numerical methods for bifurcation analysis. Reviews of the first edition: ... Read more

Book Description

Emphasizing the "why" as well as the "how," this useful and well-written introductory text explains methods for obtaining approximate solutions to mathematical problems by exploiting the presence of small, dimensionless parameters. Geared toward undergraduates in engineering and the physical sciences. Preface. Bibliography. Appendixes.
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Book Description

The six articles in this EMS volume provide an overview of a number of contemporary techniques in the study of the asymptotic behavior of partial differential equations.These techniques include the Maslov canonical operator, semiclassical asymptotics of solutions and eigenfunctions, behavior of solutions near singular points of different kinds, matching of asymptotic expansions close to a boundary layer, and processes in inhomogeneous media. Asymptotic expansions are one of the most important areas in the theory of partial differential equations. Readers should find the wide variety of approaches of interest. ... Read more

Book Description

The use of symmetries and conservation laws in the qualitative description of dynamics has a long history going back to the founders of classical mechanics. In some instances, the symmetries in a dynamical system can be used to simplify its kinematical description via an important procedure that has evolved over the years and is known generically as reduction. The focus of this work is a comprehensive and self-contained presentation of the intimate connection between symmetries, conservation laws, and reduction, treating the singular case in detail. The exposition reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds. This is followed by a discussion of momentum maps and the geometry of conservation laws that are used in the development of symplectic reduction. ... Read more

Book Description

Scattering theory is, roughly speaking, perturbation theory of self-adjoint operators on the (absolutely) continuous spectrum. It has its origin in mathematical problems of quantum mechanics and is intimately related to the theory of partial differential equations. Some recently solved problems, such as asymptotic completeness for the Schrödinger operator with long-range and multiparticle potentials, as well as open problems, are discussed. Potentials for which asymptotic completeness is violated are also constructed. This corresponds to a new class of asymptotic solutions of the time-dependent Schrödinger equation. Special attention is paid to the properties of the scattering matrix, which is the main observable of the theory. The book is addressed to readers interested in a deeper study of the subject. ... Read more

Book Description

This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS63.The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameter-dependent problems are considered. The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities. ... Read more

Book Description

One-dimensional dynamics has generated many results, and avenues of active mathematical research with numerous inroads to this research remain to be pursued by the advanced undergraduate or beginning graduate student. While much of the material in this book is not covered elsewhere, some aspects present new research topics whose connections are drawn to other research areas from the text. Although the material presented is not meant to be approached in a linear fashion, anybody with an interest in dynamics will find many topics of interest. ... Read more

Book Description

Using the same innovative and proven approach that made the authors’ Engineering Mathematics a worldwide bestseller, this book can be used in the classroom or as an in-depth self-study guide. Its unique programmed approach patiently presents the mathematics in a step-by-step fashion together with a wealth of worked examples and exercises. It also contains Quizzes, Learning Outcomes, and Can You? checklists that guide readers through each topic and reinforce learning and comprehension. Both students and professionals alike will find this book a very effective learning tool and reference.

Distinctive Features

- Uses a unique programmed approach that takes readers through the mathematics in a step-by-step fashion with a wealth of worked examples and exercises.

- Contains many Quizzes, Learning Outcomes, and Can You? checklists.

- Ideal as a classroom textbook or a self-learning manual. ... Read more

Book Description

The theory of differential operator equations has beendescribed in various monographs. But the initial physical problemwhich leads to these equations is often hidden. When the physicalproblem is studied, the mathematical proofs are either not given orare quickly explained In this book, we give a systematic treatment ofthe differential equations with application to partial differentialequations obtained from elastostatic problems. In particular, we studyproblems which are obtained from asymptotic expansion with two scales.We approximate and, when it is possible, expand the solution ofproblems by elementary solutions. This book is intended for scientists (mathematicians in the field ofordinary and partial differential equations, differential-operatorequations; theoretical mechanics; theoretical physicists) and graduatestudents in Functional Analysis, Differential Equations, Equations ofMathematical Physics, and related topics. ... Read more

Book Description

The theory of composite materials is the study of partial differential equations with rapid oscillations in their coefficients.Although extensively studied for more than a hundred years, an explosion of ideas in the past four decades has dramatically increased our understanding of the relationship among the properties of the constituent materials, the underlying microstructure of a composite, and the overall effective moduli that govern the macroscopic behavior.This renaissance has been fueled by the technological need for improving our knowledge base of composites, by the advance of the underlying mathematical theory of homogenization, by the discovery of new variational principles, by the recognition of how important the subject is to solving structural optimization problems, and by the realization of the connection with the mathematical problem of quasiconvexification.This book surveys these exciting developments at the frontier of mathematics and presents many new results. ... Read more

Book Description

The Authors' goal is to communicate an exciting new approach to Differential Equations - through Modeling, Visualization and Dynamical Systems. This new way of looking at ODEs blends the tried and true analytical methods with mathematical modeling, applications to engineering and the sciences, and geometric visualization via numerical solvers. The resulting rich insight and highly motivated learning offers students a powerful, stimulating, yet accessible experience that brings them to a deep understanding of ODEs! ... Read more

Reviews (11)

On second thought
I wrote a first review, and the author hunted down my email address and emailed my differential equations teacher. In the email, he said, I should wait until I finished the course until I reviewed his book. I realized how wrong I was to shoot my mouth off. I should have been more sagacious and patient in order to tell the truth.

First the good: I only spent 40 bucks on this book and should be able to get my money back. And the author spent tons of time designing little computer cartoons because there's nothing I like better than being distracted by a funny cartoon.

The bad: If you don't have ADD before you pick up this book, you will after. Printed on wonderfully shiny paper, with multicolored graphs, headers, footers, pictures, and once in awhile even something haveing to do with differential equations, this book is next to impossible focus on. That's part of the reason some students like this book. They don't have to read. They can just look at the pictures then ask someone else for help.
Do you want to learn about differential equations? Well, if you buy this book, you might. If you pair this book up with another book that explains why this stuff makes sense. And then read only that book. Good understanding of the more difficult problems come from a good foundation. This book spends 2 chapters on the basics. But boy, you want to graph stuff, here's your chance. (You can even have an assignment to graph a kitten out of differential equations, i mean man, that's worth a star right there.) The author succumbs to greedius maximus, wherein he crams as much crap into a book to sell as many copies as possible, instead of focusing on one thing and doing it well. Because no one really needs more than 20 pages to describe all of second order differential equations. The computer can do all that for you.
Oh, and if you want to learn how to solve differential equations for something like physics class, good luck. You have two choices in this book, you can either guess and make up your own way of doing things, or you can use the cookbook approach. You won't really know why you want to take the exponential, but that doesn't matter because you just need a grade. So you follow the clever boxed text that says do this, this, than this. And voila, you have an answer. And to anyone who says, well, we have to graph most differential equations because we can't solve them, i say, wonderful? So, I can just move onto stuff no one understands and expect to make sense of it by not understanding the equations we do know how to solve.

And since I need to plug Dover to make my 20 dollar commission, buy Morris Tenenbaum's Ordinary Differential Equations book. It's not fancy, but it's well written and 800 pages long. Which is funny, because Borrelli's book is 790 pages long and tries to cover ODE's, PDE's and Linear Algebra. Telling detail? I think so. ( I bet you could even buy a couple of awesome Dover books on PDE's and Linear Algebra and still undercut the 115 dollar selling price by about 3/4. )

An Open Letter of Thanks to the Authors
Several of my students have commented spontaneously and favorably about your book.Just today a student told me that she really liked it that the modeling projects were not just in the blue pages between chapters but sprinkled all the way through the text - which is exactly why I chose the book in the first place, and which I guess is whyyou wrote the book in the first place.

As to ODE architect - our students at Macalester are already somewhat Mathematica savvy (from Calc II which is Mathematica bootcamp) and some of them are Matlab savvy as well. I had originally planned to push matlab in DE, but got lazy.I just told the students that they are free to use any computer software they like and whenever they like and gave them no instruction. I expect them to be able to solve (as definite integral) first order linear and of course we do explicitly the classic second order constant coefficient undriven - and with sinusoidal driving functions but not much else do we look for solutions as formulas.[By the way, I was very pleased you took the Phasor approach (Ce^{iwt}} to undetermined coefficients when Right Hand Side is harmonic - brings back my first training as EE.] About the time I assigned a drug model with intermittent treatment schedule etc, I began to see (without my prompting) solutions submitted with ODE architect, which students thought of using and figured out all on their own.The original issue for them was that Mathematica did not make it easy to use square waves as driving functions, or even really possible to do it without cleverness that I had and they did not.Students report that it is easy to use ODE architect and I think it is their preference now (for most of them).

I am really more interested in students coming out of the course
understanding a bit about how to construct a DE to model a problem, how to read the DE that does model something by interpreting terms. I want them to realize how many choices and simplifications and even oversimplifications have to be made - even choice of variables is tough and there is rarely a single right choice, to realize that models have limits, that simple models can be insightful first step even if quantitatively wrong and that there is often a second step that jazzes a model up a bit, that big teams spend years developing models, etc - more
interested in all that than in "solving a DE". I do want students to be able to read a graphical solution - either as solution variable vs t or in phase plane, to understand how to visualize a DE as a slope field, etc.If you do all that, then there is just no time for tricks to solve with formulas.

About every other week, at a random point I say "how could we get
numbers", put up a blank table of values, ask students to fill in the first entry (initial condition) so they can see that initial condition is a table entry, and then pick or have them pick a step size and work out the next two or three approximate entries with basic intuitive Euler method.I bill this as "the general solution method" and they all understand it and accept it now as the norm. Once in a while now I surprise them with a formula for a solution.One day - really just for something different - I threw up Hermite equation and said lets try undetermined coefficients (power series) and they just did it themselves in class - but I will not do more with power series except one exercise from your book.

I am now teaching linear systems of first orders with constant
coefficients.That is a bit different, we are doing the linear algebra to decouple and so are getting formulas, perhaps a nice change of pace.

Maybe the above remarks will give you a clue about why I like your book.And why I will use again again next time I teach the course.

Great book for math enthusiasts
First, I would like to warn students wishing to introduce themselves to Differential Equations (DEs) to avoid this book if they do not have a strong mathematical background. The book does not use a linear approach common in other books, and tends to integrate DEs with other subjects such as engineering, physics, biology, and other fields of mathematics while spreading out the topics. At times, the book tends to skip algebraic steps, making it confusing for those who are not as strong in algebra. First-timers will find this book hard to follow on their own, but with the guidance of a good professor, it should not be too hard to tackle.

Unlike other textbooks that teaches one topic and proceeds to give thousands of examples, this book does not do that. Instead, it uses the "modeling approach" to show how DEs relates to other fields of science. A person interested in mathematics and science will find this book very intriguing because of how well it relates math to everything else in life. Problems in this book are generally harder than problems of average DEs books, but once the students become used to them, it will be much more helpful. Not only does this book help the students understand the new concept of DEs, it aids them in reviewing the calculus and algebra (along with complex numbers, linear algebra, and trigonometry).

Overall, this is a perfect book for someone who likes math but finds most "advanced" high school textbooks too simple. This book does not merely repeat examples until the student understands the material. The student is expected to work out practice problems on his own and check his answers with the back of the book. This book uses proofs to discover theorems instead of just stating it while leaving the motivated student perplexed on how mathematicians came up with the theorem. Finally, this book includes the ODE (Ordinary Differential Equations) CD, which assists the student in the learning process with visual aids and graphic demonstrations. While this program may not be as powerful as Mathematica or Maple, it runs much faster and is more convenient in learning DEs.

I would not recommend this book for a science or math class
The book doesn't provide students with a good picture of basic techniques in DE. In fact, it doesn't teach them any technique on a regular basis. I teach Numerical Methods for Differential Equations in a math class which had this book as a textbook for their DE course. Unfortunately, the lecturer followed the book too closely. Kids have a very vague understanding how to work with DE's. Any reference to this book doesn't help - a simple concept may be spread across a few chapters and eventually shall be extracted from examples.

Best differential equations book I've used!
This book's clear writing style, fantastic use of illustrations and examples, and good chapter organization make it the best differential equations book I've used.

I can understand a first time student might have problems with this book. The text isn't perfect. It requires a professor to help guide the student along. But one shouldn't expect to learn a rich and demanding subject like differential equations alone. ... Read more

Book Description

This book proveds a clear, concise explanation of Laplace transforms, or operational calculus--now necessary knowledge for engineers, physicists, mathematicians and other scientists. Definitions, principles and theorems are illustrated and reinforced by hundreds of fully worked out problems. Also included are chapters on complex variable theory and Fourier series and integrals, so important to discussions of the complex inversion formula.

Reviews (6)

It helped me through control systems
This book taught me both the basics and some of the finer points of LaPlace Transforms to get me past that hurdle so that I could begin focussing on the actual material presented in my BioControl Systems course. Many people got so caught up on the mathematics of LaPlace Transforms that they did not even get to the point where they could begin understanding control systems. I bought this book from Amazon at the beginning of the semester and it turned out to be a life-saver for me. I think that had I not sat down with this book for a weekend and taught myself LaPlace Transforms, I would have not passed that class.

Granted, this is a single case for a single class of a single bioengineering student; nevertheless, for my part I strongly recommend this book. I was put in a class where the teacher expected the students to have an understanding of the mathematics from the start. The majority of us didn't have that background, and this book clearly, simply, and without too much complication prepared me for my class which was exactly what I wanted it to do. It has been one of the best investments (as far as school books go) of my college career.

I must leave you with one parting word of wisdom. This book, and I don't think any other book dealing with such an advanced topic, is not easy to read. You will not be able to thoughtlessly master the material. You will work to understand it; your brain may hurt at times. But this book presented the information in a much-more-easy-to-digest manner than any of my college math textbooks, and for that, I am grateful.

Not for Engineers
This books looks like it was written by a mathematician for math students. I'm not saying that's bad, but with the screaming title, I feel like it will attract a lot of engineering students looking for help in their lower division engineering classes where Laplace Transforms are an integral part of the course. This text is not your best choice.

Looking @ the titles of some of the 8 chap. should make you suspicious:
Chap. 2 - The Inverse Laplace Transform,
Chap. 3 - Applications to Differential Equations,
Chap. 4 - Applications to Integral & Difference Equations,
Chap. 5 - Complex Variable Theory,
Chap. 7 - The Complex Inversion Formula,
Chap. 8 - Application to Boundary-Value Problems.

It's my guess that if your're an undergraduate engineering student (particularly EE), you're looking for a little less of Lerch's & Green's theorems, complex variable theory, & working inverse Laplace transforms by hand, and instead more engineering explanations of the complex S-plain, what's really happening when an f(t) is transposed into an F(s), how does the little function "e" raised to the "-st" power perform its magic, how does Laplace & Fourier transform differ, how does this relate to Phasors, & how can I solve many engineering problems without having to even write differential equations? In other words, you probably don't need another terse, yet cold math book. What you may be looking for is something that addresses S-Domain circuit/system analysis written from the engineering point of view.

One suggestion, staying with Schaum's, is SIGNALS and SYSTEMS where Hsu does an OK job with engineering transforms including Laplace. It's more systems oriented than circuits, but you'll get a better feel for the application of transforms to engineering problems & the engineering math behind them from this book.

Wonderful reference, lotsa problems
I used this book (among others) for an undergraduate course on 'Fourier and Laplace Analysis' in my sophomore year in engineering. The author had presented the concepts of Fourier series and transforms before progressing to Laplace transforms. Many important topics like Convolution, Initial & Final Value Theorems as well as the applications of Laplace transforms in solving differential equations were presented in a clear-cut, understandable way.

Using this book was a rewarding experience.

A good supplement
If you are not already in a calculus class and are well versed in the terminology, you may find yourself a little lost with this one. This book assumes that you understand integrals and other mathematical theories. I would not use this to teach myself about Laplace transforms.

As a supplement, this is a fairly good book. As with most books in the series, there are various step-by-step instructions to show you how these work and to explain the various functions and theories. There are supplementary exercises at the end of each chapter with the answer right there for you to test yourself.

Useful not only on Laplace Transforms
This book is excellent! It contains a lot of exercises in several levels, from basic to advanced ones. The great advantage took ver the other books on this matter is that it's not necessary any previous knowledge about Complex Variables. The book is specialy useful for students not so used to the Math tricks. I used this book in a course on Applied Mathematics at Federal University of Rio Grande do Sul. I've found this book useful not only for learning Laplace Transforms but also can be used as a reference guide and introduction to Complex Variables, Partial Differential Equations, Integral Equations and a little taste about Circuit Analysis. Be sure of having one of this at your professional library. ... Read more

Book Description

Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook. In a systematic introductory manner, this unique book deliniates boundary layer theory for ordinary and partial differential equations, multi-timescale phenomena for nonlinear oscillations, diffusion and nonlinear wave equations. The book provides analysis of simple examples in the context of the general theory, as well as a final discussion of the more advanced problems. Precise estimates and excursions into the theoretical background makes this workbook valuable to both the applied sciences and mathematics fields. As a bonus in its last chapter the book includes a collection of rare and useful pieces of literature, such as the summary of the Perturbation theory of Matrices.

Detailed illustrations, stimulating examples and exercises as well as a clear explanation of the underlying theory makes this workbook ideal for senior undergraduate and beginning graduate students in applied mathematics as well as science and engineering fields.

Book Description

Computational Mathematics in Engineering and Applied Science provides numerical algorithms and associated software for solving a spectrum of problems in ordinary differential equations (ODEs), differential algebraic equations (DAEs), and partial differential equations (PDEs) that occur in science and engineering. It presents detailed examples, each including a complete analysis of a computer code written in transportable Fortran 77. Each example also includes a discussion of the problem equations, the coding of the equations, and the computed numerical solution. The benefits of using quality general-purpose library routines to solve ODE/DAE/PDE problems are illustrated as well. This popular, classicbook is a valuable reference for methodologies in numerical mathematics applicable to a broad spectrum of problems encountered across many disciplines- virtually all fields of science and engineering. It also serves asan excellent text for senior undergraduates or beginning graduate students in computational science. ... Read more