Book Description

This book explores the standard problem-solving techniques of multivariable mathematics — integrating vector algebra ideas with multivariable calculus and differential equations. Unique coverage including, the introduction of vector geometry and matrix algrebra, the early introduction of the gradient vector as the key to differentiability, optional numerical methods. For any reader interested in learning more about this discipline.

Reviews (3)

Sometimes it takes a second read, or third, or fourth....
I liked this book because it is written at a slightly more sophisticatedlevel than most lower division math books.Admittedly, it is difficult tounderstand some of the proofs and examples on the first read.It justtakes some time, after a second or third read, before the text begins tomake sense.Then you'll realize the examples are presented quite well andyou have everything you need to solve the problem sets.And you knowyou've learned the material well if you understand the text and you can dothe problems, which are oriented more to make you think than compute.

A coherent view of multivariable mathematics
For those with sufficient preparation (say, a good BC Calculus course andan enjoyment of mathematics), this text offers a very fine presentation ofmultivariable calculus. Certainly, some of the material is challenging andsome of the exercises require insight, but after finishing this book, orsubstantial portions of it, you will have a coherent view of multivariablecalculus, as well as some appreciation of significant, but elementary,applications of linear algebra. I particularly recommend this text to thosewho have learned multivariable calculus in one of the "fat" threesemester calculus texts, and feel that, although they could solve all theproblems, they don't really have any sense of what the subject is allabout.This text has a distinguished history: it is the latest incarnation of a vector calculus text (Calculus of Vector Functions) first published in 1962 by Crowell and Williamson. Spivak described that text (and I hope Dover someday reissues the third edition) as "one of the first, and still one of the nicest, treatments of advanced calculus using linear algebra."

Naughty Book
This book was used for a two-course introductory math series at Stanford in 1996-7 and 1997-8.The book drew so many complaints that it was abandoned after two years.Personally, I found it difficult to understandmany of the formal proofs and explanations provided.Many shortcuts weretaken in solving the example problems which made them difficult to follow. The answers to problems in the back of the book were frequently incorrect.This is a poorly written book for all students except those extremelyinsightful in mathematics. ... Read more

Reviews (2)

Nice begginers text
This text is a great begginners guide to chaotic systems, it provides very clear explanations and proofs as well as some examples to help you along.

Excellent book. Explains concepts clearly.
I went from knowing absolutlely nothing about dynamical systems to being able to look at a point on the Mandelbrot Set and visualize what the corresponding Julia Set looks like. Ever wonder why weather cannot be predicted accurately?? Read this book... ... Read more

Book Description

This graduate level textbook offers graduate students a rapid introduction to the language of the subject of ordinary differential equations followed by a careful treatment of the central topics of the qualitative theory. In addition, special attention is given to the origins and applications of differential equations in physical science and engineering. Of special interest to mathematics students is a multifaceted approach to existence theory, for solutions and for invariant manifolds, including an integrated new treatment of smoothness of solutions and invariant manifolds based on the fiber contraction principle. Also, supplementary material throughout the text provides connections between the theory of ordinary differential equations and other advanced mathematical topics; for example, differential geometry, Lie group theory, analysis in infinite dimensional spaces, and even abstract algebra. Applications-oriented students are provided with case studies of important physical models, expecially, coupled oscillators. In particular, the pendulum-rotor model is treated in detail. Of special interest is a treatment of the stability of the inverted pendulum, a discussion of the Fermi-Ulam-Pasta model, and an exposition of the theory of capture into resonance.

Through its extensive use of examples, exercises and real-world applications, this book provides science and engineering graduates with a thorough grounding to the theory and application of ordinary differential equations. ... Read more

Amazon.com

Very useful CD-ROM for all numerically inclined scientists and engineers. Produces TeX source code for selected formulas. Multiplatform-ROM for Mac, Windows, and UNIX. ... Read more

Reviews (6)

CD-ROM version may not work for you.
The paper version is a real touchstone for the practice of all manner of applied mathematics.The CD-ROM version belongs in the discount bin.Here is why:

1)The CD-ROM is edition 5; but edition 6 has been out for 4 years.

2) The DynaText software, which is needed to read/browse/search the book, is showing signs of age.It works fine on the computers of a decade ago but not necessarily on the machines of today.See the review of J.F.Groote.

The product is advertised as working on Macs but will not work on most Macs.Specifically, it does not seem to work on either G4 or G5 hardware with OS X, even under the so-called "Classic" mode.I believe that the problem is that the browser is shipped as an executable that requires a specific architecture.

It is usable under Windows, but you might need to use one of the backwards-compatibility options to run the installer.

It will not apparently run under any form of Linux, the most recent (and rapidly becoming the most popular) transmogrification of Unix.Again, DynaText is put on the CD-ROM as a binary executable; if you are not using SunOS 4 or 5, Solaris or SGI IRIX 5.2 then you can not use this product.

This software is unusable on mac's and unix systems.
I bought this software hoping that it would help me to find required mathematical formulas faster. At home on my powermac (OSX.1, OS9.2) I only see messed up windows. Furthermore, the formulas are unreadable, using an archaic font. Trying to save the day, I went to my linux machine at work reading "Your operating system, Linux 2.2.19-7.0.1, is not supported by this software. It appears that the software is only suitable for some SUN and SGI machines. It only appears to run properly on a windows machine. From an editor, who I remember, is one of the few persons finding errors in Knuth's TeX system, I expected much better.

A fun book
I bought Gradshteyn & Ryzhik because I had to write an answer to some homework problem in some physics class that I took. The problem had contorted itself into a perverse elliptic integral and its recovery was beyond my means, so I went to the bookstore, looked for something fat and Soviet, and found this gem. I forked over the cash for it, figuring that it was a long-term investment.

I took it home and dutifully plagiarized some of its lines to satisfy my physics professor. For the next few months, that was the mode in which I used this book: read physics problem, translate into elliptic or hypergeometric beast, look up answer in G&R, cover up my tracks, get 9 or 10 points on the problem. Occasionally, I would own up to having looked something up.

The book served its purpose well. Subsequently, I studied some integrals of the spinning top that were more or less right out of Nikiforov's book on special functions (another excellent source for those of you that would like to "earn" a PhD), and G&R stood well by its side. Indeed, I discovered how much fun it was to look up an integral whose complicated solution had been derived elsewhere, and then to look for patterns by analyzing the immediate neighbors of the given integral on the preceding and subsequent lines in G&R.

After I was done with answering questions from physics professors, the book sat on the shelf taking up more room than several of its neighbors put together. Nonetheless, its binding was good, its typesetting clear, and its terse and copious stream of forbidding integral forms was pleasing to the eye.

Some time passed, and one day I asked myself just what would motivate anybody to write such a large collection, so I started rummaging through its pages looking for a pattern. I realized that its organization was excellent (which would explain why I was able to find the answers for my homework), and I also found some sections that were just plain fun. The very beginning lists some sums of infinite series that can be derived during lunch or while waiting for a friend at a cafe (e.g. sum of k^3 = [1/2(n)(n+1)]^2 ). Then one can read about numbers and functions named after Euler, Jacobi, Bernoulli, Catalan... each line, more or less, is cross-referenced, so after you have given up trying to derive that darned product representation of the gamma function, you can go to the book in the library and see how Whittaker did it.

After about 15 years of owning this book, I am nowhere near done with it. If you like math, and you want insurance against being bored, this book just might do the trick. As a bonus, it puts cute matrix stuff in the back (e.g. the "circulant") which one can read when desiring a break from the integrals. I know the book seems expensive, but think of if as spending about two bucks a year on it.

I see that one can now obtain a CDRom version of G&R. An intriguing option, specially because it outputs in TeX; but really, how can anyone resist the large, stubby charm of its paper version?

G&R can help you to deal with members of the opposite sex. I once used it to scare away a girlfriend that was becoming much too annoying, by pretending to be thickly engrossed in the process of memorizing every single integral in the "special functions" chapters. As for my mother, she was particularly proud of me when I showed her that I could actually understand "randomly selected" pages from this book (I don't suppose that I am giving anything away by remarking that books open naturally on sections that have been previously examined).

For those of you that are concerned about home security, G&R is also a weapon. Some people surround themselves with baseball bats or, if they are particularly reckless, a handgun or two... I prefer to keep a fully-loaded G&R by my pillow, which I can hurl at any prowler at a moment's notice. Its shape is surprisingly well adjusted to the hand for the purposes of hurling, and if the covers are bound by a rubber band, the book maintains its shape quite stably as it sails across the room. Sell your Smith & Wesson and buy yourself a Gradshteyn & Ryzhik. You won't regret it.

Daunting at first but worth it.
Before it was much use, I had to read the section as to how the book is organized. As the other reviewers state the integrals are comprehensive and as far as I have used correct. The integrals are very useful, but this book includes many other features that I have found helpful as a graduate student.The sections on Hermite and Legendre polynomials are especially helpful for students of Electricity and Magnetism, Quantum Mechanics, and Mathematical physics (you won't have to hunt in several books to find what you need).The included identities for hyperbolic and trig functions are very helpful simplifying homework answers, mostly because of their comprehensive nature.This book is great because it seems to have everything and most people will not need to buy another table.The binding is good also, so it should last many years with normal care.This is a very good investment.

Gigantic, but well organized and highly accurate
Gradshteyn and Ryzhik is to the CRC Mathematical Tables as the unabridged Oxford English Dictionary is to Webster's Collegiate.Besides being big,it's easy to find things in, because of the way the integrals are organizedinto classes.Like any other integral tables, you'll probably have to makea change of variables or two to get your problem into a standard form, butsince the classes are well covered, you have a big target to shoot for, soyour chances of finding your integral tabulated are excellent.

Anunscientific sampling indicates that this book has remarkably few errors. It really helped me through grad school. ... Read more

Book Description

This book covers the impact of noise on models that are widely used in science and engineering applications. It applies perturbed methods, which assume noise changes on a faster time or space scale than the system being studied. The book is written in two parts. The first part presents a careful development of mathematical methods needed to study random perturbations of dynamical systems. The second part presents non-random problems in a variety of important applications. Such problems are reformulated to account for both external and system random noise. ... Read more

Reviews (7)

Flat spheres and more
Highly stimulating and extremely hard to read, written for mathematicians in physics. However, the chapter on Riemannian Geometry can be worked through, up to a point, without any knowledge of exterior differential forms, and is notable if for only one fact alone: a simple calculation is provided that explains explicitly that spheres in four and eight dimensions (3-spheres and 7-spheres) are flat with torsion! I don't know another reference that a physicist without special background in math can consult to understand this highly nonintuitive fact.

Just a "better than nothing" book
It's not the best way to learn geometry / topology for physics. It's better than nothing, though, if you are familiar with the topics already. There are many "holes" in Nakahara's book, which you would spend much more time and hard working in a "big" library. than you should to fill in. It's not worth that money and struggle. It's the last one you should consider about owning.

If you are a physics graduate who needs a nice guide to "understand" the aspects and skills of geo / top, I would recommend the following: (1) Milnor's Topology from the Differentiable Viewpoint, and (2) Kreysig's Differential Geometry. The first one was old, and so it does not assume much knowledge about the topic. The latter is a kind-of-Bible for the topic, and all solutions are provided for the problems. These two books will help you a lot if you care about the meaning, not only for those classroom exams or just showing off that you know something about it. Frankel is the next to put on your bookshelf as a detailed and rigorous development for your preparation to be a theoretical physicist.

If you have only a rough idea about topology, Hocking and Steen are the best choices, and they are Dover!!

Anyway, if I could find a cheap used Nakahara, I would get it as a reference.

Best in its genre
I suppose I should preface this by saying that I read this book *after* reading similar books, so my ability to understand this book is probably better than others, but that said, I think that my comparative evaluation is free from this bias...

There seem to be a few books on the market that are very similar to this one: Nash & Sen, Frankel, etc. This one is at the top of its class, in my opinion, for a couple reasons:

(1) It's written like a math text that covers physics-related material, not a book about mathematics for physicists. I prefer this; you may not. As a consequence, this book is more rigorous than its alternatives, it relies less on physical examples, and it cuts out a lot of lengthy explanation that you may not need. Of course, there are drawbacks to all of these "features" -- you need to decide what you need and what's best for you.

(2) It's most comprehensive, with Frankel coming in second, and Nash & Sen least comprehensive (though they have quite a bit on Fibre bundles and related topics). Nakahara has a chapter on complex manifolds, which is absent from the other two. Nakahara also concludes with a nice intro to string theory, which is absent from the other two as well (though nothing you couldn't find in Polchinski or the like). Actually -- I modify this slightly. Frankel covers less subjects than Nakahara, but with more depth (though also more wordiness -- I quit Frankel about 2/3 through because it wasn't succinct enough and I got tired of it).

Depending on your tastes, I would recommend this book before the other two.

It presupposes that you have an understanding of algebra (groups, rings, fields, etc.) but it has an introduction to the necessary components of topology within. Frankel has presupposes both algebra and topology; Nash & Sen presupposes only algebra.

Excellent book
A very nice blending of rigor and physical motivation with well chosen topics. Plenty of examples to illustrate important points. Especially noteworthy is its description of actions of lie algebras on manifolds : the best I have read so far.

Most of the topics are intepreted in terms of their topological/geomtrical structure (and the interplay between those two), but that's what the title of the book says. So you will learn things again in new ways, and gain a powerful new set of tools. If nothing else, it gives you a nice warm fuzzy feeling when you read other field/string theory books that glosses over the mathematics.

One minor rant : the notation of the book can be better. I personally uses indices to keep track of the type of objects (eg. greek index=components of tensors, no index=a geometrical object etc..), but Nakahara drops indices here and there "for simplicity". But that's my personal rant.

Good book. Buy it.

A must for any theoretical physicist
With an excellent balance between mathematical rigor and pedagogical simplicity, Nakahara remarkably captures in a single volume much of the mathematics a physicist will ever need. (If he wrote a few chapters on group theory, 'much' might be replaced with 'all'). Containing as much as it does, it is not something to breeze through. Depending on your mathematical background, you may only want to read a few chapters (and if the Homology chapter is tripping you up, just keep moving). But invest the time with it, and you will be rewarded with a solid grasp of the mathematical pictures underlying most modern physics. And once you read it and see physics from this perspective, you'll be amazed you had ever thought you understood the physics it describes. It should be said, though, that some of the latter chapters, in particular 12, are horribly sloppy. There are dozens upon dozens of errors, many at a deep conceptual level. Nonetheless, it is a monumental text, and I recommend it heartily. ... Read more

Book Description

Following in the footsteps of the authors' bestselling Handbook of Integral Equations and Handbook of Exact Solutions for Ordinary Differential Equations, this handbook presents brief formulations and exact solutions for more than 2,200 equations and problems in science and engineering."Parabolic, hyperbolic, and elliptic equations with constant and variable coefficients"New exact solutions to linear equations and boundary value problems"Equations and problems of general form that depend on arbitrary functions"Formulas for constructing solutions to nonhomogeneous boundary value problems"Second- and higher-order equations and boundary value problemsAn introductory section outlines the basic definitions, equations, problems, and methods of mathematical physics. It also provides useful formulas for expressing solutions to boundary value problems of general form in terms of the Green's function. Two supplements at the end of the book furnish more tools and information: Supplement A lists the properties of common special functions, including the gamma, Bessel, degenerate hypergeometric, and Mathieu functions, and Supplement B describes the methods of generalized and functional separation of variables for nonlinear partial differential equations. ... Read more

Book Description

A relatively new field, domain composition methods draw on parallel computing techniques and are proving a powerful approach to the numerical solution of partial differential equations. This book illustrates the basic mathematical concepts and looks at a large variety of boundary value problems. ... Read more

Book Description

This book develops the statistical approach to inverse problems with an emphasis on modeling and computations.  The framework is the Bayesian paradigm, where all variables are modeled as random variables, the randomness reflecting the degree of belief of their values, and the solution of the inverse problem is expressed in terms of probability densities.  The book discusses in detail the construction of prior models, the measurement noise modeling and Bayesian estimation.  Markov Chain Monte Carlo-methods as well as optimization methods are examples that are often non-trivial but easy to follow.  Besides the simple examples, the book contains problems as discretization errors, and statistical model reduction.  Furthermore, the techniques are then applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems.  The book is intended for researchers and advanced students in applied mathematics, computational physics, and engineering.  The first part of the book can be used as a text book on advanced inverse problems courses. ... Read more

Book Description

Differential equations are vital to science, engineering and mathematics, and this book enables the reader to develop the required skills needed to understand them thoroughly. The authors focus on constructing solutions analytically and interpreting their meaning and use MATLAB extensively to illustrate the material along with many examples based on interesting and unusual real world problems.A large selection of exercises is also provided. ... Read more

Book Description

In the past three decades, bifurcation theory has matured into a well-established and vibrant branch of mathematics. This book gives a unified presentation in an abstract setting of the main theorems in bifurcation theory, as well as more recent and lesser known results. It covers both the local and global theory of one-parameter bifurcations for operators acting in infinite-dimensional Banach spaces, and shows how to apply the theory to problems involving partial differential equations. In addition to existence, qualitative properties such as stability and nodal structure of bifurcating solutions are treated in depth. This volume will serve as an important reference for mathematicians, physicists, and theoretically-inclined engineers working in bifurcation theory and its applications to partial differential equations. ... Read more

Book Description

Covers the fundamental properties of partial differential equations (PDEs) and proven techniques useful in analyzing them. Uses a broad approach to illustrate the rich diversity of phenomena such as vibrations of solids, fluid flow, molecular structure, photon and electron interactions, radiation of electromagnetic waves encompassed by this subject as well as the role PDEs play in modern mathematics, especially geometry and analysis. ... Read more

Reviews (13)

A good book, but a bit tough for newbies to the subject
Despite its title, this book is not really written at an introductory level -- at least not at an introductory *undergraduate* level. For example, more than a passing familiarity with rigorous "epsilon-delta" type proofs is useful when reading Strauss' book, and being comfortable with topics like the convergence of sequences of functions couldn't hurt, either. In short, a background in real analysis, at least in one variable, is probably good to have before attempting to work through this text -- not so much because the material is heavily dependent on real analysis, but because an analysis course primes you for the kind of thinking that you need to do a lot of to sift through this often-dense material at a reasonable pace.

I don't believe this book deserves to be criticised so harshly. It does tend to jump from around a bit from one topic to the next, but it covers an impressive amount of ground concisely and with adequate clarity. If you're a total newbie to PDEs, try Stanley Farlow's Dover book instead, then come back to Strauss to get to the next level. The Schaum's Outline on Fourier Analysis is also good if you want lots of practice solving actual engineering-type problems.

If you have the appropriate math background and motivation to study PDEs at an intermediate level, then Strauss' book is probably one of the better ones.

A Poor Text
My biggest problem with this book is that the author states what is blindingly obvious but fails to examine some of the more subtle areas. It seems that by stating that a double integral is for two dimension and a triple for three one is just filling up space. Most of the remarks are of this kind. The exercises, furthermore, are not inspired. They are mostly just complete the proof, or redo the proof for a different dimension type of problems. While such questions are required, there are no questions which explore the finer details of the subject.

Moreover, there seems to be no feeling of continuity. It's a very staggered flow and does not make for enjoyable reading. The lack of discussion, rigorous proofs, precise definitions for such a rich subject makes this text almost worthless. Perhaps covering less but in greater detail would serve better as an introduction to PDEs.

The best I've encountered so far
I'm writing my first review just to improve this books ratings, since in my opinion, this book doesn't deserves anything below 4 stars.

This book contains the most comprehensive exposition of PDEs at undergraduate level I've seen so far, all the problems that I've came across are discussed here, the author does all the important intermediate steps and presents all the subjects very easily. Moreover, all the subtleties (namely, why we dropped that solution or why the eigenvalues are like that.) are discussed. The author also offers depth understanding of the physical model that every PDE is modelling.

All the necesary mathematical background is an ODE and Multivariable Calculus courses.

Don't waste your money on this crap!!!
This book isn't worth the paper it is printed on! I would give it ZERO stars if Amazon gave me the option.

This is the required textbook for my class in PDEs, and I cannot imagine why any instructor or math department would choose this book, unless it was the author himself or a stockholder in the publishing company. Is worthless as an undergraduate textbook on partial differential equations, even for a mathematics major.

It is incredibly lacking in detail and description for such a complex subject. There is a dearth of examples and the explanations insufficient for the student. There are numerous times in the book where the author says: "Some of these problems are worked out in the exercises" or "it can easily be shown" or "This case is left as an exercise." There is one example where the author even says: "That was stupid: We could have guessed it! (see p. 58). Simple for who? Maybe for a mathematics professor or graduate student, but not for a person learning about the material for the first time!! One reviewer, who liked this text and who thought other reviews were unfair, remarked: "At some point in math, you have to move beyond the spoon fed approach of a typical lower division calculus textbook and fill in the gaps and figure out the examples for yourself." Perhaps you can do this if you are learning PDEs on your leisure time, but if you are at a university on the quarter system and are taking several other demanding classes at the same time, you just don't have the time to "fill in the gaps" yourself! Additionally, filling in the gaps requires a certain level of insight and intuition that not all of us have. After all, not everyone who uses partial differential equations is a mathematician. Some of us are engineers and scientists in other fields, who need practical and thorough approach to learning PDEs. If this describes you, then DO NOT buy this book!

I am tempted to rip out the pages of this book and use them for toilet paper! Unfortunately, this textbook is used as the required text for a 3 quarter PDE series at UC-Davis, so I am stuck with it for another 2 quarters!

Very poor introduction!
This book is an unsuccessful attempt at incorporationg a vast amount of PDE-related topics into small amount of space. Its biggest drawback is the lack of motivation for physical problems as elementary as the diffusion equation or involved as the Klein-Gordon equation. Ideas behind the theory of PDE is missing almost completely, with many sections simply stating related problems without explaining where they come from or how to solve them. There is no concrete methodology in the presentation of the topic, and even as a reference this book is useless, because material is scattered throught the book - i.e. material is not organized properly. I would rate this book absolete and completely useless, since it is not suitable for self-study, nor is it a good reference. Furthermore, the problems in the book are merely a computational barage - they develop no conceptual understanding. To sum up: if you are not familiar with PDEs, this book will not teach you anything; if you are familiar a little with PDEs, this book will not deepen your knowledge. Forget about it! ... Read more

Book Description

Inverse Modeling of the Ocean and Atmosphere is a graduate-level textbook for students of oceanography and meteorology, and anyone interested in combining computer models and observations of the hydrosphere or solid earth. A step-by-step development of maximally-efficient inversion algorithms, using ideal models, is complemented by computer codes and comprehensive details for realistic models. Variational tools and statistical concepts are concisely introduced, applications to contemporary research models are examined in detail and further advanced research topics are discussed. ... Read more

Book Description

This text offers a broad, self-contained, introduction to the basic concepts of symmetry analysis and is intended primarily for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. The software requires Mathematica 2.2 or higher.MathReader 4.0 is included to permit the user without access to Mathematica to read the sample notebooks and follow the procedure used to find symmetries. ... Read more

Reviews (1)

Readable and Useful
This book is useful as both a primer on the subject and a research reference. It succeeds on both counts where a book by G. Baumann with a similar title fails.

The author does not assume any level of mahematical knowledge or sophistication beyond standard mathematical course work required of engineering students. It may be of importance to know that Professor Cantwell uses this book to teach a course at an engineerng department.

What makes this book especially valuable is the Mathematica package included on the CD-ROM. The symmetry calculations are often very tedious and complex. Thereore, there is a strong need to automate at least some of the work. A beginner can simply use some of the sample notebooks provided by the author and understand the method. A researcher can start with any of those notebooks, replace the author's equations with the ones of interest, and follow through the steps of the procedure.

If you are going to buy only one book on this subject, this has to be it! ... Read more

Book Description

Early training in the elementary techniques of partial differential equations is invaluable to students in engineering and the sciences as well as mathematics. However, to be effective, an undergraduate introduction must be carefully designed to be challenging, yet still reasonable in its demands. Judging from the first edition's popularity, instructors and students agree that despite the subject's complexity, it can be made fairly easy to understand. Revised and updated to reflect the latest version of Mathematica, Partial Differential Equations and Boundary Value Problems with Mathematica, Second Edition meets the needs of mathematics, science, and engineering students even better. While retaining systematic coverage of theory and applications, the authors have made extensive changes that improve the text's accessibility, thoroughness, and practicality.New in this edition:"Upgraded and expanded Mathematica sections that include more exercises"An entire chapter on boundary value problems"More on inverse operators, Legendre functions, and Bessel functions"Simplified treatment of Green's functions that make it more accessible to undergraduates "A section on the numerical computation of Green's functions "Mathemcatica codes for solving most of the problems discussed"Boundary value problems from continuum mechanics, particularlyon boundary layers andfluctuating flows"Wave propagation and dispersionWith its emphasis firmly on solution methods, this book is ideal for any mathematics curricula. It succeeds not only in preparing readers to meet the challenge of PDEs, but also in imparting the inherent beauty and applicability of the subject. ... Read more

Reviews (1)

A Classic ODE Text
This classic text on ordinary differential equations has withstood the test of time and after 30 years is still considered to be one of the finest books in its field.

After reading Hartman's book the mathematician is well equiped to contribute to research in the area of differential equations. ... Read more

Book Description

This is a book about modelling, analysis and control of linear time- invariant systems. The book uses what is called the behavioral approach towards mathematical modelling. Thus a system is viewed as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. In the first part of the book the structure of the set of trajectories that such dynamical systems generate is analyzed. Conditions are obtained for two systems of differential equations to be equivalent in the sense that they define the same behavior. It is further shown that the trajectories of such linear differential systems can be partitioned in free inputs and bound outputs. In addition the memory structure of the system is analyzed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. An essential feature of using the behavioral approach is that it allows these and similar concepts to be introduced in a representation-free manner. In the third part control problems are considered, more specifically stabilization and pole placement questions. This text is suitable for advanced undergraduate or beginning graduate students in mathematics and engineering. It contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits. ... Read more

Reviews (1)

Systems theory done right!
This is an excellent book on mathematical control theory. As opposed to the classical state-space approach, the behavioural theory gives a more fundamental and natural way of looking at physical systems. The book deals with the notions of controllability, observability, stability and feedback in a beautiful mathematical framework. A more appropriate title would be "Systems theory done right"! ... Read more

Book Description

In this book the author presents the theory and techniques underlying perturbation methods in a manner that will make the book widely appealing to readers in a broad range of disciplines.Methods of algebraic equations, asymptotic expansions, integrals, PDEs, strained coordinates, and multiple scales are illustrated by copious use of examples drawn from many areas of mathematics and physics. The philosophy adopted is that there is no single or best method for such problems, but that one may exploit the small parameter given some experience and understanding of similar perturbation problems. The author does not look to perturbation methods to give quantitative answers but rather uses them to give a physical understanding of the subtle balances in a complex problem. ... Read more

Reviews (1)

Great Intro to Perturbation Methods
This is a wonderful first introduction to perturbation methods. Extremley readable, my only criticism of this text is its brevity. In some places, it lacks detail and doesn't go very deeply into several areas. However, it is the type of book that one can easily pick up, read and learn something usefull. The author's do lot's of examples and once this text is mastered, the student is certaintly ready to read Kevorkian and Cole's classic text on the subject. ... Read more

Book Description

This book is intended for students who wish to get an introduction to the theory of partial differential equations. The author focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. These are maximum principle methods (particularly important for numerical analysis schemes), parabolic equations, variational methods, and continuity methods. This book also develops the main methods for obtaining estimates for solutions of elliptic equations: Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. Connections between elliptic, parabolic, and hyperbolic equations are explored, as well as the connection with Brownian motion and semigroups. This book can be utilized for a one-year course on partial differential equations. Jürgen Jost is Director of the Max Planck Institute for Mathematics in the Sciences and Professor of Mathematics at the University of Leipzig. He is the author of a number of Springer books, including Postmodern Analysis (1998), Compact Riemann Surfaces (1997) and Riemannian Geometry and Geometric Analysis (1995). The present book is an expanded translation of the original German version, Partielle Differentialgleichungen (1998). ... Read more

Book Description

This book gives a clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. These methods allow one to analyze physics and engineering problems that may not be solvable in closed form and for which brute-force numerical methods may not converge to useful solutions. The presentation is aimed at teaching the insights that are most useful in approaching new problems; it avoids special methods and tricks that work only for particular problems, such as the traditional transcendental functions.

Intended for graduate students and advanced undergraduates, the book assumes only a limited familiarity with differential equations and complex variables.

The presentation begins with a review of differential and difference equations; develops local asymptotic methods for differential and difference equations; explains perturbation and summation theory; and concludes with a an exposition of global asymptotic methods, including boundary-layer theory, WKB theory, and multiple-scale analysis. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach the reader how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions; over 600 problems, of varying levels of difficulty; and an appendix summarizing the properties of special functions. ... Read more

Reviews (8)

Extremely useful
Great for anyone taking Partial differential equations, mathematical physics, and the related courses. Carl Bender is a master of the field as well as a great book writer, as well as Orszag. The only complaint is the type setting--a bit too small. But not a big problem

Excellent
This is an essential textbook for all applied mathematicians, physicists and research oriented engineers. It is very well written, and explains an enormous lot. It explains it all very well too. I've used chapter 3 and 6 in class, and they were full of insights and information that you cannot find in any other textbook.

Very useful
Very useful, in contrast with the cookbooks on 'mathematical physics' otherwise available. Systematic, with good examples and workable but challenging homework problems (I used this book for years while teaching advanced 'math methods in physics')Where else do you learn about Fuch's theorem? Good, systematic approach to asmptotic expansions, especially evaluation of integrals. Provided examples of deterministic chaotic systems before that subject was in vogue. Best description (as motion in phase space) of torque-free rigid body in free fall. Also good on boundary layer theory. Excellent text!

Best math text available!
I have the fortune of having Professor Bender teach the content of this book to me. His dynamic lecturing style, sense of humor, and astounding cleverness are all visible through the text of this book.

If you can't get to Washington University to take a class with him, at least buy the book. His writing style and frequent examples make the most elusive and suble concepts quite clear. I can't wait for his and Orzag's second book to be released!

The Best Mathematical Lore Book Of All Time
I learned more mathematics from Bender & Orszag than from any other math book I own. I'm an applied physicist, and as any physicist knows, a sleazy approximation that provides good physical insight into what's going on in some system is far more useful than an unintelligible exact result.

This book covers approximate methods for solving differential and difference equations, asymptotic methods for integrals, and asymptotic and extrapolation methods for sums. There are a great many beautiful plots, and lots of discussion of the actual lore of doing--alternative ways of attacking the same problem, things to watch out for, what sorts of problems a given method is best at.

I think the most valuable parts of this book are the examples and problems, both of which are the best anywhere.

It's really great to see this old friend (first published in 1978) back in print. If you have ugly differential equations or integrals to solve, buy it! ... Read more