Book Description

Green's functions are an important tool used in solving boundary value problems associated with ordinary and partial differential equations. This self-contained and systematic introduction to Green's functions has been written with applications in mind. The material is presented in an unsophisticated and rather more practical manner than usual. Consequently advanced undergraduates and beginning postgraduate students in mathematics and the applied sciences will find this account particularly attractive. Many exercises and examples have been supplied throughout to reinforce comprehension and to increase familiarity with the technique. ... Read more

Book Description

This introduction to dynamical systems theory treats both discrete dynamical systems and continuous systems. Driven by numerous examples from a broad range of disciplines and requiring only knowledge of ordinary differential equations, the text emphasizes applications and simulation utilizing MATLAB®, Simulink®, and the Symbolic Math toolbox.Beginning with a tutorial guide to MATLAB®, the text thereafter is divided into two main areas. In Part I, both real and complex discrete dynamical systems are considered, with examples presented from population dynamics, nonlinear optics, and materials science. Part II includes examples from mechanical systems, chemical kinetics, electric circuits, economics, population dynamics, epidemiology, and neural networks. Common themes such as bifurcation, bistability, chaos, fractals, instability, multistability, periodicity, and quasiperiodicity run through several chapters. Chaos control and multifractal theories are also included along with an example of chaos synchronization. Some material deals with cutting-edge published research articles and provides a useful resource for open problems in nonlinear dynamical systems. Approximately 330 illustrations, over 300 examples, and exercises with solutions play a key role in the presentation. Over 60 MATLAB® program files and Simulink® model files are listed throughout the text; these files may also be downloaded from the Internet at: http://www.mathworks.com/matlabcentral/fileexchange/. Additional applications and further links of interest are also available at the author's website.The hands-on approach of Dynamical Systems with Applications using MATLAB® engages a wide audience of senior undergraduate and graduate students, applied mathematicians, engineers, and working scientists in various areas of the natural sciences.Reviews of the author’s published book Dynamical Systems with Applications using Maple®: "The text treats a remarkable spectrum of topics…and has a little for everyone. It can serve as an introduction to many of the topics of dynamical systems, and will help even the most jaded reader, such as this reviewer, enjoy some of the interactive aspects of studying dynamics using Maple®." – U.K. Nonlinear News "…will provide a solid basis for both research and education in nonlinear dynamical systems." – The Maple Reporter ... Read more

Reviews (2)

Agree with Prior Reviewer
I cannot quite honestly give this book (*first* edition, not second) a full five-point-zero stars because it somewhat comes apart the closer one gets to the final chapters. I read this book a few years ago, so I apologize for lack of specificity. However, I completely agree with the prior reviewer who stated that this book is better than Kunz's and Luebbers' book, which I appears to be a slightly edited compilation of previous publications --- even if that is completely untrue. In fact, in my opinion, Taflove's book (again, first edition) is a *much* better textbook than Kunz and Luebbers.

The Book News review is somewhat misleading. Taflove derives the difference equations in full, painstaking detail. (Perhaps the Book News reviewer fell asleep during that portion.) For me, this was the most valuable and educational portion of the book. Example applications have their place, but only after understanding the basic principles. Taflove did an excellent job in describing these principles, which go far beyond the basic Yee algorithm (e.g. extrapolation techniques and incorporation of BC's). Those readers familiar with other FD books should understand what I'm saying here: Anyone who reads this book and understands it will not only be conversant about FDTD but should also be able to write solid working codes. With the K&L book, this is very questionable.

A good overview of FD-TD method
A good intro book for the FD-TD method with many applications. The list of references at the end of each chapter is also very useful. Some of the material is now outdated and needs corrections, but otherwise a great reference for CEM. I would recommend this book over the Kunz & Luebbers FD-TD book. ... Read more

Book Description

KEY BENEFIT Emphasizing physical interpretations of mathematical solutions, this book introduces applied mathematics and presents partial differential equations. KEY TOPICS Leading readers from simple exercises through increasingly powerful mathematical techniques, this book discusses hear flow and vibrating strings and membranes, for a better understand of the relationship between mathematics and physical problems. It also emphasizes problem solving and provides a thorough approach to solutions. The third edition of , Elementary Applied Partial Differential Equations; With Fourier Series and Boundary Value Problems has been revised to include a new chapter covering dispersive waves. It also includes new sections covering fluid flow past a circular cylinder; reflection and refraction of light and sound waves; the finite element method; partial differential equations with spherical geometry; eigenvalue problems with a continuous and discrete spectrum; and first-order nonlinear partial differential equations.An essential reference for any technical or mathematics professional. ... Read more

Reviews (13)

does the job!
I am no mathematican or otherwise great spirit, so I'll simply tell you how it helped me in my first PDE class, or not. I found the book generally easy to read, and understand. In the beginning it is nice to have very simple examples fully worked out in the text. Unfortunately the worked through examples get rarer in the more advanced chapters. I also think the book is fairly well structured, and together with the good index I could find inormation easily. My major complaint is that there are not enough exercises with answers in the back. While in your usual calculus book every second problem has an answer, often only one out of say seven has an answer.

ok that it's not rigorous IMO, it's just an intro
I don't mind that this book isn't very rigorous; after all it's just an intro. The rigour can come later. I had this text for an intro PDEs course that had many students from physics or engineering, so I totally believe that this is the right book for them. Maybe if math students want more rigour they could learn the proofs of everything. This book is a pretty good 1-stop text for everything you'd want to do in undergrad PDEs. There are enough examples and problems to make things clear. It's definitely a keeper if you're going to carry on with PDEs.

Comprehensive, detailed, easy to read -- a good PDE text
This PDE text by Haberman covers the ideas about separation of variables, Sturm-Liouville problem, finite difference numerical method, Green's function, Fourier transform, Laplace transform, and the method of characteristics. It presents the materials in quite plain, detailed manner. To me, the best part of this book relative to another books is that of Green's function. I've read Arfken, Farlow, and Strauss's texts, but have never got a satisfactory understanding.

The Strauss's one is the worst. To a beginner or non-mathematician, it is impossible to accept that kind of crazy things. The Farlow's one doesn't pay enough effort on this topic. It just goes through in a few pages. The Arfken's one (Mathematical Methods For Physicists) gives a concise presentation in quite physical way, but not for beginner. It is more like a summary.

Haberman introduces Green's function in his book with two chapters and in a quite different manner. He doesn't, like most physicists do, introduce it by Poisson's equation, but by heat equation and Fourier series; the ordinary definition of Green's function with delta function is given later. Though I think this is not a good idea and the presentation is not good, I do agree that it is much easier for beginners to understand. He makes no haste going into the three-dimensional case. Instead, he works on one-dimensional cases, then two and three-dimensional cases systematically. The point is, I think this won't make it too mathematical like the Strauss's one or too physical so that it is too constricted. In addition, he derives Green's functions in deductive way, instead of only taking a look at the physical suggestions. This makes the results convincible and gives readers a more comprehensive understanding.

Perhaps the most annoying thing of this book is that it is too wordy. However, this may be another advantage-the text is hard not to understand!

Someone says that Haberman hardly works on subjects other than heat equations. That kind of comment is misleading. He does work on wave and Laplace's equations. He just use heat equation as a main thread.

If you're learning PDE for physics or engineering or other applications, this book is quite suitable for self-studying. If you only want to study the most basic ideas about PDE, then Farlow's may be a light choice. If you want to study more, you can read Haberman's text.

Feedback from using book in a course
This book is below my expectations as a good introductory book. It doesn't have enough examples, and the examples are too straightforward in some cases. Too much attention is sometimes paid to development of the proofs, which can be left out if this book is as the title suggests : "elementary", because it's more useful to show the reader how to solve the problems. In terms of the organisation of the book, it's a bit confusing (this is especially obvious if you compare this book with Farlow). I think an excellent book can be produced if this book is merged with Farlow and with plenty examples thrown in. i'm not sure how this book was selected as a required text for my math course in Boundary Value Problems because i'd hope that there are better books out there in this 21st century.

An Applied Math Text for PDEs
Haberman's book clearly explains how to solve various kinds of PDEs and does provide insight into the meaning of the techniques and solutions. It is a good applied math text and those who are looking to use the techniques for other pursuits will find the book useful. It is not a math text, and may lack "rigor" for those who want it. ... Read more

Book Description

Viewing stained glass from different angles or in various lights is necessary to discover its many qualities. Likewise, viewing solutions of differential equations from several points of view is essential to fully understand their behavior. Lomen and Lovelock provide an active environment for students to explore differential equations by using analytical, numerical, graphical, and descriptive techniques, and for students to use ODEs as a natural tool for modeling many interesting processes in science and engineering. ... Read more

Reviews (1)

One of the best Differential Equations textbooks ever
As a student of Professors Lomen and Lovelock I can say with confidence that this is one of the best Differential Equations textbooks I've worked with. The book clearly explains all the concepts, provides numerous examples, and covers everything that there is to be known. Perfect as a supplement to your class lectures or as a way to teach yourself what you might not have learned in the past. ... Read more

Book Description

This book and CD-ROM compile the most widely applicable methods for solving and approximating differential equations. The CD-ROM provides convenient access to these methods through electronic search capabilities, andtogether the book and CD-ROM contain numerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.

* For nearly every technique, the book and CD-ROM provide:
* The types of equations to which the method is applicable
* The idea behind the method
* The procedure for carrying out the method
* At least one simple example of the method
* Any cautions that should be exercised
* Notes for more advanced users
* References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs ... Read more

Reviews (2)

Zwillinger's Handbook of Differential Equations
This and its predecessor of the late 1980s are the best compendiums of differential equation solution and approximation methods that I have ever seen in terms of (a) comparison of different methods, (b) number of methods compared, (c) description of details of each method, (d) organization such as alphabetizing under each category and categorization of methods, (e) description of and comparison of where each method can be applied in the physical and other sciences, both deterministic and statistical/probabilistic ("stochastic"). This accomplishment cannot be overemphasized from the point of view of Creative Genius - in my opinion, comparing and contrasting and organizing and summarizing data and information are fundamental requirements for creative genius. The book may be intended as a reference book, but it should really be used also as a textbook provided that the teacher overviews the areas and gives some supplementary background and latest results. Both the student and reference user can easily be overwhelmed by the sheer number of methods, and I would recommend putting short descriptions of each (1-2 lines on front and 1-2 lines on back) on flash cards to keep them and their relationships fresh in your mind (shuffle the cards, learn them backwards and forwards, learn them alphabetically, in separate categories, then non-alphabetically and in mixed up categories, etc.). I would recommend that future editions list some of the unsolved equations and open research questions in the field.

Indispensable.
For anyone that finds differential equations beautiful; for the theoretical scientist in whatever field; this is nearly as indispensable as Abromowitz and Stegun (The Big Ugly Blue Book). ... Read more

Reviews (1)

Its a handbook for numerical solutions of ODE & DAE.
This book is excellent. The concepts about stiff, initial value problems, boundary value problems and differential-Algebraic equations (DAE) is treated with relative deep.

The numerical methods for many cases is covered.

The bad is that don't show the code. The code is in a web (NETLIB) and is writed in Fortran Language.

Is very expensive! ... Read more

Book Description

Joussef Jabri presents min-max methods through a comprehensive study of the different faces of the celebrated Mountain Pass Theorem (MPT) of Ambrosetti and Rabinowitz. Jabri clarifies the extensions and variants of the MPT in a complete and unified way and covers standard topics: the classical and dual MPT; second-order information from PS sequences; symmetry and topological index theory; perturbations from symmetry; convexity and more.He also covers the non-smooth MPT; the geometrically constrained MPT; numerical approaches to the MPT; and even more exotic variants. A bibliography and detailed index are also included. ... Read more

Book Description

This book provides a comprehensive treatment of symmetry methods and dimensional analysis. The authors discuss aspects of Lie groups of point transformations, contact symmetries, and higher order symmetries that are essential for solving differential equations. Emphasis is given to an algorithmic, computational approach to finding integrating factors and first integrals. Numerous examples including ordinary differential equations arising in applied mathematics are used for illustration and exercise sets are included throughout the text. This book is designed for advanced undergraduate or beginning graduate students of mathematics and physics, as well as researchers in mathematics, physics, and engineering. ... Read more

Book Description

This book aims to provide the student with some basic modeling skills, which will have application to a wide variety of problems. Models in three different areas are considered: growth and decay process; interacting populations and heating/cooling problems.The main mathematical technique used is that of solving differential equations and the range of applications and mathematical techniques presented provides a broad appreciation of the scope of this type of modeling. ... Read more

Book Description

Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics.

* Phase plane analysis for systems of two linear equations
* Use of equations of variation to approximate solutions
* Fundamental matrices and Floquet theory for periodic systems
* LaSalle invariance theorem
* Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory
* Appendix on the use of Mathematica for analyzing difference equaitons
* Exponential generating functions
* Many new examples and exercises ... Read more

Book Description

Method of Variation of Parameters for Dynamic Systems presents a systematic and unified theory of the development of the theory of the method of variation of parameters, its unification with Lyapunov's method and typical applications of these methods. No other attempt has been made to bring all the available literature into one volume. This book is a clear exposition of this important topic in control theory, which is not covered by any other text. Such an exposition finally enables the comparison and contrast of the theory and the applications, thus facilitating further development in this fascinating field. ... Read more

Book Description

A comprehensive review guide to help you refresh your study. This guide is particularly useful for midterms and final exams, condensing a semester's worth of information into one concise volume. ... Read more

Reviews (2)

Not For Differential Equations Students!!!!!!!!!
This is not a good book for people that are taking Differential Equations in college, but rather for people that are taking calculus and would like to get started with simple differential equations. I especially didn't like the fact that the book didn't even derive Euler's fomula for second order, homogenous differential equations, y=(e^(ax)(cosbx+sinbx)) when the characteristic roots are a+bi and a-bi. Nevertheless, this book provides a good START.

Very Good Mechanical 'How to'
This book provided me with almost what I wanted from such a title, that is a good bare 'how-to' review of ODE's (no PDE's here despite the rather general title). You'll find no 'theorem/proof/lemma' approach but rather 'heres an example-do 'em like this'-which does have its place for those seeking a 'quick fix' and can actually make concrete some ideas. I felt there were omissions that could have been included instead of the brief 'review of calculus' and 'a few applications'. These would include at least some attempt to deal with solving DE's by power series at ordinary singular points, some coverage of simple numerical (say Euler) solutions, and a mention of 'slope fields' in the 'introduction to DE's' section. For myself I also like the non-ornate presentation..it is free of the 'soap box/multi-windowed/cross referenced' pedagogical style that tends to distract some (me for one). A commendable feature is that this book could actually be 'read' (in the old fashioned contiguous way), and learned from by most high school/freshman level students. ... Read more

Book Description

Finite Element Methods For Maxwell's Equations is the first book to present the use of finite elements to analyze Maxwell's equations. This book is part of the Numerical Analysis and Scientific Computation Series. ... Read more

Book Description

In this appealing and well-written text, Richard Bronson gives readers a substructure for a firm understanding of the abstract concepts of linear algebra and its applications. The author starts with the concrete andcomputational (a 3 x 5 matrix describing a stores inventory) and leads the reader to a choice of major applications (Markov chains, least squares approximation, and solution of differential equations using Jordan normal form). The first three chapters address the basics: matrices, vector spaces, and linear transformations. The next three cover eigenvalues, Euclidean inner products, and Jordan canonical forms, offering possibilities that can be tailored to the instructors taste and to the length of the course. Bronsons approach to computation is modern and algorithmic, and his theory is clean and straightforward. Throughout, the views of the theory presented are broad and balanced. Key material is highlighted in the text and summarized at end of each chapter. The book also includes ample exercises with answers and hints. With its inclusion of all the needed pedagogical features, this text will be a pleasure for teachers and students alike.

* Gives a firm substructure for understanding linear algebra and its applications
* Introduces deductive reasoning and helps the reader develop a facility with mathematical proofs
* Begins with the concrete and computational (a 3 x 5 matrix describing a stores inventory) and leads the reader to a choice of major applications (Markov chains, least squares approximation, and solution of differential equations using Jordan normal form)
* Covers matrices, vector spaces, linear transformations, as well as applications to Jordan canonical forms, differential equations, and Markov chains
* Gives computational algorithms for finding eigenvalues and eigenvectors
* Provides a balanced approach to computation and theory
* Highlights key material in the text as well as in summaries at the end of each chapter
* Includes ample exercises with answers and hints, in addition to other learning features ... Read more

Reviews (2)

Well written, but too many typos and mistakes.
Overall this is very well written, an excellent introduction to the subject. It would definitely be a five-star book if it weren't for all the mistakes. A few typos are acceptable, but too many of the example problems and solutions had incorrect, confusing errors. I spent most of my reading time trying to sort these out!

Very good and easy introduction
As I started my studies at Uni and we got this horrible Algebra teacher I was looking for some good book to help me pass this course. This book met all my requirements. This book starts with a very easy example of a matrix and builds up from there with easy to follow steps. Even though the book is very easy to read and explains Algebra very comprehensively it still meets the universitiy-level. Everything stated is formally proved or left as an exercise. An excellent book for a guy that thought he'd never understand linear algebra. This book proved me wrong. It may lack some topics, but the ones in the book surely can't be found elsewehre explained as good as in there. ... Read more

Book Description

This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. ... Read more

Reviews (6)

An Excellent Book
When I became a quant, I needed to learn stochastic calculus and stochastic differential equations. Luckily, I found this book, which covers a lot of difficult concepts in a rigorous but accessible way. Oksendal is an excellent writer: his proofs are very clear (and usually not too terse), he provides very illustrative examples, and he does a great job of anticipating where the reader might get stuck. In addition, the problems at the end of the chapters do a good job of reinforcing central theorems and ideas. After reading this book, you'll be able to read most of the academic financial literature and all finance textbooks.

I've read lots of math books, and this is undoubtedly the best one I've ever seen. The only necessary backround is a solid understanding of measure theory.

Good reference - not so good text-book
This book is excellent if you already know why you want to know the material in it. Then it is concise, to the point, and very well-written. I turn back to it over and over again; my copy is very worn by now.

When I first started reading it, I was not too pleased with it. As a text-book it suffers from not motivating the theory, and not connecting it with parallel approaches. The subtitle mentions applications. Now, what one person considers applications is what the next person considers abstractions. My point of view is truly applied - I want to use SDE's to model real-world phenomena (actually, not financial ones) and are less interested in SDE's per se. So I would have liked more connections with physics (for instance advection-diffusion transport phenomena) and I would have liked the material to be more solidly anchored in general stochastic processes. Nevertheless, I appreciate that the book wouldn't have been as concise, then.

Simple, but rigorous book
This a perfectly written book on stochastic calculus, especially needed for junior (but rising!) financial quants. All themes are carried out with a profound pedagogical talent. For a practitioner, the book loses nothing to Karatsas and Shreve, but is a much shorter, simpler and joyable reading. Yet, it is a systematic text book that covers most classical results with (important!) accessible proofs. For example, the Kolmogorov equations (forward and backward) are derived, not just stated as in most other texts, Girsanov's theorem is relatively well covered (although the author has not demonstrated its computational side well enough, but this is a common disease). Ideas are illustrated by practical problems (including those from quantitative finance). What I also liked, Oksendal's SDE theory is much closer to "differential equations", than what is often presented by probabilists. A must for every practitioner who works with stochatic processes.

Practical review of Oksedal's SDE's (wrt finance)
As a so-called practicising 'quant' in a top Wall Street Investment bank, I came upon this book from colleagues who raved about the exposition of the material found in this book.Indeed even though I have an engineering and advanced mathematical background, I find the material to be useful in helping to understand the more research oriented finance journals. From a practitioner's view point the most fundamental aspect of the book is the statement where it states the solutions of SDE's can be thought of as inherent Browian motions for it is the latter which enables one to price the financial instruments one commonly hears of in the press.I would recomend first understanding the physical and mathematical aspects of Browninan motion before tackling the abstract field of stochastic calculus so that meaningful interpretations can be drawn.Nevertheless the book gives excellent penetrating coverage of what SDE's are.For budding so-called 'rocket-scientists' who want to make mega-bucks on the markets, my advice would be to first master partial differential equations (because this is the only way to pragmatically price things like exotic derivatives) then for their own enlightenment they can read this book if only just to keep up with the jones's.

An excellent introductory book to SDEs
This is a book I recommend as a TA in a mathematical finance Masters program. It gives a mathematically rigorous presentation of Stocastic Differential Equations without getting bogged down in too much detail, as do many books from a probability/stochastic processes background. It also illustrates the beautiful connection between SDEs and the heat equation. I recommend this book to anyone trying to read Karakas and Shreve for the first time. ... Read more

Book Description

This new book updates the exceptionally popular Numerical Analysis of Ordinary Differential Equations.
This book is...an indispensible reference for any researcher."-American Mathematical Society on the First Edition.

Features:
* New exercises included in each chapter.
* Author is widely regarded as the world expert on Runge-Kutta methods
* Didactic aspects of the book have been enhanced by interspersing the text with exercises.
* Updated Bibliography. ... Read more

Book Description

This book is a revised and updated version, including a substantial portion of new material, of the authors' widely acclaimed earlier text "Perturbation Methods in Applied Mathematics". A new chapter dealing with regular expansions has been added, the discussion of layer-type singular perturbations has been revised, and the coverage of multiple scale and averaging methods has been significantly expanded to reflect recent advances and viewpoints. The result is a comprehensive account of the various perturbation techniques currently used in the sciences and engineering, and is suitable for a graduate text as well as a reference work on the subject. ... Read more

Reviews (1)

A Classic Text in Perturbation Methods
A classic in singular perturbation techiques, this book should be on the shelf of every applied mathematician. It's focus is mainly upon multiscale methods, although a brief review of regular perturbation techniques is present. The author's carefully develop the theory of multiscale methods and provide numerous applications to real world engineering and scientific problems. While I would not recommend this as a first book on perturbation theory due to it's complexity and at times dense notation, anyone who is serious about singular perturbations should buy this book. ... Read more

Book Description

Scientists and engineers attempting to solve complex problems require efficient, effective ways of applying numerical methods to ODEs and PDEs. They need a resource that enables fast access to library routines in their choice of a programming language.Ordinary and Partial Differential Equation Routines in C, C++, Fortran, Java, Maple, and MATLAB provides a set of ODE/PDE integration routines in the six most widelyused languages in science and engineering, enabling scientists and engineers to apply ODE/PDE analysis toward solving complex problems.This text concisely reviews integration algorithms, then analyzesthewidelyused Runge Kutta method ( since hyphenation is used here, I added it below; hyphenation could also be dropped since itis not used in the book). It first presents a complete code before discussing its components in detail, focusing on integration concepts such as error monitoring and control. The format allows you to understand the basics of ODE/PDE integration, then calculate sample numerical solutions within your targeted programming language. The applications discussed can be used as templates for the development of a spectrum of new applications and associated codes. ... Read more

Book Description

Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity. ... Read more