Book Description

This new Fifth Edition of Zill and Cullen's best-selling book provides a thorough treatment of boundary-value problems and partial differential equations. This edition maintains all the features and qualities that have made Differential Equations with Boundary-Value Problems popular and successful over the years.Written in a straightforward, readable, helpful, not-too-theoretical manner, this new edition keeps the reader firmly in mind and strikes a perfect balance between the teaching of traditional content and the incorporation of evolving technology. ... Read more

Reviews (12)

excellent text for self-learners and non-freaks
Right after high school, I enrolled in a d.e. course at the local junior college (ok, I was a masochist). We used the Zill text, although not the boundary value problem edition. Needless to say, that book was a godsend b/c the instructor was horrible, so after awhile, I only showed up for class for exams, and self-studied on my own from that book. I recall that the book was fun and easy to understand.

Why is it good? It explains things in clear language. The proofs are laid out clearly. There are lots of example problems with solutions. This was critical in the portion of the book where he explains how to solve d.e.'s with variable coefficients. The book makes differential equations look interesting, which is important to capture readers. Zill also has a calc book, and mygoodness, that book was sort of repulsive b/c of the 70's style printing and the nasty brown colors. Looks are always a big thing, back then and now.

I'm not sure how applicable this text is for hard-core math majors, but definitely, if you are in engineering and don't require any weird esoteric understanding of the proofs that math people might need, this is text worth referring to. I can't comment on the BVP, though... However, it helped me to earn an A+ at Cal that first semester as a freshman, so he must be doing something right.

P's and Q's
Overall a good book; however, it is filled with small, yet significant, errors in the solutions, study manual and a few theorems. These errors though not major may cause confusion serious confusion.

Good book, for the most part.
The problem sets for each section were good. I used this book for Penn State's distance education ODE/PDE class. However, book should be supplemented with lectures, though. The chapter on Cauchy-Euler equations was lacking because it didn't tell you "why can we use this approach to solve these types of equations" (I had to ask my prof to show me why). On the plus side, it did have an intro to PDE's in the latter chapters, and was fairly thorough in the number of techniques covered for solving various types of DE's.

Classic Old Text
This is a book from the old school of ODE's. The absolute focus of this book is analytical methods and beats the algebra and integration drum to the exclusion of anything else. If you want to learn how ODE's were solved 25 years ago then this book is for you. If you are looking for a book that deals with more modern theory, or handles modeling in a constructive manner then this book is NOT a good choice.

interesting
Great for self study or as a course textbook. The problems are nice, and so are the explanations. ... Read more

Book Description

This Seventh Edition maintains the all the winning qualities that have made A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS a best-seller over the years. Written in a straightforward, helpful, not-too-theoretical manner Zill's approach keeps students with differing levels firmly in mind.The new edition strikes a perfect balance between the teaching of traditional content and the incorporation of evolving technology. ... Read more

Reviews (15)

good for non-math people
Easy to follow examples. Great conceptual models. This book has plenty of useful applications in the real world: physics, biology, engineering, and chemistry. There is no math flood to drown non-math students. Great intro to Ordinary Diff. Eq.

decent
It's been a long time since I had this book for a course (so take this with a grain of salt...), & I had a pretty good instructor, but this book still helped reinforce the ideas. I don't think it makes a difference whether a book has a solution manual, just plug your solution into the equation to check your answer. A solution manual for a differential equations text is a bit superfluous, IMO, since solutions don't all look the same. Another good text is the one by Rainville/Bedient.

Lacking pedagogical stimuli or skill ?
Maybe this was an attempt to be unique in presentation of the subject ; yet , contorting paraphrased material into a potato - salad of words is an obvious sign of bad technical writing ; perhaps , poor confidence in subject , or who knows what ?!?! . The layout of this text is the worst I've seen in a mathematics text -- both , calculations and " explanations " are blobbed as run - on , rambling sentences contained into page - sized paragraphs ; unbearable amount of conceptual abstraction almost at every definition of critical importance . There lies a clue that descriptive terms were chosen by dictionary research of most subtle synonyms of such; moreover , an overuse of unnecessary adjectives , of same descent , to increment the confusing flush . This text is obviously designed to be NOT USER FRIENDLY on purpose !! .
To me , that defeats the whole goal of even attempting to write books for students . This one should , in its full definition , be banned from all pedagogical institutions -- those , where are those with a desire to learn . I personally did not encounter difficulty of solving this " book's " chapter problems ; however, due to the diffused presentation of theory , am still lacking satisfaction of conceptual clarity of such a rich subject .

An Enjoyable Book Overall
I enjoyed using this book in my DiffEq class. It gives lots of examples and a variety of homework problems. It proved to be very useful for me.

Do not recommend
I am using this book for my D.E. class. The solutions manual [is bad], solving only every third problem. I found the reading quite difficult to understand and the pages are boring and bland!!! ... Read more

Book Description

Maintaining a contemporary perspective, this strongly algebraic-oriented text provides a concrete and readable text for the traditional course in elementary differential equations that science, engineering, and mathematics readers take following calculus.Matters of definition, classification, and logical structure deserve (and receive here) careful attention for the first time in the mathematical experience of many of the readers. While it is neither feasible nor desirable to include proofs of the fundamental existence and uniqueness theorems along the way in an elementary course, readers need to see precise and clear-cut statements of these theorems, and understand their role in the subject. Appropriate existence and uniqueness proofs in the Appendix are included, and referred to where appropriate in the main body of the text. Applications are highlighted throughout the text. These include: What explains the commonly observed lag time between indoor and outdoor daily temperature oscillations?; What makes the difference between doomsday and extinction in alligator populations?; How do a unicycle and a two-axle car react differently to road bumps?; Why are flagpoles hollow instead of solid?; Why might an earthquake demolish one building and leave standing the one next door?; How can you predict the time of next perihelion passage of a newly observed comet?; Why and when does non-linearity lead to chaos in biological and mechanical systems?; What explains the difference in the sounds of a guitar, a xylophone, and a drum? Includes almost 300 computer-generated graphics throughout the text.This text, with enough material for 2 terms, provides a concrete and readable text for the traditional course in elementary differential equations that science, engineering, and mathematics readers take following calculus. ... Read more

Reviews (3)

Very good
Fast and its just brand new, he never opened the books

As good as it gets
Differential equations are difficult to teach (though not conceptually difficult), and that fact becomes obvious when you look at most DE books. However, there is the occasional text that teaches the subject in a most comprehensible way. I have used other DE books, among them S. Goode's "Introduction to Differential Equations and Linear Algebra", and let me tell you -- it [is bad]. Plain and simple. It was the only math class I've ever taken which left me with what felt like an incomplete understanding of the subject. And then I used this book for a course at MIT and I realized why I hadn't learned anything previously. The old book [was bad]. And this was pretty good. The only reason I give it four stars instead of five is because it doesn't have any particular line of development. But that's not that important, and this book is a great way to learn differential equations.

Good book but a strong background on calculus required.
This book will tell you everything you need to learn on differential equations. It covers thoroughly the methods for solving first and second order differential equations. The book also extends into Fourier transforms. I used this book at MIT for the differential equations class and found it very useful. Within its contents, matlab exercises are present and some simple projects which lets the student apply its knowledge. The only problem with the book is that it can be hard to read at certain points. Also the author assumes a strong background in calculus. ... Read more

Book Description

This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications.The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the book.For mathematicians and those in the field of computer science. ... Read more

Reviews (18)

A Good Text, Typos Aside
I am currently using this text for an intro level differential equations course, and I feel that this book is well suited as such. It should be easily acessible to anyone with a basic intro calculus foundation and it is ideal for self-study. On the other hand, this text does contain a noticible number of typos, both in "back-of-the-book" answers and example problems. A potential reader should note that this book is fairly applied in its nature (as the title would indicate--engineers take delight, theoreticians take dismay), so one shouldn't expect more than an introduction to the theory of differential equations (ie. don't expect much proof or mathematical rigour).

Very Good Book
I don't know why everyone else attacks this book! I used it in a third semester math class at Cornell which was 1/3 vector calc (we used Thomas' Calculus, another great book), 1/3 differential equations, and 1/3 Fourier Series, partial differential equations, boundary value problems. We covered Chapters 1-3, parts of 4 and 6, and all of chapter 9.

The book is excellent. The explanations are clear. The example problems are not just "plug and play." The problems at the end of each section are not bad. I learned about oscillations and mechanical vibrations in physics and then learned about them from this book (3.4/3.6)...the difference was amazing. Their derivations made sense, and the characteristic polynomial technique they use is 1000 times simpler than the trial solution method that many introductory physics books on mechanics use.

The book's only weak point is the discussion of stability and the phase plan in 6.1. They develop it through a bunch of examples instead of talking about the general theory behind it. But this is a minor problem.

Pretty good
Not a bad book at all. Physical applications well explained, theory OK but not as good in my opinion. Unfortunately, contains a fair number of typos, and the book is physically weak (the binding of mine is splitting after only 4 months of use) for a book of this price. Still, pretty good overall.

One bad apple spoils the pair...
This book would be excellent... if it weren't for one mysterious member of the pair, Edwards or Penney who can't teach for his life and/or is lazy. I would've guessed two authors wrote this text even if they only claimed it had one author and called him edward penney... You see, every couple of sections or so there are a lot of typos and poor overly wordy "proofs" , stupid joke proofs that are almost like winking and smiling between one professor and another while the student sits there dumbfounded. One proof in particular goes: "Theorem 2 says yes!" Oh yeah? Unfortunately I am not as comfortable with math as you with your doctorate degree sir I don't just "see" the truth of a claim as you probably do -or maybe you are just bluffing. You see, I also take the types of proofs this guy does to be as though they were designed to make him look more intelligent to other professors who may be teaching out of the book. Mr. Edwards or Penney you know who this guy is! Ditch him as a fellow author for your next edition! As far as the other mysterious author, his explanations and proofs are patient and lucid and involve a good bit less words (words are nonsense! The whole point of math is to learn how to think with fewer stupid words so you can understand more fundamental and abstract ideas which cannot be expressed in words!) As a piece of advice, I would like this text to be a bit less concrete in its explanations of mathematical generalities. It weighs them down and confuses people who have an intuition for their logical consequences, it almost makes them feel constrained and stupid and it is irritating to learn about a general fact through the use of a stupid example and then have the generality taken for granted thereafter without proof!

A good differential equations textbook
I think the strength of this textbook is the amount of material it encompasses: this book is used in two separate courses in my school--introduction to DE and engineering analysis. I didn't appreciate the textbook so much until I completed my differential equations course and then looked back at the sections on mechanical vibrations to review for my physics course. I then realized that the explanations and derivations were extremely satisfying, much more than your average introductory physics text. Also, the emphasis on the qualitative aspects of DEs, such as slope fields and phase portraits, aid in the coneptual understanding of the otherwise rigorous computation aspects of the topic. My only complaint is that the proofs could've been done in a more understandable manner. ... Read more

Book Description

This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: 1) representation formulas for solutions, 2) theory for linear partial differential equations, and 3) theory for nonlinear partial differential equations.

Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and much more.

The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he emphasizes the modern interplay between functional analytic insights and calculus-type estimates within the context of Sobolev spaces. Treatment of all topics is complete and self-contained. The book's wide scope and clear exposition make it a suitable text for a graduate course in PDEs. ... Read more

Reviews (6)

Excellent
Evans succeded in writing a text on partial differential equations which can serve a broad spectrum of users: from pure mathematicians interested in hard theorems about the properties of solutions to various types of PDEs to sophisticated practitioners interested in solving specific problems leading to PDEs. The book covers in sufficient detail and great clarity the basic types of PDEs including modern topics such as optimal control, Hamilton-Jacobi equations, and viscosity solutions. Emphasis is pretty evenly distributed between general qualitative properties of solutions, and techniques for explicit construction of solutions in representative cases.

PDE making sense
This is a textbook for a first-year graduate course in PDE (for mathematics students). You should take courses in analysis (on the level of Rudin) and measure theory before you expect to understand everything in this book.

This is by far the best book on PDE. The text is extremely clear, and most of the rather technical proofs are prefaced with "heuristic" calculations to help the reader understand what is going on. The chapter on the calculus of variations is the best exposition I have found of the subject, and Evans completely dispenses with the awful "delta" notation which never made any sense.

The text doesn't make much use of the Fourier transform and doesn't even mention distributions, and this gives his book a definite nonlinear flavor (which is a good thing). This should become the standard introduction to PDE on the graduate level.

Dense, but quite good
This book is a mathematician's book and not an engineer's--it hasn't a bit of material on approximating solutions of PDEs (which subject could fill several volumes by itself), and devotes a great deal of space to proving existence, regularity, and other properties of solutions to non-linear PDEs. The exposition is extremely compressed (many moderately difficult proofs are reduced to a paragraph or two).

It is also very much a graduate course (as the title indicates). Undergraduate students are advised to stay away unless they have excellent teachers, or are very good, or both.

difficult
As a graduate student in engineering, I found this book to be somewhat difficult to understand. That in itself isn't a major problem, but I have just found other books which present the material in a much clearer fashion. Part of the problem is Evans' fascination with non-linear equations to the point of muddling even simple formulations.

This will become the standard text in PDE
This is a very well written textbook for graduate-level students as well as an excellent reference for researchers. The outlook of the author, a leader in his field, is non-linear and very broad and includes maechanics and geometry. Any department library needs this book. ... Read more

Reviews (8)

good books never have thousand pages
This book talks about multivariable calculus that is not included in high school curriculum. The book is concise but covers all the thing I want to know. It is not bulky book that makes you look good; it will lead you to be good at calculus. Of course please master your skill in single variable calculus before trying this one.

Not as advanced as it claims
It is good and clear book. Excellent for undergrad students who want to dig into calculus a bit deeper. But it is too easy for an advanced undergrad or a grad student in any technical field. I recommend the books published by Springer.

I adore the author
Any student who is taking analysis/advanced calculus course should read chapter 2 of this book, especially if he is confused or is struggling on the excellent but relatively abstract/concise texts of Rudin, Apostal, Bartle, Marsden et al. I've never seen a book which can explain the concept of Jacobian and Inplicit function theory in such a clear way!!

More Than I Could Have Expected
This book is simply the best that I have found for math texts. Kaplan does not expect much from the reader; he explains basically everything besides Calculus I material. Kaplan's writing is lively and is (relatively) easy to read. He gets to the point and keeps everything easy to follow. I am still in awe about how much material (look below) he was able to fit into this relatively small book and still keep it so clear. The examples are clear and concise. The problems in the book compliment the understanding of the material; they start out easy and guide the reader to do more difficult problems. This book is MORE THAN SUFFICIENT FOR SELF-STUDY.

Contents: Linear Algebra, Partial Derivatives, Vector Calculus, Multiple Integrals, Sequences and Series, Fourier Series, Complex Variables, and Ordinary/Partial Differential Equations. This is a conservative list.

The price may appear steep, but the content and clarity of this book more than make up for it.

The perfect book
Although my regular textbook is excellent(Larson, Calculus,7th edtion), but there are just ideas and theories which are not explained or expanded. I love Kaplan's Advanced Calculus for the following reasons:
1. It is very logical, everything goes step by step. If there is anything you have not learned or have forgotten, he refers you to specific earlier sections. And if there is something he does not explain, he refers you to other resourses.
2. The book is lean and super clean. Although I do appreciate our regular textbooks's wordiness which is great for a beginner like me, I also love reading this book which goes straight to the core.
3. While some books look lean but are actually dry and really hard to chew, this book is easy to follow. And it really gives you a feeling that you are learning math, you are not just learning some techniques.
4. Even though there are a couple of out of date notations like a reviewer has pointed out, like he writes "ln" as "log", but it really does not interfere reading and understanding.
In short, the book is a gem, every page is worth its paper. ... Read more

Book Description

This example-rich reference fosters a smooth transition from elementary ordinary differential equations to more advanced concepts. Asmar's relaxed style and emphasis on applications make the material accessible even to readers with limited exposure to topics beyond calculus. Encourages computer for illustrating results and applications, but is also suitable for use without computer access. Contains more engineering and physics applications, and more mathematical proofs and theory of partial differential equations, than the first edition. Offers a large number of exercises per section. Provides marginal comments and remarks throughout with insightful remarks, keys to following the material, and formulas recalled for the reader's convenience. Offers Mathematica files available for download from the author's website. A useful reference for engineers or anyone who needs to brush up on partial differential equations.

Reviews (3)

Partial Differential Equations and Boundary Value Problems
I think this book is Possibly the best Mathematic book for Engineer I've ever read. This is due to the fact that the material is so much clear and the examples are so easy to follow. The book's explanation is precise and accurate. The exercises on every chapter are helpful. I practise almost most of the exercise problems. In fact, I score an "A" on the first Test. I will recommend it to everyone without hesitation.

Initial impressions
Nakhle: Just a quick note to thank you for your book! It arrived Thursday, and I've been reading it and doing the exercises both on paper and in Mathematica 3.0. After a quick review of the whole book and a thorough reading of the first 70 pages so far, I can say I just love it! If I'd only had a book like this in college and graduate school I'd have become a much better electrical engineer. Yours is one of the best expositions of both Fourier series and partial differential equations I've used. Although I haven't gotten very far into the boundary value problems and the orthogonal functions areas of the book yet, my initial review indicates they will be excellent also. I am enjoying your book immensely, and I thank you very much for it. I'll update this with a more thorough review when I have a chance to finish the book, but I wanted to share my initial impressions so others might weigh them into their own decisions to get this excellent book.

A clear introduction to PDEs, Fourier series
This text not only provides a simple and easy-to- read-the-first-time guide to solving PDEs with Fourier series, it also is chock-full with all the necessary details and includes many interesting problems. I took a course out of this book as a sophomore in college and found it very interesting and useful. The style and difficulty is very similar to a typical undergraduate ordinary differential equations book, except this is better organized.

The subjects include a small bit on characteristics for first-order equations, a chapter on trigonometric series, PDEs in rectangular, polar, and spherical systems and associated eigenfunction expansions, Sturm-Liouville theory, the fourier transform, Laplace/Hankel transforms for PDEs, grid-type numerical methods, sampling & discrete Fourier analysis, and quantum mechanics (the Schrödinger equation).

This book is definitely great for applied mathematicians, physicists, or engineers who really need a solid introduction to the topic, written by someone who knows all the details. Any treatment in "mathematical physics" courses on PDEs will fall short of this book's content.

Of particular importance are the inclusion of special sections for Bessel functions, Legendre polynomials, associated Legendre functions, spherical harmonics, etc. All the details of solution and many exercises are included.

The most interesting parts of the book are towards the end, with the Sampling Theorem and discrete Fourier transform; and the proof of Heisenberg's uncertainty principle.

This book is also useful for more theoretical mathematicians or mathematical physicists who need an introduction to PDEs before taking a more difficult course on general theory.

In short, I think that even though this book is of great utility to non-mathematicians, it is proper to learn these concepts and techniques in a proper math setting where care is taken. This text is a solid foundation for confident application and a springboard towards more advanced subjects. ... Read more

Book Description

This book strikes a balance between the traditional and the modern—combining the traditional material with a modern systems emphasis.Chapter topics cover an introduction to differential equations, first-order equations, modeling and applications, second-order equations, the Laplace Transform, numerical methods, matrix algebra, an introduction to systems, linear systems with constant coefficients, nonlinear systems, power series solutions, Fourier series methods, and partial differential equations. ... Read more

Reviews (1)

Great Book for ODE's
I used this book for a course in ODE's. The edition that was available for purchase at our school's bookstore also included a book by the authors for using MatLab for solving ODE's, The combination of the two were great. The book is logically structured and generally easy to read. The authors use many examples from a variety of fields. The MatLab book was a phenomenal help: it's the best intro to MatLab that I've found, and was very useful in helping to solve problems. My only beef with the book is that since this is a first edition, there are several errors in the odd numbered solutions at the end of the book, which caused many sleepless nights. ... Read more

Book Description

This revision of the market-leading book maintains its classic strengths: contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. Like its predecessors, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences. Sound and Accurate Exposition of Theory--special attention is made to methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace development of the discipline and identify outstanding individual contributions. ... Read more

Reviews (48)

Good, but a supplement is recommended
This is a good book on ordinary differential equations. Examples are very helpful to learn how to do problems. They are pretty much the best way to learn how to solve the equations. Also, there are answers to every problem in the textbook, so you can check your answer. However this book has some nuances which you should consider: Main important points on how to solve ODEs are not highlighted (only some are, and those are mostly the theorems). The important stuff IS in the chapters, but you gotta pick it out for yourself. For that reason I recommend getting some used ODE book for cheap, that has all the important concepts highlighted (Edwards/Penney comes to mind).

Great Book!
I personally liked this book. It's easy to read and study on your own without the aid of a teacher. Its weakness is perhaps the lack of demonstrations, but since I'm a physics major I wasn't extremely concerned with them.

An aggravating textbook if you think spatially
It is interesting that the reviews of this book are so polarized, probably a result of different ways of conceptualizing math. I lean very much towards spatial (three dimensional)thinking, and this book has proven utterly worthless to me.

This is unfortunate, because most aspiring engineerers think spatially, and most are required to take a differential equations course.

My specific complaints are numerous:

1) Far too few examples
2) Exremely disorganized (examples in the book will reference a formula, concept or previous example in previous sections rather than restating the problem. I spend a lot of time flipping pages back and forth, which significantly interferes with my train of thought.)
3) Essential components of an example will be presented in paragraph form, but the reader would be much better served by presenting the information in a table or at least using a block quotation.
4) The answers in the back of the book are regulary presented in an unusual form that requires unnecessary algebraic manipulation.
5) The language is unnecessarily theoretical.
6) The examples don't really present a step-by-step method for solving a problem, but devolve into further abstraction.
7) Further discussion of essential subject matter is presented in the problems section rather than in the heart of the chapter.

If you find yourself asking the questions, "What purpose does this technique serve? Why do we need to know this? How will this help me solve a problem in the real world? or Will you draw a picture of that?" then this book is likely of little value.

And if you have a bad teacher, you may just be sunk. I just bought REA's Differential Equation Problem Solver and Tennenbaum's "Ordinary Differential Equations". I hope it helps.

Great Book, Can Be improved with a few more solved problems!
This is as good as any book gets on this subject. I suggest you keep another book as backup for extra problems for you to work your way through. The explanations here are excellent, its just that there are too few solved examples to drill the idea into your head. But as far as understanding concepts goes, this is THE book on ODEs. Go for it!

sorry but no good
I'm a student that reads all my text books and relies heavy on them. This book starts off doing a great job on first order differential equations. However, as the book move on it falls short on examples,and doing a poor job explaining more advance topics. I had real trouble with the applied sections on secound order non-homogeneus equations. I have read the older additions of this book and think they were much better. Sorry !!!!! ... Read more

Book Description

Emphasizing the physical interpretation of mathematical solutions, this book introduces applied mathematics while presenting partial differential equations.Topics addressed include heat equation, method of separation of variables, Fourier series, Sturm-Liouville eigenvalue problems, finite difference numerical methods for partial differential equations, nonhomogeneous problems, Green's functions for time-independent problems, infinite domain problems, Green's functions for wave and heat equations, the method of characteristics for linear and quasi-linearwave equations and a brief introduction to Laplace transform solution ofpartial differential equations.For scientists and engineers. ... Read more

Book Description

This tried-and-true book of differential equations expands upon the authors' Differential Equations: Computing and Modeling, 2nd Edition. It covers the core concepts and techniques of elementary linear algebra—matrices and linear systems, vector spaces, eigensystems, and matrix exponentials—that are needed for a careful introduction to linear equations. Complimenting this solid foundation, the book emphasizes mathematical modeling of real-world phenomena, and offers a fresh new computational flavor evident in figures, examples, problems, and projects throughout.Chapter topics include: first order differential equations, mathematical models and numerical methods, linear systems and matrices, vector spaces, linear equations of higher order, eigenvalues and eigenvectors, linear systems of differential equations, matrix exponential methods, and nonlinear systems and phenomena.A geometric visualization for those interested in science and engineering. ... Read more

Book Description

Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton’s Interpolation Formulas, more.
... Read more

Reviews (9)

Wow -- Perfect ODE book for an undergrad
For math background, all that is needed for this book is a first semester in calculus. If you are looking for a book to learn ordinary differential equations (ODEs) from or for a second book for a class, buy this one. The book (which covers methods of solving/applying ordinary differential equations) are explained in just the right amount of detail--it isn't a novel, but it isn't something you should get too bogged down in. Also, there are LOTS of examples, which are all very helpful! The problem sets were put together very well--there are lots of problems and they start out easy and get harder. Also, one of the best things about this book is that it has most of the answers to problems! This makes this book more than sufficient for self-study. This is my favorite Dover Publications book!

Very impressive...
After going through this book and finishing a few weeks ago, and looking at some other comparable titles, I have to come to the conclusion that this is quite possibly overall the best introductory text on ODEs out there.

The book consists of six major subtopics: first-order equations, general nth-order linear equations, systems and nonlinear equations, series solution methods, numerical solution methods and existence/uniqueness theorems. Most of the subjects tend to be divided into two or three chapters, with the first one or two containing the theoretical aspect and computational techniques and the other consisting of applications to real world problems.

At some 800-odd pages the book is quite long, but the sheer amount of material covered is simply astounding; the book has several types of special ODEs and solution methods that I have not seen anywhere else, and the authors go to great lengths to make every concept fully clear to the reader while still being quite rigorous. I am personally somewhat pure-math oriented but also needed some practice with applied problems, and this text is sure to please both students of mathematics as well as those of the sciences due to the very large amounts of subject material contained in both areas. (the book is split about 55-45 in theory/application)

One very nice thing is that if there is some doubt as to whether or not the reader is comfortable with something from another subject (i.e. real analysis), the book does not assume that the reader is familiar wih that topic, but rather it goes through a short review of the topic that is self-contained enough for readers who have not heard of the topic before to get a good idea of it. There are a variety of well-designed problems that provide plenty of practice along with some that expand upon the original concepts, and the average difficulty generally seems about right for the target audience. The numerical methods are also surprisingly robust considering that the book was written in 1963 and calculators/computers were not all that standard. Also, as was remarked earlier, this is one of the very few texts out there that contains the answers to all of the exercises, making it perfect for the self-study that I used it for; other authors/publishers should learn from this.

All things considered, this ranks among the best textbooks on any subject that I have ever seen, and coupled with the extremely low price, it definitely lies in the "must buy" category.

Excellent...Very well written
This is definitively the best introduction book to the differential equations that I Know until this moment. Although there are other excellent books on this topic, this one has the particularity that for each one of the topics that tries, has a collection of carefully elected exercises for the author, in such a way that the student won't feel frustrated of finding exercises that don't have a direct content with the exposed theory, also ordered in upward difficult . Each chapter is divided in lessons where it introduces step to step the elements that will serve him later on in particular in the understanding of some differential equation. With detail and accuracy, the only resource that is needed is to know how to integrate, the rest is in the book. The author doesn't consider that the reader knows something, it simply supposes that he doesn't know it, and then it enriches the text with methodological explanations that make that the text is almost self contained, without for it, to subtract depth in the topics. It is for my a true pleasure to sit down to read this book, of which I always learn on what should be made when one thinks of writing a book: to think of the more general possible reader.

Good but not perfect
Sure maybe you are a Math major then this book is a 5. But for us Physics/Engineering majors this book is a 4.

No Hardcover, No Solutions Manual, Format is bland, hard to write your own notes, and the physical quality is weak. More suited for a tom clancy novel than a Textbook.

All in all though if this were your only book in ODE...you would learn ODE well. Answers to most problems and good examples. Easy to follow. I think most of the problems areas are cause by the publisher trying to save money and lower the retail price than the author's ability to produce a quality text book. I hope the authors get picked up by Wiley or Adison-Wesley not a weak discount publisher like Dover.

WORTH MORE THAN MONEY
Harry Pollard was my professor for the second course in real analysis at Purdue in 1962 (he must have been writing this book then). He made differentials and manifolds crystal clear in the same easy way in which this book is written. Many authors belabor an 800 page text, and for some students this is overdone. However, if you want to get a genuine feel for ODE's as something more than a collection of techniques, you can profit highly from a leisurely but thorough tour through this book. ... Read more

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Great practical math
For those of us who would like to learn and master concepts of Linear Algebra and Differential Equations without too much useless theories, this book is for you. Teaches all concepts well, many examples and good explanations. Also really light!!! ... Read more

Book Description

The authors stress a more balanced approach, one that includes analytic, numeric, and graphical techniques. The book emphasizes modeling and qualitative theory throughout the course. It employs technology significantly and consistently, presents linear and nonlinear systems in parallel, and includes an introduction to discrete dynamical systems.This text grew out of the Boston University Differential Equations Project, funded in part by the National Science Foundation. ... Read more

Reviews (11)

Not for math majors.
I have only seen the preliminary edition of this book. I think that it is too spread out, its exercises involve long calculations but never any challenge and that it involves long sections of non-math that could very well be omitted. Often one has to skip five or six pages to get to the next available mathematics. It is a good book for someone that wants to learn a little bit of differential equations during their bed time reading, but should not be used for a sophomore level differential equations course.

An excellent introductory differential equations text
I have been teaching differential eequations for over 20 years so am very familiar with the "traditional" approach along with the more "modern" treatment. I have been using this text in my courses for several semesters now and really like it. Finally students can get a real feel for the topic which is/was completely absent from more traditional texts. Frankly, the traditional approach gives one the impression that differential equations (at this level) is simply a collection of party tricks. Nothing could be further from the truth!!

I have discovered that a different kind of student excels with this format; one who is not afraid to actually think about the material - what a refreshing change from the common, mindless "crank and grind" student approach!! Sadly, the latter group doesn't really learn any mathematics, just how to calculate - a task computers handle much better!!

The problems are fine and allow considerable classroom discussion and flexibility. The CD (DETools) has some shortcomings but you can't beat it for the price! The topic is fundamentally geometric in nature and much can be learned from playing with DETools.

Some reviewers complained about the numerical aspect of the text. Having worked as an industrial mathematician, I must say that more, rather than less, about numerical techniques would be good. In the real world, forget analytic methods (they simply don't apply) and reach for RK4 and better.

If you're looking for a text to use in your DE class, try this one. One warning, you can never go back!!

Horrible paedagogical dreck
This book is a DE text for students who've had the misfortune to have been subjected to "reformed calculus"--- i.e., calculus without algebra. There is very little substance here, only high-school level chit-chat and "qualitative analysis" of nearly trivial problems. The writing style is insulting to anyone other than brain-dead pedagogs.

A Student¿s Perspective
As a recent differential equations student, I have mixed feelings about this book. I did thoroughly read those portions of the book covered by my instructor, and I did learn enough from it to get an A in the class. So I'll concede that it does a fairly good job as a textbook. In fact, I found it relatively easy to understand, which surprised me given the subject. However, the book has two serious shortcomings.

First, it's too verbose. The authors probably could have cut the size of this book in half without sacrificing any of its clarity or utility; in fact, they would likely have improved upon both had they done so. Mind you, I'm not suggesting that it's boring, it's just too long for a student in a hurry.

The second shortcoming is its questionable value as a reference book. Most math books with which I'm familiar have extensive indexes, and do a good job of highlighting important concepts and formulas. This book does neither. The index for this 786 page book is just over nine pages long. That might not sound bad, but many of the entries refer back to specific examples and homework problems with arcane names like "Magic Fingers", "Glass Harmonica", and "Robo-lobster", even while many key words were omitted. To make matter worse, the authors (according to their preface for students) made it a point not to mark important material in a way that would make it stand out. They also wrote many of their more advanced examples in a way that forces students to derive the intermediate steps on their own. This is arguably educational, as it forces students to practice earlier material while they're reading, but I can only imagine the hell it's going to put me through when I have to refer back to the book years from now.

In short, if you have a lot of time on your hands, this is a great book from which to learn differential equations. However, it's a terrible reference book, and nearly impossible to skim. In fact, it's even hard to study from.

An Interesting Approach
Short story:

Overall a rather good book with a unique approach that focuses on qualitative techniques; it serves as a book which develops in the reader an understanding of differential equations rather than as a manual for simply solving them. It has, however, a few shortcomings, such as overemphasis on numerical methods and unchallenging problems.

Long Story:

This book was used in my first course in differential equations at Middlebury College, where I am a physics and math double major.

Advantages:

*A qualitative approach is employed to the solution but more importantly the understanding of differential equations. This approach forces the reader/student to use his/her inherent intelligence and creativity, rather than simply memorizing some formulas and techniques and mindlessly plugging and chugging.

*Applications are clearly related to the material rather than being the product of a trite, inconsequential link between the underlying mathematics and a real-world situation (all too often that is the case with math books).

*The CD Rom, when used appropriately, is useful in "bringing to life" the material and is a rather fun visual aide.

*Topics are usually well-explained (though in some cases the explanations seem rather murky and for that reason I would not recommend this for self-study).

Divadvantages:

*Too much emphasis on numerical methods. With computers around today to solve such problems in such ways, it would be better to keep numerical solutions to a minimum.

*Too strong a focus on biological/ecological problems and offered too few applications to areas like physics.

*Analytical methods could have been addressed a bit more thoroughly, as well as exemplified more frequently in the text. In place of solved problems, it seems, there were instead lines of computer code.

*The CD-Rom is pretty useless except as a fun toy; if you want something that will actually do the math for you, especially in the case of numerical problems, I recommend setting up an Excel document that can do Euler's method etc.

*The problems tended to be unchallenging. ... Read more

Book Description

With the success of its previous editions, Principles of Real Analysis, Third Edition, continues to introduce students to the fundamentals of the theory of measure and functional analysis. In this thorough update, the authors have included a new chapter on Hilbert spaces as well as integrating over 150 new exercises throughout. The new edition covers the basic theory of integration in a clear, well-organized manner, using an imaginative and highly practical synthesis of the "Daniell Method" and the measure theoretic approach. Students will be challenged by the more than 600 exercises contained in the book. Topics are illustrated by many varied examples, and they provide clear connections between real analysis and functional analysis.

* Gives a unique presentation of integration theory
* Over 150 new exercises integrated throughout the text
* Presents a new chapter on Hilbert Spaces
* Provides a rigorous introduction to measure theory
* Illustrated with new and varied examples in each chapter
* Introduces topological ideas in a friendly manner
* Offers a clear connection between real analysis and functional analysis
* Includes brief biographies of mathematicians ... Read more

Reviews (1)

One of the best
An ideal text for a first-year graduate students in mathematics studying Real Analysis. The exposition is complete and very clear, including a lot of optional material for the curious. A detailed introduction to Functional Analysis is also included. Those needing the infamous Radon-Nikodym theorem and theory of signed measures will need to skip around since this is presented in the very last chapter (not a big problem). Also, consult the authors' companion text Problems in Real Analysis, which could be very useful to those preparing for a qualifying exam in analysis at the PhD level. Overall, a highly recommend text. ... Read more

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A must have for the serious scientist.
Ruel Churchill 's Operational Mathematics is a very easy to follow full featured course covering LaPlace transform techniques. If you have ever wanted to solve differential equations with algebra, LaPlace transforms are for you. I used this book in a collage graduate course in integral transforms. Churchill ties in real world problems with each chapter to enhance your learning. Complex variables, Fourier series, Fourier transforms and inverse integral analysis are all covered in a very well done manner. A truly fun math experience. ... Read more

Book Description

This book is a text for a one-semester course for upper-level undergraduates and beginning graduate students in engineering, science, and mathematics. Prerequisites are a first course in the theory of ODEs and a survey course in numerical analysis, in addition to specific programming experience, preferably in MATLAB, and knowledge of elementary matrix theory. Professionals will also find that this useful concise reference contains reviews of technical issues and realistic and detailed examples. The programs for the examples are supplied on the accompanying web site and can serve as templates for solving other problems.Each chapter begins with a discussion of the "facts of life" for the problem, mainly by means of examples. Numerical methods for the problem are then developed, but only those methods most widely used.The treatment of each method is brief and technical issues are minimized, but all the issues important in practice and for understaning the codes are discussed.The last part of each chapter is a tutorial that shows how to solve problems by means of small, but realistic, examples. ... Read more

Book Description

Arem's CONQUERING MATH ANXIETY is a comprehensive workbook that provides a variety of exercises and worksheets along with detailed explanations of methods to help "math-anxious" students deal with and overcome math fears. The author offers tips on specific strategies, as well as relaxation exercises. The book's major focus is to encourage students to take action. Expertly constructed hands-on activities help readers explore both the underlying causes of their problem and viable solutions. Many activities are followed by illustrated examples completed by other students. This edition now comes with a "free" relaxation CD-ROM, and a detailed list of Internet Resources. ... Read more

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Conquering Math Anxiety
I found this to be an exceptional book. It provides excellent practical strategies to be successful in math. It covers everything from psychological/personal blocks that may hinder students from learning math to practical success strategies that students can apply immediately. I especially enjoyed the discussion on learning styles and the accomodations that can be used for better understanding of coursework. I found the chapters on positive self-talk, conquering test anxiety and study skills very helpful as well. Every math teacher should have this book on their shelf! ... Read more

Book Description

Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained. ... Read more

Reviews (2)

A great reference resource
This classic diffusion text continues where many other texts end, and covers a broad variety of problem types. This is an excellent resource for diffusion solutions for less-common boundary conditions and assumptions, including thorough mathematical developments of the solutions and many references to the original works. Non-mathematicians will often need to roll up their sleeves to digest portions of the derivations, but the insight into the solution processes is often very revealing. This makes this book an invaluable reference, although it is probably not well suited as your only book on diffusion.

Classic solutions to diffusion problems.
This book is a classic, collecting analytical solutions to common differential equations arising from common problems in mass transport. ... Read more

Book Description

This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, (including both linear problems and nonlinear conservation laws).These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are applied to eliminate numerical oscillations.The methods were orginally designed to capture shock waves accurately, but are also useful tools for studying linear wave-progagation problems, particulary in heterogenous material. The methods studied are in the CLAWPACK software package. Source code for all the examples presented can be found on the web, along with animations of many of the simulations.This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods. ... Read more

Reviews (2)

Good book to start with. Highly recommended.
This book starts from simple things and moves to pretty complicated staff graciously. It is useful even as an introduction to the hyperbolic equations. Finally, this is the only book I use at most every day. This is the book I would strongly recommend to all students who study this field and to researchers. It has a very good and comprehensive reference.

The author develop even the software (unfortunately, this is FORTRAN, not C). The source is available and well discussed in the book (there is a whole chapter). I did not use it but found this is a very good practice. It should be useful for student also.

Many things are really nice. For example, the book gives a very good view of the nature of oscillations in high order schemes, not only formulas. And so on...

However, there are few things I was not satisfied.

1. There are no comprehensive discussion about non-uniform and non-rectangular grids. It is not good, for example, for people who works in spherical coordinates (for example in some brunches of geophysics).

2. There is no information about FCT methods that are still very popular because they give a very straightforward way to use 4th and higher order methods. However, there is a reference to the Oran and Boris book, for instance.

3. It is sometimes really pure mathematical description especially for non-linear equations. It was really inconvenient for me. Fortunately, good reference helped.

There are more things were bothered. However, this is personal. The author works with the advection equation a lot, but does not like to discuss more the conservation form of continuity equation which I would prefer. In spite of author's efforts, I think still that the wave propagation method is not so convenient as flux method even for non-conservative equations. But it depends.

Finally, this book is definitely fine and, I think, it is the best among all books in this field (maybe except the Hirsch book which is "Numerical computation of internal and external flows" 1988). I would highly recommend it to buy.

nice introduction
This book provides a nice introduction to the mathematics behind finite-volume methods. After reading through the first half of the book on scalar conservation laws and systems, papers in JCP no longer seem as intimidating. The book is laid out very well, and the notation is consistent throughout. It is the best of the bunch when compared to Toro's Riemann problem book and Laney's Computational Gasdynamics text. ... Read more