Book Description

An essential aid for those in math, science, and engineering.The 39 comprehensive chapters of this book cover the field from separable equations to second order equations, systems of equations, and non-linear equations.A particularly large number of applications are included.Problem-solving strategies and methods of attack are included at the beginning of every chapter for each topic covered. ... Read more

Reviews (4)

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

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

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

It's alright
I thought that this book was THE problem solver as it claimed but I didn't like the format and it sure does not appeal to many college students. ... Read more

Book Description

"Dynamical Systems with Applications using MAPLE" covers standard material for an introduction to dynamical systems theory. The text begins with a tutorial guide to MAPLE and thereafter is divided into two main areas: continuous systems using ordinary differential equations and discrete dynamical systems. In the first part of the text, differential equations are used to model examples taken from various disciplines, including mechanical systems, chemical kinetics, electric circuits, interacting species, and economics. In the second half, both real and complex discrete dynamical systems are considered and examples are taken from economics, population dynamics, nonlinear optics, and materials science.

Approximately 200 illustrations, over 250 examples, and exercises with solutions play a key role in the presentation. The book has a hands-on approach, using MAPLE as a tool throughout.Common themes such as bifurcation, bistability, chaos, instability, multistability, and periodicity run through several chapters. Some chapters deal with recently published research articles and provide a useful resource for open problems in nonlinear dynamical systems.

The text is aimed at senior undergraduates, graduate students, and working scientists in various branches of applied mathematics, the natural sciences, and engineering. ... Read more

Reviews (8)

More information
Thought I'd give a more in depth review than the others here.

Most advanced math textbooks contain one or two chapters that turn me off. I must say that every chapter in this book had useful information or very good applications.

The opening chapter is a brief introduction to Maple V (some Maple 8 commands are posted on the books website). Note that Maple 9 is now out and no doubt Maple X will soon follow.

Chapters 1-7 cover planar systems in some detail, vectorfield in DEplot is a real winner here. Chapters 8 and 9 cover 3D and nonautonomous systems - the poincare command in Maple is a real time saver.

Chapters 10-12 cover a lot of research results on limit cycles - the most lucid I have seen in any textbook.

The remaining half of the book concentrates on both real and complex discrete systems. There are the usual cobweb diagrams, bifurcation diagrams and Mandelbrot set. Where this book comes into its own, however, is in Chapters 16-20.

Lasers and nonlinear optics are investigated using complex iterative maps. Fractals and even multifractals are discussed in some detail. The book ends with a chapter dedicated to chaos control.

Overall, the book is concise with pertinent examples and applications. It is not dogged down with math notation, theorems and proofs.

Strogatz, Perko and Allgood are good books to practice more Maple programing techniques.

This is great book
This is only book I find with program files that work right away. Graphics in Maple is excelent for chaotic system and algebra very powerful. I like to rotate figures in 3D and use animation. I learn more about optics, it nice to see complex numbers used in applications. Lots of other applications also.

Book is best for students who want to get programs working quickly. There is a website with working programs. You should also look at Maple Application website for many many examples.

I recomend book to everyone.

Not ready for print
This book is rife with errors, omissions, grammatical and programming mistakes, hand-waving and is generally misleading about theorems.Only if you know very little about linear algebra and diff eq. will you not notice this -- this book only skims the surface of topics (breaking down easy cases in R^2 so poorly that when the same topic comes up in R^3 it's "a whole new thing") and theorem statements are often confusing compared to better sources at best.In all fairness, the book is very ambitous, but there is not enough content in the book to tackle actual problems not couched in its own terms. Many of the graphs and examples are nice, but they do not make up for the lack of editing, organization, and rigor (of even the usual "applied math" variety -- no one is expecting pure math here) in this book.The first two chapters are deceptively nice -- things begin to drop off quickly.Update:The ever dropping price of a new edition does not lie -- if you can, pick up Perko instead.

very nice introduction to dynamical systems
This book is a very nice introduction to the theory of dynamical
systems. It covers all aspects and even more than usually thaught
in a class on dynamical systems. Especially, I like to see
many examples for various applications. These examples and the
Maple programs make it well suitable for students to learn
on dynamical systems by themself.

The MAPLE programs and web pages make this book unique.
A great book. Great web pages and short, easy to copy and edit
Maple programs. Lots of material not covered in other books on this topic. Maple is my favorite package. The others are not
as user friendly. I felt I must write again since amazon have been showing excerpts from book. What a geat idea. Chapters in this book that interested me were fractals, multifractals and
optics. Authors web-site is given on back cover of book. Enjoy! ... Read more

Book Description

Time Domain Electromagnetics deals with a specific technique in electromagnetics within the general area of electrical engineering. This mathematical method has become a standard for a wide variety of applications for design and problem solving. This method of analysis in electromagnetics is directly related to advances in cellular and mobile communications technology, as well as traditional EM areas such as radar, antennas, and wave propagation. Most of the material is available in the research journals which is difficult for a non-specialist to locate, read, understand, and effectively use for the problem at hand.

* Only book currently available to practicing engineers and research scientists exclusively devoted to this subject
* Includes contributions by the world's leading experts in electromagnetics
* Presents the most popular methods used in time domain analysis are included at one place with thorough discussion of the methods in an easily understandable style
* In each chapter, many simple and practical examples are discussed thoroughly to illustrate the salient points of the material presented
* All chapters are written in a consistent style that allows the book to be of use for self-study by professionals as well as for use in a graduate-level course in electrical engineering ... Read more

Book Description

Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.

Several features make this book unique. The first is the systematic use of bordered matrix methods in the numerical computation and continuation of various bifurcations. The second is a detailed treatment of bialternate matrix products and their Jordan structure. Govaerts discusses their use in the numerical methods for Hopf and related bifurcations. A third feature is a unified treatment of singularity theory, with and without a distinguished bifurcation parameter, from a numerical point of view. Finally, numerical methods for symmetry-breaking bifurcations are discussed in detail, up to the fundamental cases covered by the equivariant branching lemma. ... Read more

Book Description

Liberal Arts mathematics books often cover much more material than can be addressed in a one-semester course. Karl Smith has created a solution to this problem with his new book: THE NATURE OF PROBLEM SOLVING IN GEOMETRY AND PROBABILITY. Loyal customers of Karl Smith's books laud his clear writing, coverage of historical topics, selection of topics, and emphasis on problem solving. Based on the successful NATURE OF MATHEMATICS text, this new book is designed to give you only the chapters and information you need, when you need it. Smith takes great care to provide insight into precisely what mathematics is--the nature of mathematics--what it can accomplish, and how it is pursued as a human enterprise. At the same time, Smith emphasizes Polya's problem-solving method throughout the text so students can take from the course an ability to estimate, calculate, and solve problems outside the classroom. Moreover, Smith's writing style gives students the confidence and ability to function mathematically in their everyday lives. This new text emphasizes problem solving and estimation, which, along with numerous in-text study aids, encourage students to understand the concepts as well as mastering techniques. ... Read more

Book Description

This new edition of Mathematics for Dynamic Modeling updates a widely used and highly-respected textbook. The text is appropriate for upper-level undergraduate and graduate level courses in modeling, dynamical systems, differential equations, and linear multivariable systems offered in a variety of departments including mathematics, engineering, computer science, and economics. The text features many different realistic applications from a wide variety of disciplines.
The book covers important tools such as linearization, feedback concepts, the use of Liapunov functions, and optimal control. This new edition is a valuable tool for understanding and teaching a rapidly growing field. Practitioners and researchers may also find this book of interest.

* Contains a new chapter on stability of dynamic models
* Covers many realistic applications from a wide variety of fields in an accessible manner
* Provides a broad introduction to the full scope of dynamical systems
* Incorporates new developments such as new models for chemical reactions and autocatalysis
* Integrates MATLAB throughout the text in both examples and illustrations
* Includes a new introduction to nonlinear differential equations ... Read more

Reviews (1)

more modeling concepts
This is not a new cover on an older book. Having enjoyed Beltrami's first book I was glad to see a second. The new continues the subject of modeling not math. Well written, the author's book ties the conceptual difficulites of the subjects with the necessary math to get the point accross and guide the reader to new frontiers of insight again in the sense of the physical model not the math. This is a very important point! One does not lose sight of the over-all objective as with some math intensive proof types. The beauty of the work is getting the necessary across with the least. One disappointment though. The book was to short. I hope the author continues another work. Perhaps some more indepth of previous covered material. All examples and problems are easily solved in Mathcad, which already has the depth but sometimes not the explanation. ... Read more

Book Description

Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. For more information on this book, see http://math.vanderbilt.edu/

Key Features
* Covers some hard-to-find results including:
* Bessagas and Meyers converses of the Contraction Fixed Point Theorem
* Redefinition of subnets by Aarnes and Andenaes
* Ghermans characterization of topological convergences
* Neumanns nonlinear Closed Graph Theorem
* van Maarens geometry-free version of Sperners Lemma
* Includes a few advanced topics in functional analysis
* Features all areas of the foundations of analysis except geometry
Combines material usually found in many different sources, making this unified treatment more convenient for the user
* Has its own webpage: http://math.vanderbilt.edu/ ... Read more

Reviews (1)

From an amateur's point of view.
I've always wanted to know more math. Finally, I've discovered a big book that makes the tough stuff accessible without sacrificing detail or over-simplifying the hard concepts. For someone with a little bit of college math - calculus and maybe a few more courses - this is it. Analysis, abstract algebra, set theory, topology .... It's all here despite the focus on foundations. And it's organized in a way that makes it possible to follow the thread of a topic throughout the book without reading everything from the beginning. A CDROM version (the one I'm using) not only allows the sort of random access that makes surfing the book convenient but also presents the text in either HTML or PDF format. Open it up in a Java-enabled browser and you can play with the fonts until it suits your reading style. Ideally, for the reader, the CDROM might have been bundled with the book.

Books geared to self instruction need to enlist the readers' aid in educating themselves. Good teachers have that knack. It is a gift to be able to make complicated ideas understandable by building up gradually from simple and familiar concepts to ones that are unusual, obscure, or even initially incomprehensible. Eric Schecter must be a good teacher because in reading his book I am learning more math than I ever thought I would or could. I need to leave questions about the quality of the math itself in depth or scope to the judgment of the professionals but the text appears to make few concessions of substance to us amateurs. Armchair or would-be mathematicians as well as teachers and researchers might find this book a place in their personal libraries. ... Read more

Book Description

Superb introduction devotes almost half its pages to numerical methods for solving partial differential equations, while the heart of the book focuses on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included, with solutions for many at end of book. For students with little background in linear algebra, a useful appendix covers that subject briefly.
... Read more

Reviews (1)

It's about time this book is back in print.
Kudos to Dover for bringing this book back in print. We used
this book in a partial differential equations course at the
University of Pittsburgh a year ago. Unfortunately, the book
was out-of print then, and we had to use photocopies of the
original Harper & Row edition. (and the school bookstore charged
us about twice the $$ as the Dover edition costs.) The text
begins with the heat equation, and then progresses to more
complicated PDEs. The nice thing is that discrete methods are

introduced right from the start. I remember having a lot of fun
plugging discrete solutions of PDEs into Microsoft Excel and
seeing what the solutions looked like. The chapter on Fourier
Series is good, generalized Fourier series are covered, and
you will learn concepts such as pointwise and uniform convergen-
ce. Following that, there is a chapter on boundary-value
problems which covers Dirichlet, Neumann and Sturm-Liouville
problems. For both Cartesian and curvilinear coordinates. I
can't tell you what is in the later chapters, but if the rest
of the book is like the first three chapters, then it is a great
book, well worth the money. ... Read more

Book Description

This text intends to transform students from passive observers of mathematics to participants in it. The book employs a spiral development of ideas to blend the requirements of problem solving, analytical thinking, computational technique, and applications, and emphasizes the interplay of algebraic and geometric concepts. It includes an extensive number of exercises, ranging from routine to challenging. The Third Edition offers 40 percent new material, including manynew applications. It incorporates MATLAB to demonstrate how computational software tools can be used in this field.

* Offers a proven, successful approach to Linear Algebra
* Contains a practical presentation, illuminating examples, and exceptional exercises, thus enabling instructors to emphasize computational techniques, theoretical material, and applications
* Includes a wide variety of effective applications
* Provides a student friendly writing style
* Begins with the familiar and proceeds to the new in a well-motivated manner
* Acknowledges current reforms and proceeds from there
* Explains how to solve some examples in MATLAB, demonstrating how such software tools can be used in this field
* Includes student projects at close of chapter exercise sets ... Read more

Reviews (2)

Excellent text
This is an outstanding, well-written, and interesting text. Highly recommended for university coursework.

This book is great!
Yaqub's book is the best "first" book for a "first" upper divsion course in linear algebra. It provides a good transition from the freshman calculus to that of more advanced courses. The book is not terse but is verbose and easy to read. Hence, concepts jump off the page at you. This book develops mathematical maturity, which is needed in higher courses. ... Read more

Book Description

The subject of differential and difference equations is an old and much-honored chapter in science, one which germinated in applied fields such as celestial mechanics, nonlinear oscillations, and fluid dynamics. In recent years, due primarily to the proliferation of computers, dynamical systems has once more turned to its roots in applications with perhaps a more mature look. Many of the available books and expository narratives either require extensive mathematical preparation, or are not designed to be used as textbooks. The authors have filled this void with the present book. ... Read more

Reviews (1)

A great introduction to dynamical systems
As a postgrad student searching for textbooks to cover all those things I learnt about dynamical systems in my undergrad studies, this one was one of my first choices. It is easy to read, which is surprising, considering it'sa maths textbook. It is systematic in its treatment of dynamical systems.The important things are easy to find, since the index is verycomprehensive and the layout of the page makes formulae stand out. The manydiagrams help those of us who think about dynamics geometrically. All inall, a great book, which I use on a regular basis as a reference. ... Read more

Book 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

Book Description

This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life. ... Read more

Book Description

Uses an analytical and techniques-oriented approach to present a concise introduction to the subject focusing on time-evolution problems. Emphasizes hyperbolic and parabolic problems and includes a range of applications—chemistry, porous media, biological problems, traffic flow, reactors, heat transfer and detonation. Packed with exercises, examples and illustrations. ... Read more

Reviews (1)

Nonlinear PDE's
There seem to be few textbooks on this particular subject accessible to students; most deal with linear PDE's, so the book fills a gap. 'Nonlinear Partial Differential Equations' assumes the reader is already familiar with differential equations,so is not suitable as an introduction to the subject. It is written at an advanced level, but concepts are very clearly spelled out. Logan takes the reader through all the necessary mathematical steps in explaining a new concept. He does not skip steps in his analysis. Chapter One introduces canonical equations and transformations, but Logan's treatment is very sparse and there are better texts available for these subjects. Logan's book concentrates mostly on how PDE's can be reduced to ordinary differential equations via similarity methods etc. Most standard types of nonlinear systems are dealt with, including reaction diffusion processes, chemically reacting fluids and shock wave development. I like this book and that's why I bought it from Amazon, but be careful, there are one or two typing errors in the maths. ... Read more

Book Description

Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra.Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to the modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods. ... Read more

Book Description

The CLASSIC EDITION of Zill's respected book was designed for instructors who prefer not to emphasize technology, modeling, and applications, but instead want to focus on fundamental theory and techniques.Zill's CLASSIC EDITION, a reissue of the fifth edition, offers his excellent writing style, a flexible organization, an accessible level of presentation, and a wide variety of examples and exercises, all of which make it easy to teach from and easy for readers to understand and use. ... Read more

Reviews (1)

too much theory
they prove EVERY single theorem in the most grating way... good chapters on applications though. ... Read more

Book Description

This book is an introductory graduate text dealing with many of the perturbation methods currently used by applied mathematicians, scientists, and engineers. The author has based his book on a graduate course he has taught several times over the last ten years to students in applied mathematics, engineering sciences, and physics. The only prerequisite for the course is a background in differential equations. Each chapter begins with an introductory development involving ordinary differential equations. The book covers traditional topics, such as boundary layers and multiple scales. However, it also contains material arising from current research interest. This includes homogenization, slender body theory, symbolic computing, and discrete equations. One of the more important features of this book is contained in the exercises. Many are derived from problems of up- to-date research and are from a wide range of application areas. ... Read more

Book Description

Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings.

Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem.

There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane).

A collection of independent survey articles in the field of GeometricFunction Theory
Existence theorems and qualitative properties of conformal and quasiconformal mappings
A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane). ... Read more

Book Description

To understand multiscale phenomena, it is essential to employasymptotic methods to construct approximate solutions and todesign effective computational algorithms. This volume consistsof articles based on the AMS Short Course in SingularPerturbations held at the annual Joint Mathematics Meetings inBaltimore (MD). Leading experts discussed the following topicswhich they expand upon in the book: boundary layer theory,matched expansions, multiple scales, geometric theory,computational techniques, and applications in physiology anddynamic metastability. Readers will find that this text offersan up-to-date survey of this important field with numerousreferences to the current literature, both pure and applied. ... Read more