Book Description

This volume teaches calculus in the biology context without compromising the level of regular calculus. The material is organized in the standard way and explains how the different concepts are logically related. Each new concept is typically introduced with a biological example; the concept is then developed without the biological contextand then the concept is tied into additional biological examples. This allows readers to first see why a certain concept is important, then lets them focus on how to use the concepts without getting distracted by applications, and then, once readers feel more comfortable with the concepts, it revisits the biological applications to make sure that they can apply the concepts. The book features exceptionally detailed, step-by-step, worked-out examples and a variety of problems, including an unusually large number of word problems.The volume begins with a preview and review and moves into discrete time models, sequences, and difference equations, limits and continuity, differentiation, applications of differentiation, integration techniques and computational methods, differential equations, linear algebra and analytic geometry, multivariable calculus, systems of differential equations and probability and statistics. ... Read more

Book Description

Reviews (6)

Very Good To Have On Your Shelf
The counterexamples here are a wonderful aid to educating intuition about definitions in Real Variables. It may sound strange, but I always thought of this book as entertaining reading: If you glance at the table of contents, you'll may find youself saying, "wait, no, that can't -- well, I guess so, but what does that look like?" In later conversations you may find youself saying: "wait a second, I seem to recall seeing somewhere a continuous nowhere differentiable function," or someting of the sort. Unfortunately, there are not a whole lot of these creatures in the book, but they are worth spending some (enjoyable) time with.

Gives you the extra edge
In this book, the authors present counterexamples of notions that seem "obvious" by handwaving or instinct. Some of the (counter)examples are well-known (ordered space which is cauchy complete but not complete) and some are highly contrived (two non homeomorphic topological spaces which is countinuous one-to-one image of each other). The latter categories is what makes this book useful.

You cant learn analysis by reading this book -- but you can learn how analysis works. I personally recommend this book to those who wants to work in analysis at least until graduate school. Mastering the book is a good preparation for oral exams and quals, and would increase your general understanding of the subject.

Topics range from real number system, differentiation and integration, sequence and series, measure, function in two variables, plane sets, topological space and function space.

A Bestiary of Analysis Monsters
For 200 years after it was invented by Isaac Newton, calculus lacked a rigorous foundation. In the 1800's the missing rigor was finally provided by the ingenious theory of limits, developed by Bolzano, Cauchy, Weierstrass, and others. This development, in turn, revealed the need to formulate and understand the structure of the real numbers. This structure was provided by Cantor, Dedekind, and Peano, who showed how the real numbers can be constructed from set theory.

But it was a Faustian bargain, because immediately a host of bizarre and counterintuitive examples were discovered - continuous functions that were nowhere differentiable, nonmeasurable sets, one-to-one pairing of points between the line and the plane. These peculiar entities were deeply disturbing to many.

Poincare said "Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose... In former times when one invented a new function it was for a practical purpose; today one invents them purposely to show up defects in the reasoning of our fathers and one will deduce from them only that."

These counterexamples displayed features that were nowhere to be found in the physical universe. When Richard Feynman was a physics graduate student at Princeton, he would tease his mathematician friends that mathematics was so easy that he could instantly decide the truth or falsehood of any mathematical statement they could give him. One day they challenged him with the grand-daddy of all the paradoxes, the Banach-Tarski paradox: That the unit ball in R3 could be divided into a finite number of pieces, and the pieces could, by rigid translation and rotation, be reassembled into two unit balls. But they made a mistake: instead of saying "unit ball in R3", they said "apple". Feynman quickly pointed out that the nonmeasurable pieces, that they had so rigorously defined, must split apart even every electron of the apple.

When I was a graduate student in mathematics, "Counterexamples in Analysis" was my favorite book, and I had a lot of fun amazing my fellow graduate students by quoting from it. Since then, however, I have swung around more to the viewpoint of Poincare and Feynman: "Logic sometimes makes monsters." From either viewpoint, however, the counterexamples are immensely entertaining.

Great for the coffee table
It can happen to anybody. There you are, minding your own business, when the though hits you: Does every continuous function have a derivative somewhere? You try to prove that it must. It sure seems like it must. How could it not? Hours slip by, and you've made no progress. What do you do? You pick up Gelbaum and Olmsted's classic "Counterexamples in Analysis". There on page 38 is an example of a continuous function that has no derivative; none; anywhere. No wonder you couldn't prove it.

It turns out that questions of the form "Does A always imply B?" entail proofs with two very different flavors, depending on whether the answer is affirmative or negative. The affirmative variety can be very difficult, as it usually deals with an infinity of things. But a negative answer requires only one solitary example of an A that is not a B; this is affectionately known as a "counter-example". These are the slickest little proofs around--often a one liner--and they can provide a lot of insight. Here's a trickier one: Are all linear functions continuous? Surprisingly, the answer is "no", which means there is a counter-example. Gelbaum and Olmsted show how to construct a discontinuous linear function. Case closed. They also provide examples of

A perfect nowhere dense set

A linear function space that is a lattice but not an algebra

A connected compact set that is not an arc

A divergent series whose general term approaches zero

A nonuniform limit of bounded functions that is not bounded

I won't give away any more (although there are hundreds). The book has chapters on real numbers, functions and limits, differentiation, sequences, infinite series, set and measure on the real axis, functions of two variables, metric and topological spaces, and more. Each section begins with a brief summary of the basic concepts and definitions, then launches into a list of terse counter-examples. This is simply indispensable for students of mathematical analysis, as it can help to explain why you cannot weaken those seemingly stringent hypotheses to various theorems; if you do, one of these quirky counter-examples will rush in and ruin your day. This is a great book to have on hand. I highly recommend it. (I won't tell you how it ends.)

Indispensable for students of real analysis
Graduate students of mathematics, just buy this book - no questions asked. You need the examples and this level of understanding. For the price there are just no questions - buy it! ... Read more

Book Description

The wide-ranging debate brought about by the calculus reform movement has had a significant impact on calculus textbooks. In response to many of the questions and concerns surrounding this debate, the authors have written a modern calculus textbook, intended for students majoring in mathematics, physics, chemistry, engineering and related fields. The text is written for the average student -- one who does not already know the subject, whose background is somewhat weak in spots, and who requires a significant motivation to study calculus.

The authors follow a relatively standard order of presentation, while integrating technology and thought-provoking exercises throughout the text. Some minor changes have been made in the order of topics to reflect shifts in the importance of certain applications in engineering and science.This text also gives an early introduction to logarithms, exponentials and the trigonometric functions.Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the "Rule of Three") to give students a full understanding of calculus. This text places a significant emphasis on problem solving and presents realistic applications, as well as open-ended problems. ... Read more

Amazon.com

David Goldberg's Genetic Algorithms in Search, Optimization and Machine Learning is by far the bestselling introduction to genetic algorithms. Goldberg is one of the preeminent researchers in the field--he has published over 100 research articles on genetic algorithms and is a student of John Holland, the father of genetic algorithms--and his deep understanding of the material shines through. The book contains a complete listing of a simple genetic algorithm in Pascal, which C programmers can easily understand. The book covers all of the important topics in the field, including crossover, mutation, classifier systems, and fitness scaling, giving a novice with a computer science background enough information to implement a genetic algorithm and describe genetic algorithms to a friend. ... Read more

Reviews (14)

I didn't like it
Well... The book is not bad but chapter III lacks clarity...
Chapter III is supposed to give mathematical insights into genetic algorithms. It starts by proving the schema theorem (which is OK) and then tries to cover the math related to GA's. This chapter is very difficult to follow. Unless you are familar with GA's and the math related to them this chapter is difficult to understand

I wish all books were like this !!
This is one of the best books I've read for genetic algorithms and AI. I wish all books were like this. It is not pedagogical in its style (unlike Computational Intelligence - Engelbrecht), it is well written, very insightful and slowly takes you into the depths of GA/AI, so it's great to follow. This book contains source codes in Pascal (which is easy to translate to any other language - although you'd want to write your own based on OOP), pseudo codes, examples, and plenty of ways to understand the way GA's work. BUY THIS BOOK and you'll save yourself a lot of sweat and mind boggling wierd explanations from supposedly good authors. I'll never sell this book.

One reader wrote a comment about how this book could be cut in half, and is not suitable for CS majors, my response to that: "I'm a CS major, doing my Ph.D., my professor, my colleagues and almost everyone in the field has a copy of this book, maybe you never got past chapter2 in his book. If you want proof of theorems, there's lots of research papers available, almost all of which refer to Goldberg's book."

The Best Book in AI so far
This book got me so excited that I was not able to continue reading. I had to put it down and walk about. The power of the learning classifier system (SCS) has yet to be fully explored. A system that organizes data (classifies) and learns new rules (generate new rules via the genetic algorithm) is a combination that still takes my breath away. The only negative to this book are the trivial problems the algorithms solve. There is none for the "bucket brigade" version of the SCS. Overall though it is an awesome book presenting a very powerful algorithm that has yet to be fully explored.

Provided me with the elements of a solution
I was looking for an automated approach to finding an optimum run sequence through a changeover matrix. The programming examples gave me the elements I needed to experiment and then fine tune the approach for a working search algorithm. I found the book a good companion in my "voyage of discovery".

For me, the book works two levels, the basic pieces to "play with" are presented clearly in chapters 1 and 3, and practical implementation suggestions are spread throughout the text.

By developing programs in Visual Basic, experimenting with search parameters and re-reading sections of this book - I learned something new!

Could be cut down to a third without loosing information
This is the only book I have read about Genetic algorithms, but it seems that it covers the field pretty well.

In the preface it says that it is aimed a beginning graduate students, and since I have a M.Sc. in Computer Science and I just wanted to read it for fun I thought it would be for me. But I found that it uses way to many words to explain very basic things (e.g. almost a page to explain binary numbers) while many of the difficult equations just was presented without proper proof. So the book could have better if it had been cut down to a third and then supplemented with the proper proofs. So if you are a Computer Science graduate I cannot recommend this book. Given the fine books that Addison-Wesley usually publish I was quite disappointed with this one.

But if you are a student in other fields and just want an "intuitive" impression of Genetic Algorithms without the mathematical rigor it is probably good.

Chapter 1: An introduction to genetic algorithms with examples. This chapter is excellent.
Chapter 2: The mathematical theory behind genetic algorithms. This is not done very well since many of the equations isn't proven or explained properly.
Chapter 3: A Pascal program for the sample in chapter 1. This seems unneccesary since any proficient programmer easily could have implemented the program based on the information in chapter 1.
Chapter 4: The history of genetic algorithms and a number of applications all taken from research. Both seem unneccesary.
Chapter 5: An extension of the techniques presented in chapter 1. This is good.
Chapter 6-7: Introduction to machine learning. Is ok.
Chapter 8: A concluding chapter without any real new information. ... Read more

Book Description

This carefully organized, very readable book covers everyessential topic in discrete mathematics in a logical fashion. Placingeach topic in context, it covers concepts associated with discretemathematical systems that have applications in computer science, engineering,and mathematics. The author introduces more basic concepts at thefreshman level than are found in other books, in a simple, accessibleform. Introductory material is balanced with extensive coverage ofgraphs, trees, recursion, algebra, theory of computing, and combinatorics.Extensive examples throughout the text reinforce concepts. More combinatorics/algebraic structures than in most books. Detailed discussion of and strong emphasis on proofs. Extensive, in-depth presentation of topics. Large selection of applied and computational problems, ranging from the elementary to the more advanced. More topics in probability and more statistical interpretations than other texts. Comprehensive discussion of topics such as finite state machines, automata, and languages. Earlier introduction of matrices and relations, Boolean algebras and circuits than most texts. Includes algorithms for many constructive tasks that occur in discrete systems. ... Read more

Reviews (1)

A pretty good book
While the table of contents is very good, too much time is wasted in developing preliminaries. The text should quickly move into the core of the subject, but instead spends 220 pages developing the elementary material. A good reference for teachers of discrete mathematics with emphasis in combinatorics and not in computer science. ... Read more

Book Description

Reviews (7)

It is the Globally Optimal Solution!
I can't say more than what already been said by other reviewers. To recap,

F = {all excellent combinatorial optimization books}
cost(this_book) <= cost(y) for all y in F.

;)

Inexpensive, excellently written, and quite interesting!
I had this book on my shelf for two years before taking a serious look at it, and only wish I had read it much earlier in life. Christos Papadimitriou has written quite a gem! On one hand this book serves as a good introduction to combinatorial optimization algorithms, in that it provides a flawless introduction to the simplex algorithm, linear and integer programming, and search techniques such as Branch-and-Bound and dynamic programming. On another, it serves as a good reference for many graph-theoretic algorithms. But most importantly Papadimitriou and Steiglitz seem to be on a quest to understand why some problems, such as Minimum Path or Matching, have efficient solutions, while others, such as Traveling Salesman, do not. And in doing so they end up providing the reader with a big picture behind algorithms and complexity, and the connection between optimization problems and complexity.

After reading this and Papadimitriou's "Introduction to Computational Complexity" (which I also highly recommend), I now consider him one of the best at conveying complex ideas in a way that rarely confuses the reader. I also had the priviledge of attending one of his talks on complexity, and he seems just as effusive and transparent as a lecturer as he does a writer. Ah, for once I bought a Dover book that did not disappoint.

It worths exponentially much more than its price
One could buy this book for different reasons: interests in combinatorial optimization, of course; interests in what Papadimitriou has to say, since his thoughts on this subject are definitely invaluable; perhaps the price is a good reason alone.
Whatever the reason, however, I think that would be a rare event to remain duped.

I was preparing my exam in Computability and Complexity when I first used it. I've been wonderfully surprised by the amount of definitions, algorithms, concepts I've found in this book. I think one could use this book for a simple course on Algorithms, on Computability and/or Complexity, on the whole Combinatorial Optimization, and the book would be always and costantly useful.

The chapters on algorithms and complexity, or those on NP completeness have proved to be gems. The chapters on Approximation and Local Search are great, and they feature a bunch of detailed and excellent quality stuff (e.g. there is a detailed treatment of Christofides' algorithm to approximate the TSP, that is quite an idiosyncratic topic).

All in all, a very great book, with a value exponentially greater than the very insignificant price.

A great book and a great deal
As a computer science graduate student I carried Papadimitriou and Steiglitz with me almost every day. Its target subject is combinatorial optimization, but going through this book, you might think that graph theory and computational complexity are just subfields of combinatorial optimization. It builds a beautiful theory that brings these and other fields together, and with a fraction of the page count of, say, Cormen, Rivest Leiserson. Now that it's a Dover book, it's a fraction of the price I paid, and I was gladly willing to pay that.

A Masterpiece on Combinatorial Optimisation
Christos Papadimitriou, my hero is a hope for all of us who wish to master the fascinating field of Combinatorial Optimisation. Especially recommended are the chapters on matching, NP Completeness and Approximation Algorithms.

As another reader has remarked, this book is quite old though (published first in 1982). For a more to date book on Combinatorial Optimisation, one might want to look at Cook, Cunningham, Pulleyblank and Schrijver's book on Combinatorial Optimisation (published in 1998). ... Read more

Reviews (6)

This book Is Really VERY good at teaching you algebra.
Ok, I have got to tell you up front that I have NEVER been a Math wiz, but after reading this book I can do algebra. I have never really gotten the hang of algebra. However I will be starting College in the fall, and I knew that if I was to have a chance of making it Past the first few weeks, I'd better Learn Algebra, and fast! So, I found this book, and I was sceptical, but after only 10 pages or so, I started to get a grasp of how Algebra Really works. Now I have read the book, and now I have a good understanding of how Algebra works. (I CAN DO IT NOW!) I would recomend this book to anyone struggling in algebra. However I must warn you This book does OVER simplify things in a few cases. Just don't get confused, or sidetracked. That is the only reason I could not give this book a 5 star rating.
In conclusion this book works.

Now I Get It!
Time to go back to college. Math was never my strongest subject. In fact it was my weakest. I had forgotten almost everything I learned in Algebra.
I tried two books that claimed to make algebra a breeze. Promises. Promises.
Then I bought PAINLESS ALGEBRA for a mere $8.95 and was pleased to find clear step by step explainations. Explanations that didn't require three readings before they made sense.
I think the best way to approach the book is by reviewing the previous chapter before you begin a new chapter.
A minor complaint: Too few exercises, as is the case with most of these types of books. But you can always find a workbook that will have problems for you to work out and the answers.
Being mathematically challenged I recommend this book.

This Book Works
I have always had a fascination for higher mathematics, but I've never bothered to learn much of anything about it. When I bought this book, I had forgotten just about everything I ever knew about Algebra 1. I couldn't remember the difference between a coefficient and a variable. I ought to be embarrassed, but I am now too old to care what people think of me for reading a book that's obviously designed for kids. Now I'm starting to think that, if math is really this much fun, I'll be reading PAINLESS DIFFERENTIAL EQUATIONS in another year or two.

I'm going back to college because of this book!
In '93, I withdrew from college because I could not pass pre-algebra. I never took algebra in high school, so I was lost in my college pre-algebra class by the second week. My professor told me to withdraw in order to save my GPA which was quite high.

Fast forward to 2001. I bought this book and it really opened my eyes! I can see where I made my mistakes in class and I can understand the concepts that my prof. and a tutor could not get me to understand. Everything seems so simple now--some of my past mistakes were very simple ones!

This book is real easy to understand. The book breaks down each concept and the problems are broken down step by step so it's real easy to see what you have to do. It took me only a half-hour to memorize the Order of Operations and apply that to the problems. If you use this in tandem with a book you have for a class, it will make things really easy. The books takes you from the beginning (what a variable is) all the way to graphing two dimensions on a graphing table.

My husband who was a math whiz in school looked at this book and said it's an Algebra 1 book. I'm hoping to understand the concepts thoroughly so I can take a Pre-Algebra placement test and pass for credit.

The only negative things I have to say are that there aren't enough problems to work on. And, my husband said it was a shame that there was only ONE problem (at the end of the book) that shows graphing in three dimensions. He said since the author put that in, she should have continued on with more problems for that concept, or she should have left it out.

I'm just so happy about the fact that I can finally understand Algebra! It's like a lightbulb went off in my head. Now, I'm going back to college to finish my degree!

Easy To Read & Understand
My 12-year-old wanted to learn more about algebra. He is teaching himself by reading this book. The author clearly explains topics without a lot of confusing text. There are cartoons and illustrations in the book to break up the monotony. It's kind of like a workbook. Highly recommended. Wish there was a "Painless Geometry." ... Read more

Book Description

This new ADVANTAGE SERIES, one-semester prealgebra text smoothly bridges the gap between arithmetic and beginning algebra and is suitable for a variety of course formats, including lab (both supervised and self-paced), lecture, group, and a combination of all three. With a heavy emphasis on important study skills and habits, PREALGEBRA, Third Edition, aims to instill mathematical confidence and help build a solid foundation for students going on to future math courses. The text provides a complete and thorough treatment of algebra and arithmetic, allowing students to better understand the relationship between the two. Group activities, scientific calculator exercises, critical thinking problems, and exercises requiring written answers are included throughout the text, in accordance with the latest NCTM Guidelines. As part of the ADVANTAGE SERIES, this new version will offer all the quality content you've come to expect from Van Dyke/Adams/Rogers sold to your students at a significantly lower price. ... Read more

Book Description

The new edition exhibits the same strengths from earlier editions including the Rule of Four, an emphasis on modeling, exposition that students can read and understand and a flexible approach to technology.

• The conceptual and modeling problems, praised for their creativity and variety, continue to motivate and challenge students.
  

Reviews (43)

Absolutely irritating
My College Calculus professor uses this book as a suppliment to provide examples for the class use. Everyone hates the problems as they are vague and lack any explanation on how to solve the problem or even where to begin. It appears to me that someone wrote a book simply to create problems that cannot be solved by the book's explanations. Calculus requires a working understanding of the ideas and concepts of the base math before an sort of obscure application should be used. I would not recommend this book to anyone, unless they already have a good understanding of calculus and wish to delve further into the application of the math to the real world. In that case, buy the book. For the other 95% that are just wanting to learn calculus; go buy a different book that teaches you something first.

Awful
Ok this textbook does not teach at all. It basically just provide examples that is it. IT doesn't say why you do it or explain the calculus at all. The way the book explain calculus does not help at all when it comes to doing the problems. The answers in the back of the book does not match the problems throughout the chapters.

As an undergrad, this book is not student friendly at all. I basically did not use the textbook and depended on the professor and math tutoring. I love math and I understand it, but this book does not help. I am unable to learn from this textbook.

Terrible
This is an absolutely terrible textbook. Hardly any explanations in any of the sections for problem solving. And the homework problems rarely relate directly to the material in the preceding section. The student solutions manual has only every fifth problem and, not unexpected from the attitude of the authors, none of the difficult homework problems are among those that are solved anywhere.

The Best Way To Learn Calculus
I got my PhD and am now a professor of physics. A long, long time ago, I used photocopies of this book. The book hadn't been published yet, and was still under review.

A decade later, I still remember this book.

Poor students will hate this book. It requires you to think critically and analytically. It requires you to understand the material well enough to be creative in your problem solving. It is definitely more of a concepts book than it is a "do this integral", "test this series for convergence", "differentiate this function" type of book.

Good students will love this book. You often have to make connections between concepts yourself, but the exercises are obviously written to help you make the connection. This is a thinking person's book. Not a mindless student's book. And, I feel obligated to point out (even though it should be obvious), even a 4.0 GPA student can be a "mindless student". A 4.0 means nothing in this grade inflated, rampant cheating, educationally watered down society we live in.

Last words. I used this book before it got published. Our professor used photocopy handouts. I think we were guinea pigs for the book. The one criticism I have is that sometimes you really need just to solve 20 very difficult integrals in a row. Sometimes brute force calculational problem solving is just necessary, not to learn the concept, but to gain the skill required to master a subject.

The handouts I recall didn't have the 100 odd mindless calculational type problems. Most of the problems were subtle, thinking person's problems. I think the best approach would be a combination of the two: problems to teach concepts and problems to teach skill. This book (in the form I saw) had more of the former, and very few of the latter.

As far as the "back of the book" odd numbered problems being often wrong, I can not comment on that. Even as a undergrad, I never used "back of the book answers". Maybe they were wrong, and maybe they weren't. In any event, that wouldn't kill such a wonderful book for me.

Strange...but I liked this text!
I'm currently in the middle of my third semester using this text. I used this text for Calc 1, Cald 2, and am using it for Calc 3. At first, I HATED this text book. The exercises are rarely the same type of problems found in the examples, and not every odd answer is given in the back of the book (There is a solution manual that is very helpful, or if you're lucky enough your school may have the complete instructor's solution manual as a .pdf). That being said...

This book will make you a better problem solver, period. It forces you to grapple with the ideas and concepts presented in Calculus, and then apply it in different ways. Yes, there are some "plug and chug" exercises, where you just follow certain algorithms presented in the examples as a way to get to solutions. But most of the problems are much different than the examples, and if you can work through them (which any one can do with some persistence) you'll understand the material all the better. And, you'll be a better problem solver in other disciplines like computer science, physics, or engineering.

I have several people in my other classes who did not use this text, and the difference between those who learned calculus from this text, and those who learned if from a different text, is definately noticable. So, if this is your book, be prepared to struggle, but know that it will probably be worth it in the end. ... Read more

Book Description

The wide-ranging debate brought about by the calculus reform movement has had a significant impact on calculus textbooks. In response to many of the questions and concerns surrounding this debate, the authors have written a modern calculus textbook, intended for students majoring in mathematics, physics, chemistry, engineering and related fields. The text is written for the average student -- one who does not already know the subject, whose background is somewhat weak in spots, and who requires a significant motivation to study calculus.

The authors follow a relatively standard order of presentation, while integrating technology and thought-provoking exercises throughout the text. Some minor changes have been made in the order of topics to reflect shifts in the importance of certain applications in engineering and science.This text also gives an early introduction to logarithms, exponentials and the trigonometric functions.Wherever practical, concepts are developed from graphical, numerical, and algebraic perspectives (the "Rule of Three") to give students a full understanding of calculus. This text places a significant emphasis on problem solving and presents realistic applications, as well as open-ended problems. ... Read more

Reviews (3)

Some high points, but some serious flaws
Student reviewer here.This book is very attractive and well-illustrated.It has some helpful material for review and/or catching up for students in introductory Calculus classes in Chapter 0 and it spends significant time illustrating real world scenarios in which the concepts can be applied.

The problems I have with the book are the insufficient number and variety of examples provided, the arbitrary notations often used in lieu of more demonstrative ones that would be easier for beginners to understand, the poor explanation of abstract mathematical concepts and procedures, and the incomplete and at times inaccurate accompanying text, the Student Solutions Manual, which is often nothing more than an answer key for odd numbered problems that can also be found at the end of the text, begging the question: why shell out all that extra dough?

The could improve the book dramatically by getting an editor to look over the text for clarity and adding more explanation, demonstration, and homework problems, and by making the Solutions Manual more demonstrative instead of skipping steps that may not be evident to beginners.

Very Clear!
This is a very good book for undergraduate students. I use this book for my Calculus III class, and I feel the authors do a good job here because they explain every concept carefully. I love the proof that follows with every concept.
This book can be a tool book not just for a textbook. If you are looking for a claculus textbook you might consider to use this book!

Not the Best; Not the Worst
I suppose someday someone will come up with the perfect calculus textbook.It's certainly not this one.It provides basic explanations, then jumps to advanced, leaving all the but the math whiz in the dust.Example--Riemann sums--the book showed the basics, then the first problem involved a cubic equation, not even hinted at in the text.And, maybe I'm old-fashioned, but I like a book that has been fully proof read, and bound by competent binders (Kudos to McGraw-Hill for doing the right thing and offering to replace all our books.)The web page, however, is very good. ... 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

Mathematica Navigator is the only book you need to understand and use the new Mathematica 5.0. Part tutorial and part handbook, this updated guidebook provides a thorough introduction to the software plus practical information and tips for using Mathematica on a daily basis to solve mathematical problems. The book emphasizes the use of graphics, methods of applied mathematics and statistics, and programming.

While no previous experience with Mathematica is required, most chapters also include advanced material so that the book will be a valuable resource for beginners and experienced users. You'll want to keep it close by your computer for easy reference.

Based on the soon to be released Mathematica 5.0
With the CD-ROM, the whole book can be installed into the help system of Mathematica
Most chapters, while starting from the basics, go up to advanced topics
Studies several real-life data sets ... Read more

Reviews (9)

Got Mathematica? Buy This Book NOW!
The positive reviews were right on the money, this book is the best! It allowed me to start using Mathematica with ease, compared to the many hours of past frustration while working on optimizations. I fought endlessly, struggling to decipher the software's baroque navigation, cryptic errors, hostility to the user which borders on abuse - but now Mathematica and I are becoming great friends thanks to Heikki Ruskeepaa's wonderful tome. THANK YOU FOR WRITING THIS BOOK!!!

Of particular benefit is the guidance s/he provides for best practices in formatting cells to avoid common, productivity-killing pitfalls.

Absolutely Great Mathematica Textbook
While it is unlikely that there is a pure Mathematica course anywhere, the textbook for it already exists!
Mathematica Navigator by Heikki Ruskeepaa is an absolutely wonderful book that teaches you everything you ever wanted to know about Mathematica.
Out of about 10 books I've used, this book is THE BEST on Mathematica out there.

Solutions
To solve practical problems in Mathematica the navigator is very usefull. If you want to go deeper,"modeling nature" by Gaylord and Nishidate is a usefull guide.

The best book on Mathematica.
Forget Stephan Wolfram's book "Mathematica" -- Ruskeepaa's Mathematica Navigator is the indispensible book on your desk next to the computer when using Mathematica.

Mathematica Navigator
Outstanding book for Mathematica. Ruskeepaa does an outstanding job of coherently, and logically explaining how to use Mathematica in a straight forward way. If there was only one book to buy to learn Mathematica this should be the one. ... Read more

Book Description

Linear Algebra with Applications is a flexible blend of theory, important computational techniques, and interesting applications. Instructors can select the topics that give the course their desired perspective. The text provides a solid foundation in the mathematics of linear algebra, while introducing some of the important computational aspects of the field, such as algorithms. The presentation of interesting applications has been one of the most compelling features of this book provides students a well balanced coverage of standard linear algebra topics that apply mathematics by examining real-life applications, making for a enlightening learning experience. ... Read more

Book Description

Jerome E. Kaufmann and Karen Schwitters built this book's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This no-frills text consistently reinforces the following common thread: Learn the skill, use the skill to help solve equations; and then apply what they have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundamental problem solving skills necessary for future mathematics courses. ... Read more

Book Description

Designed specifically for the Calculus III course, Multivariable Calculus, 7/e, contains chapters 10 through 14 of Calculus with Analytic Geometry, 7/e. For a description, see Larson et al., Calculus with Analytic Geometry, 7/e

Book Description

In this new ADVANTAGE SERIES version of David Cohen's PRECALCULUS: WITH UNIT CIRCLE TRIGONOMETRY, THIRD EDITION, Cohen continues to offer a book that is accessible to the student through a careful progression and presentation of concepts, rich problem sets and examples to help explain and motivate concepts, and continual guidance through the challenging work needed to master concepts and skills. This book is identical to PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, Fifth Edition with the exception of the first four chapters on trigonometry. As part of the ADVANTAGE SERIES, this new version will offer all the quality content you've come to expect from Cohen sold to your students at a significantly lower price. ... Read more

Reviews (1)

The best math book I've seen--period.
This is THE math book for those preparing for the calculus or (like me) revisiting the subject. The book is clear, concise, and stands up well to heavy use. Additionally, the book has tons of examples; contains sections A & B for each chapter. The 'A' section is all that is necessary to continue to calculus, but 'B' will enhance learning if you choose to delve deeper. The study guide that accompanies the book is absolutely excellent--an average student like me can go through the whole book without an instructor if aided by the study guide. ... Read more

Reviews (2)

A recommendation from an algebra teacher!
For the last three or four years, I have recommended this book to my students' parents. I teach algebra (grade 8) and pre-algebra (grades 7 and 8) and have found that his book is written in a non-threatening, easy to understand manner. It is a perfectly wonderful reference book. Math is scary enough...this book demystifies algebra. Love it!

Algebra to Go
This is the best reference handbook that parents and teachers will fine it useful for students. Algebra to Go, "demystifies algebra for students in 8 grades and up by explaining key and often complex math topics in a way that's clear, friendly, and understandable". It is also a great refresher for parents who may have forgotten a thing or two about Algebra.. ... Read more

Reviews (1)

Wonderful Book...
Lial and Hornsby have written a number of books on Algebra. Hence, their expertise in this field of Mathematics and ability to deliver in the form most suitable for the middle and high schoolers , in particular is wonderful. Review Exercises at the end of each major subdivision provide means for readers to practice. And also ensure that the readers have gained overall expertise in the particular subdivision. Also , another advantage of this book , in contrast to many other available books, is the cumulative review exercises that engulf concepts from all the preceding chapters, which provides the means to show how these topics are interrelated. Tests provided also aid in this process. The topics are well organized and explained. Very Good Book... ... Read more

Book Description

Provides avenues for applying functional analysis to the practical study of natural sciences as well as mathematics. Contains worked problems on Hilbert space theory and on Banach spaces and emphasizes concepts, principles, methods and major applications of functional analysis. ... Read more

Reviews (6)

The definition of classic
As shown in the first line on the cover:
Wiley CLASSICS Library

Possibly the BEST math book that I have ever read
The presentation of concepts, definitions, and proofs are clear and EASILY understandable! The problems are illustrative and reinforce one's understanding of the material. I am in the middle of a class in functional analysis. It is a JOY to use this book. If you are interested in functional analysis and can't take a class in the subject, this book should prove to be sufficient by itself. It is that good! I cannot speak highly enough about this great book!

The Place to Start
Heir professor Kreyszig has done what the majority of other authors have failed to do. Namely, he has compiled a book whose only real prerequisites are a solid understanding of Calculus and some familiarity with Linear Algebra. Obviously this required level of understanding is minimal, to say the least, and this is one of the main reasons I feel so strongly that this book is number one in its category. Moreover, since the majority of "introductory" texts on Functional Analysis are primarily directed toward graduate students the aforementioned requirements coupled with a wide selection of topics makes this book easily accessible to advanced undergraduates and begining graduate students. I highly recommend this book to anyone interested in actually learning Functional Analysis and also to the ambitious self-learner since Kreyszig has included both hints and solutions to selected exercises. In regards to the exercises and examples contained in the text, they are well chosen, insightful and at no time does Kreyszig leave a major theorem/propostion to the reader. In fact, he provides many fully worked examples which are left as exercises in most other texts. My hat goes off to professor Kreyszig for such a wonderfully well written text and also to Wiley for continuing to publish this classic.

Functional analysis - as it should be taught
Most books on analysis could be subtitled "One damn theorem after another: written by mathematicians for mathematicians". This book is different. Though rigorous and concise, it takes the time to explain what theorems really mean and why concepts are worth understanding. It shows that functional analysis is a generalization and extension of many concepts from undergraduate algebra and calculus. As such, it is powerful, beautiful, and above all, useful.

The first half of the book covers the basic theory of metric spaces, normed/Banach spaces and inner-product/Hilbert spaces. Applications include approximation theory and numerical integration; differential and integral equations; and the Legendre, Hermite, Laguerre and Chebyshev polynomials. The second half of the book is devoted to spectral theory, the final chapter discussing operators in quantum mechanics. Although integration theory is not formally covered, the book does show its relationship to functional analysis.

The book provides numerous examples, counter-examples and exercises. The exercises really are do-able - mostly short but instructive - and answers are provided for odd-numbered questions.

A fantastic introduction to functional analysis
Kreyszig's "Introductory Functional Analysis with Applications", provides a GREAT introduction to topics in real and functional analysis. This book is part of the WILEY CLASSICS LIBRARY and is extremely well written, with plenty of examples to illustrate important concepts. It can provide you with a solid base in these subjects, before one takes on the likes of Rudin and Royden.

I had purchased a copy of this book, when I was taking a graduate course on real analysis and can only strongly recommend it to anyone else. ... Read more