Product Description
This traditional text is intended for mainstream one- or two-semester differential equations courses taken by undergraduates majoring in engineering, mathematics, and the sciences. Written by two of the world's leading authorities on differential equations, Simmons/Krantz provides a cogent and accessible introduction to ordinary differential equations written in classical style. Its rich variety of modern applications in engineering, physics, and the applied sciences illuminate the concepts and techniques that students will use through practice to solve real-life problems in their careers. This text is part of the "Walter Rudin Student Series" in Advanced Mathematics. ... Read more

Customer Reviews (8)

A good book, flawed by plagiarism
This is a good book.Simmons has an eye for what would motivate each step and shows enough explicitly to keep the text flowing nicely.There are lots of fairly easy problems which extend the material in the book.He points the students to other sources before getting into heavy complexity.The historical notes are particularly enjoyable.Simmons has an aversion to using complex analysis, or even just complex numbers.This means that he has to resort to trignonometric identities for many manipulations which would have been done more compactly using Eulers formula.

I would have given this book 4 or 5 stars except for one glaring fact:Large sections are copied without attribution from other authors.When I went to my bookshelf to seek clarification on some points I noticed that large sections of the chapters on Fourier series, and partial differential equations were copied without attribution from the excellent book "Mathematics of Physics and Modern Engineering," by I. S. Sokolnikoff and R. M. Redheffer (McGraw Hill, Kogakusha, 1958).I provide some details below.Although Simmons has inserted some historical and other comments, and shown some minor manipulations more explicity in a few cases, errors, sloppiness, and omissions have crept into the copy which make it less clear and accurate than the original.Sokolnikoff's excellence still comes through Simmons' light reprocessing, and it is hard to give Simmons credit for that.I would be very unhappy if I were to see my work being used without attribution the way Simmons does.One wonders what other books Simmons has copied from to produce this text.

Details

Fourier Series.Simmons pp 246 -262.Sokolnikoff pp 175 -211

Simmons rewords the text, and reorders it slightly, but the flow of the argument, points made, and equations are exactly the same.Simmons leaves out a good section on complex Fourier series because of his aversion to complex numbers.Here are examples of Simmons "light reprocessing":

Simmons:"We begin our treatment with some classical calculations that were performed by Euler.Our point of view is the the function f(x) in (1) is defined on the closed interval - Pi LE x LE Pi, and we must find the coefficients in the series expansion."

Sokolnikoff: "We take the point of view that f(x) in (18-1) is known on (-Pi, Pi) and that the coefficients an and bn are to be found."

An error has crept into Simmons copy.Simmons refers to a closed interval, whereas Sokolnikoff's original refers to an open interval by using rounded brackets.Also, Sokolnikoff's English is better.There are many examples like this.

Simmons fills in a few steps by explicitly giving trigonometric identities, whereas Sokolnikoff merely asks the reader to recall them.This makes Simmons' treatment a bit easier to read.

Simmons' treatment of "Pointwise Convergence of Fourier Series" on pp 293-297 is a complete copy of Sokolnikoff's treatment on pp 204-207.

Partial Differential Equations.Simmons: pp302 - 322; Sokolnikoff pp 431-471

Simmon' treatment of the vibrating string copied part of the derivation from Sokolnikoff, particularly the discussion around Simmons' Fig 48 (Sokolnikoff's Fig 3 in Ch. 6).Simmons copy of this diagram showing the forces on a string leaves out some critical elements making it unclear.It does not show the tension on the element of the string from BOTH left and right, it just shows the rightward tension - acting on the LEFT end of the element.Also it doesn't show the differential dy in the diagram.Quite a muddle.Sloppy.If Simmons had copied Sokolikoff's diagram accurately, it would have been much clearer.

The Heat flow example in Simmons' Sec 48 is a copy of Sokolnikoff's Ch. 6 Section 9 (p455).

Treatment of the Dirichlet problem in Simmons' Sec. 41 is a copy of Sokolnikoff's Ch. 6 Sec. 12 (p 467), except that Simmons shows explicitly some easy manipulations that Sokolnikoff had left as a problem for the student.

One of the best
I have read this book in my first year of engineering along with a few others related to calculus. But compared to this book, the other books seem a lot less effective.
The subject treatment has sufficient detail for the really interested people and is sufficiently concise for those seeking nifty tricks and methods to solve ODEs.
Some higher end stuff such as non-linear DEs has also been treated well. Though I didn't know a word about these particular equations, the book taught me well enough to handle a few types of those.
Great book!

A superb introduction - and then some
One of the best written books on the subject I've seen. As long as you're prepared to follow his anaylsis line by line (no skimming at the back there) you can give yourself some serious mathematical muscle.

He derives the first type of elliptical integral from the motion of the pendulum at page 21 (on my elderly foreign-printed software version I've had for years). That's the level it's pitched at.

One of the best books on ODEs
This is one of the best books out there for introductory ODEs. This book should be read by everyone who's interested in the physical sciences. It has many applications to physics, and that's one of the main reasons I've decided to take the course. By the way, I took the course at UCLA with professor Grossman (he reviewed the book below). He's a brilliant and a challenging mathematician, which comes at no surprise since he's a graduate of Caltech. Anyhow, I really recommend this book for all mathemticians and physicists. It's a great investment, since it can be a great reference in the future!

Excellent!!!
Each mathematic's bookhas its particularities. I had said before the Tanembaum bookwas the one better than I had on differential equations, considering its easiness reading , its methodology and its organization, but evidently these three elements can be present in many other books. This is the case of the present book, which I consider excellent. This is a great book, a very well achieved work . It introduces each element interesting the reader for the following topics, with exercises very well planned according to the exposed theory and with answers at the end of the book. Each chapter contains a historical note that will be extremely instructive and stimulants for the reader that doesn't feel pleasure for the exact sciences . Of special mention they are the chapter 6 (Some special functions of the mathematical physics), the chapter 8 (non lineal equations), and the chapter 9 (calculus of variations). The calculation of variations is an introduction to this branch, but I assure you that when reading it, you kept desires of treating other texts specialized in the topic like that of Sagan. You won't find in this book any complication, and you will be satisfied considering that it is a book for undergraduates, an excellent introduction to the differential equations.

Among the book of Tanembaum, Derry Grossman, D'prima, and the introductions of differential equations of C. R. Wylie and Kreiszig in their books of advanced mathematics for engineering, I keep this. If you plan to learn differential equations, if you want to have a really good text as introduction to the topic, then this is the book to buy, you won't lose your money. ... Read more

Product Description
Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software.

Fundamentals of Differential Equations, Seventh Edition is suitable for a one-semester sophomore- or junior-level course. Fundamentals of Differential Equations with Boundary Value Problems, Fifth Edition, contains enough material for a two-semester course that covers and builds on boundary value problems. The Boundary Value Problems version consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm-Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).

Customer Reviews (1)

Product not as described.
Item was listed as "Like new".The book I recieved might be "Good" at best.Cover is scratched with bent corners.There is a sticker on the binding.There are numerous pencil markings throughout the book.I would not recommend this seller. ... Read more

Product Description

What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.

Customer Reviews (2)

Good, practical book for FDM applied to PDE
This is a book that approximates the solution of parabolic, first order hyperbolic and systems of partial differential equations using standard finite difference schemes (FDM). The theory and practice of FDM is discussed in detail and numerous practical examples (heat equation, convection-diffusion) in one and two space variables are given. In particular, Alternating Direction Implicit (ADI) methods are the standard means of solving PDE in 2 and 3 dimensions.
In almost all cases model problems are taken in order to show how the schemes work for initial value problems, initial boundary value problem with Dirichlet and Neumann boundary conditions.
This book is a *must* for those in science, engineering and quantitative financial analysis. It digs into the nitty-gritty of mapping a PDE to a FDM scheme while taking nasty boundary conditions into consideration. The resulting algorithms are documented are are easily programmed in C++ or other language.
The book does not cover topics that are also important: operator splitting (Marchuk/Janenko), non-constant coefficient PDEs, nonlinearities. Finally, the book uses von Neumann analysis as a means of proving stability (getting a bit long in the tooth). There are more robust methods that use monotone schemes, M-matrices and the maximum principle. You should consult other specialised references.
This is Volume I of a two-volume set (Volume II deals with Conversation Laws and first-order hyperbolic as well as Elliptic problems.

(...)

Numerical Partial Differential Equations
Thomas wrote a good book on a quite specialized subject.Although finite difference schemes have been traditionally viewed as a game field for physicists, they are given today much more commercial attention asfinancial option market evolves.Those who seek standard numerical recipesare advised to read this book.You will enjoy it (easy reading) and learn. But the book may not satisfy quests of a more rigorous readership.Itabuses the Fourier method in stability analysis while considering only PDEswith constant coefficients.The bibliographical work has not been done atall.In addition, the cover does not state that this is the first book oftwo.I'd also advise to read G.Marchuk "Methods of NumericalMathematics" (Springer, 1982) where a more general approach for stabilityof numerical schemes is developed. ... Read more

Product Description
Sixth edition (1928) of classic 19th-century work considered one of the finest treatments of the topic. Differential equations of the first order, general linear equations with constant coefficients, integration in series, hypergeometric series, solution by definite integrals, many other topics. Over 800 examples. Index.
... Read more

Product Description
Written by the authors, the Student Solutions Manual contains worked solutions to all of the odd-numbered exercises in the text. ... Read more

Customer Reviews (33)

Helped a lot
I had a relatively good experience with this book in the class that I used it for. Our professor was a real #%&$! and he wasn't that great at explaining the different concepts. I found myself coming back to this book countless times for clarification and help. Never let me down.

I'll admit that the format was a bit funky as far as introducing theorems and such, but overall, the problems were good for practicing and it was a life-saver for the final.

Oi Vey
A ponderous, meandering exposition of mathematical trivia and trivial mathematics. In fairness, it must be said that the book may be of some interest to those seeking a cost-efficient alternative to a prefrontal lobotomy. It also provides the first known counter-example to the Baire Category Theorem: a book that is complete in its uselessness, and yet, is the union of a countably infinite set of nowhere-dense pages.

Poorly written, confusing book
I feel sorry for anyone purchasing this book. It's instructional value is close to nil- the only well done sections in the book are the problem sets. The "teaching" material is hopelessly confusing. If you have to have this book- make sure you have a very good teacher. Learning the material from the book WILL NOT HAPPEN.

What the....?
I would have to agree with many reviewers here, avoid this book if you can.An awful read, and just overall very poor in presentation.If you need it for a class, then you have to get it, but if you can avoid it you will be doing yourself a favor.I am currently in DE and like many people with this book, I am buying an alternate text.

terrible textbook
Differential Equations is not a hard course, but this book will add almost nothing to your educational experience. I found the book to contain a lot of dense text and very few quality examples. The software that comes with the book is interesting and fun to play around with.
I don't recommend buying this text book. ... Read more

Product Description

Product Description
Elementary Differential Equations with Boundary Value Problems integrates the underlying theory, the solution procedures, and the numerical/computational aspects of differential equations in a seamless way. For example, whenever a new type of problem is introduced (such as first-order equations, higher-order equations, systems of differential equations, etc.) the text begins with the basic existence-uniqueness theory. This provides the student the necessary framework to understand and solve differential equations. Theory is presented as simply as possible with an emphasis on how to use it. The Table of Contents is comprehensive and allows flexibility for instructors. ... Read more

Product Description
This traditional text is intended for mainstream one- or two-semester differential equations courses taken by undergraduates majoring in engineering, mathematics, and the sciences.Written by two of the world’s leading authorities on differential equations, Simmons/Krantz provides a cogent and accessible introduction to ordinary differential equations written in classical style.Its rich variety of modern applications in engineering, physics, and the applied sciences illuminate the concepts and techniques that students will use through practice to solve real-life problems in their careers.

This text is part of the Walter Rudin Student Series in Advanced Mathematics. ... Read more

Customer Reviews (4)

Point Less
This solutions manual is point less. It's just like look for answer in the back of your book.

Differential Equations
This is an awesome book. Easy to read and follow. It was exactly as described and was shipped quickly.

Pointless
This text is expensive and pointless. While it is obviously designed for upper division courses, it lacks concrete examples and a clear thought pattern. Sections do not seem to connect in a comfortable way and they should be much longer. The odd-numbered solutions pages at the end are a joke; most say "proof not shown." Do not buy.

Student's Solution Manual for Diff. Eqs.: Theory, Technique and Practice
The solutions manual is fine, with a clear analysis of the problems discussed in the text.I thought that more problems should have been
looked into, but many math books don't provide solutions to all of the problems they offer.Answers help those trying to fully understand the text material. We shouldn't be working in the dark when we try to solve the problems. ... Read more

Product Description
Written for students of mathematics and the physical sciences, this superb treatment offers modern mathematical techniques for setting up and analyzing problems. Topics include elementary modeling, partial differential equations of the first order, potential theory, parabolic equations, much more. Prerequisites are a course in advanced calculus and basic knowledge of matrix methods.
... Read more

Customer Reviews (4)

a classic text in applied mathematics
This is one of the finest textbooks on applied mathematics.It is appropriate for a wide range of levels and disciplines.A moderately paced graduate class can finish most of the chapters in a full year.The first two chapters cover material that is difficult to find elsewhere and nowhere is it better handled.The real boon to this book is the constant integration of physical reasoning with solid mathematical theory.To be sure, many of the more complicated ideas are only mentioned, but the later chapters pick these up and go much further. It covers basic heat and wave applications, but also Brownian motion and gas dynamics.A solid calculus background is needed, which includes vector calculus and convergence issues.Eigenvalues and some functional analysis are needed.Many books on elementary partial differential equations spend all their time on the big three: heat, wave and Laplace.This is too low a level for any graduate class and doesn't create the excitement other applications provide.On the other hand, this book is accessible to many people.Often, graduate texts are thoroughly awash with Sobolev spaces and weak convergence and the physical problem, i.e., the actual model, is all but ignored.This classic text is the bridge between elementary and advanced applied mathematics.In some respects, it is self-contained.Guenther and Lee have written an indispensable book.

Partial Differential Equations of Mathematical Physics & Integral Equations
Book came in excellent condition and was shipped quickly.Highly recommend this seller.

I agree with the reader from CAL
The book skip too many steps and most of the time, the equation is presented without explanation...Don't waste money.

Book that dosn't make sense
This book is one of the worse I ever see representing the mathematics for physics, the mathematics and the physics both was not explained as it should, the authors are not familiar at all with the concept of physicsmake their material in the book related to this subject unclear and vague.The book has too many gaps as I see it has too many jumps when a physicalphenomena represented using mathematics. Physical concept was most of thetimes not even mention, and I believe that the author should stick onlywith mathematics since they try to explain physics they don't reallyfamiliar with. ... Read more

Product Description
The prerequisite for the study of this book is a knowledge of matrices and the essentials of functions of a complex variable. It has been developed from courses given by the authors and probably contains more material than will ordinarily be covered in a one-year course. It is hoped that the book will be a useful text in the application of differential equations as well as for the pure mathematician. ... Read more

Customer Reviews (4)

A reference book but no longer a text book.
I agree with the previous reviewers but the student new to the subject should also know that during the 55 years since it was published there have been breakthroughs in problems that resisted all previous efforts, such as stability of solutions of equations similar to those governing the solar system and proofs of ergodic (chaotic) behavior of certain systems. Numerical mathematics today is also very different from what it was when a million-dollar computer had 100K memory.The book is still a valuable work of reference but it is not suitable as a text book because most current research explores concepts and uses methods which were developed since it was written.

This is THE book
if you want to learn more about ODEs than just how to solve them. I took a course on ODEs in a german university more than 30 years ago and the prof chose Coddington and Levinson. It was tough but I am very thankful now! It is so different from all these new "ODEs for Dummies-type" books with colour pictures all over and matlab, mathematica, maple or whatever in the foreground.

Bible for Differential Equations
Dr Coddington's books are bible for differential equations. He knows material quite well, He is one of the famous person for differential equations. Try to understand his books from top to bottom, and no one can teach you differential equations. Other suggested bible books for reading: Introduction to Differential Equations, Linear Ordinary differential equations by Earl Coddington, Differential Equations by Fritz John, Ordinary Differential Equations by Ince, Differential Geometry Vol 1-5 by Michael Spivak.

A Comprehensive Text
The text is a standard reference on the theory of ordinary differential equations (it is not easy reading but comprehensive and accurate). Topics covered include: existence and uniqueness theorems for equations with various degrees of smoothness; dependence of solutions on parameters and initial conditions; singular equations; Sturm-Liouville theory (completeness of the eigenfunctions, convergence of eigenfunction expansions and asymptotic distribution of eigenvalues); asymptotic solutions; o.d.e's in the complex plane and much, much more.The text includes at the end of each chapter a collection of problems which extend the theory developed in the chapter and lead the reader to explore related areas. ... Read more

Product Description
Superb, self-contained graduate-level text covers standard theorems concerning linear systems, existence and uniqueness of solutions, and dependence on parameters. Major focus on stability theory and its applications to oscillation phenomena, self-excited oscillations and regulator problem of Lurie. Bibliography. Exercises.
... Read more

Product Description
Well-known authors; Includes topics and results that have previously not been covered in a book; Uses many interesting examples from science and engineering; Contains numerous homework exercises; Scientific computing is a hot and topical area ... Read more

Product Description

This book offers an ideal introduction to the theory of partial differential equations. It focuses on elliptic equations and systematically develops the relevant existence schemes, always with a view towards nonlinear problems. It 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. It also explores connections between elliptic, parabolic, and hyperbolic equations as well as the connection with Brownian motion and semigroups. This second edition features a new chapter on reaction-diffusion equations and systems.

Customer Reviews (2)

A very good choice
This is an excellent book for a PDE course with a strong vias toward
elliptic and parabolic equations. Its lack of information related to hyperbolic equations is its weakest point. However, the author is an
excellent writer and it is pleasure to read this book.

Elliptic PDE's done right
I'm no specialist in PDE's but I boldly would like to review the present book.
This book is intended(in my personal view) as a in-depth-but-not-pedantic introduction to Elliptic equations (which, if one considers the original title in german "Partielle Differentialgleichungen - Elliptische Gleichungen" makes complete sense).
As any other descent book, it doesn't aim at list down results in a encyclopedic way, but rather tour-guide the reader in the beautiful subject of Elliptic PDE's.

Motivated by Dirichlet's principle, the author introduces variational methods for Elliptic PDE's and a good deal of the regularity program for that class of equations(including non-linear equations). Most of what follows the first chapter, is a successful attempt to generalize to other elliptic equations the techniques useful in the qualitative theory of the Dirichlet problem for the Poisson equation. Some of the methods, as far as I understand them, can be generalized to Schroedinger's equation too.

The interested reader can consult also the book on analysis by Elliot Lieb and the textbook on variational methods by Prof. S. Hildebrandt(and references therein). ... Read more

Product Description

Delay Differential Equations: Recent Advances and New Directions cohesively presents contributions from leading experts on the theory and applications of functional and delay differential equations (DDEs).

Students and researchers will benefit from a unique focus on theory, symbolic, and numerical methods, which illustrate how the concepts described can be applied to practical systems ranging from automotive engines to remote control over the Internet. Comprehensive coverage of recent advances, analytical contributions, computational techniques, and illustrative examples of the application of current results drawn from biology, physics, mechanics, and control theory.

Students, engineers and researchers from various scientific fields will find Delay Differential Equations: Recent Advances and New Directions a valuable reference.

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

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

Product Description
In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments.  It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods.

Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding.  Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler.

Features of the book include

• Introductory work on differential and difference equations.
  
• A comprehensive introduction to the theory and practice of solving ordinary differential equations numerically.
  
• A detailed analysis of Runge-Kutta methods and of linear multistep methods.
  
• A complete study of general linear methods from both theoretical and practical points of view.
  
• The latest results on practical general linear methods and their implementation.
  
• A balance between informal discussion and rigorous mathematical style.
  
• Examples and exercises integrated into each chapter enhancing the suitability of the book as a course text or a self-study treatise.

Written in a lucid style by one of the worlds leading authorities on numerical methods for ordinary differential equations and drawing upon his vast experience, this new edition provides an accessible and self-contained introduction, ideal for researchers and students following courses on numerical methods, engineering and other sciences. ... Read more

Customer Reviews (2)

The Definitive Reference for ODEs
An in-depth analysis from one of the best experts in the field of the latest developments in the numerical solution of ODEs with special emphasis on the Runge-Kutta methods, although Linear Multistep Methods and General Linear Methods are also thoroughly described.A must read for any researcher with interest on the numerical solution of initial value problems.

Useful, Practical, Fascinating Book by A Well-Known Authority and Teacher
This is the Second Edition of a classic work on solving differential equations numerically. The well-known author and teacher has published pathfinding papers on this topic from the early 1960's to the present. The "Butcher Tableau" is the standard short-hand display for Runge-Kutta methods.

The book sets the table by describing a set of standard problems for numerical solution. Then, as new methods are described their efficacy on the standard problems is graphed and tabulated.

Explicit and implicit Runge-Kutta Methods, Linear Multistep Methods, Taylor Series Methods and General Linear Methods are thoroughly described from the viewpoint of accuracy and stability. Symplectic Runge-Kutta methods, 'Almost' Runge-Kutta methods and Inverse Runge-Kutta Methods are among the additional covered topics of current interest.

Practical issues for the implementer of algorithms based on these methods, such as error estimation and step-size control, are well-covered. References to the topic's literature are also outstanding.

To use the book, a background in calculus and numerical analysis is essential.

Current topics in this field are well-represented. The author has taught many of the present class of researchers, and the clarity of a great teacher is apparent.

Web resources and problems at the end of each section enhance the book's value for a semester-long course. ... Read more

Product Description
A graduate level text on a subject which brings together several areas of mathematics and physics: partial differential equations, differential geometry and general relativity. It explains the basics of the theory of partial differential equations in a form accessible to physicists and the basics of general relativity in a form accessible to mathematicians. In recent years the theory of partial differential equations has come to play an ever more important role in research on general relativity. This is partly due to the growth of the field of numerical relativity, stimulated in turn by work on gravitational wave detection, but also due to an increased interest in general relativity among pure mathematicians working in the areas of partial differential equations and Riemannian geometry, who have realized the exceptional richness of the interactions between geometry and analysis which arise. This book provides the background for those wishing to learn about these topics. It treats key themes in general relativity including matter models and symmetry classes and gives an introduction to relevant aspects of the most important classes of partial differential equations, including ordinary differential equations, and material on functional analysis. These elements are brought together to discuss a variety of important examples in the field of mathematical relativity, including asymptotically flat spacetimes, which are used to describe isolated systems, and spatially compact spacetimes, which are of importance in cosmology. ... Read more