Reviews (9)

Review of Book that i bought.
Partial Differential Equations (Graduate Studies in Mathematics, V. 19) GSM/19 (Graduate Studies in Mathematics)
The best book for an introduction to PDE's for a graduated student
If you're looking for a book to learn PDE's at a basic level, please don't buy this book. In the other hand, if you have already worked on this subject it's not surprising why the book doesn't include some topics or techniques. The appendix is for remembering basic facts while you are reading, so if you don't acknowledge this subjects, you have to study them before (you can't ask a book to have an appendix that covers all the related theories you need).There are several books which cover very well the classical theory and the linear cases in the weak sense. As one of the reviews says, this is an excellent book for a GRADUATED COURSE so it is assumed you have a basic background on the subject and you know what you should know about other subjects such as analysis. The book has the basic tools forTHE NON-LINEAR CASES which can't be seen in a basic course. If you don't believe me, try to find a book which cover the same content in such an easy way.

This book opened a new world for me
After several bad lectures I had already almost given up on PDE. But when I got this book into my hands, I was immediately drawn into the subject and couldn't put it down until I finished it completely. After less than a month I felt how a new world had opened up to me, and I can since feel its effect when I go to lectures.
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Subjects:  1. Differential Equations    2. Differential Equations - Partial Differential Equations    3. Differential equations, Partia    4. Differential equations, Partial    5. Mathematics    6. Science/Mathematics   

Reviews (7)

Used to be a good book...
I used the 6th edition for a lot of the begining studying on many calculus subjects. While this book is easy, it still teaches you the stuff. You understand the material, not just get these mechanical processes to apply to the freakishly hard problems that you get. I would suggest looking for the 6th edition though...
superb
This is big, heavy, hardbound freshman text that will take you very slowly but completely into single-variable calculus.It also contains an exhaustive section on analytic geometry.
Not Happy with 7th.
I loved 6th. ed.But I'm not happy with the 7th.Bivens and Davis have clearly taken over and ruined a great textbook.I'm looking for another textbook the next time around.The other teachers at my college seem to agree.Read more

Subjects:  1. Calculus    2. Mathematics    3. Science/Mathematics    4. Calculus & mathematical analysis    5. Mathematics / Calculus   

Reviews (21)

Excellent introduction to measure & integration theory
This classic is the best book on measure theory and Lebesgue integration that I have been able to find.Royden is an outstanding writer; he is great at motivating even the most abstract of material, and he helps the reader to develop a strong sense of intuition, in areas of mathematics where most peoples' intuition can be very weak.I find the proofs and equations exceptionally easy to follow; Royden makes excellent use of notation.The index and table of notation make this book a good reference as well.Some reviewers criticize this book as being unclear, but I think this is a reflection of the difficulty of the subject, not of this book.This book covers one of the hardest subjects to learn, and it does a very good job of it.
Not very instructive to newcomers
I'm currently earning an MS in Mathematics, and am currently completing the last few weeks of my Real Analysis course using this book as its text.On the whole, I don't like this book.
Good on a second review
I earned an MS in mathematics.Part of the reason I switched to physics for my Ph.D. was my experience with real analysis through courses involving both the Rudin and the Royden books.The material, on first impression, was just so much abstract gobly-gook.Later on, with significant training in statistical physics, working on a trading floor as an econophysicist, I was introduced to the world of options pricing requiring a mastery of measure theoretic methods.The excellent book by Bingham and Kiesel on options pricing is built heavily on the material covered in Rudin and Royden.Suddenly, when this measure theory cr*p had an APPLICATION to real world problems, me dried up intellects perked up.On a second passage of Rudin and Royden, I can now see that these aren't actually that bad.Still, I think grad schools in math should drop Rudin and Royden, and build the material within these books with applications to stochastic differential equations and probability theory over the course of one year.So much pain, so much abstraction seemingly for the sake of abstraction will go away, and so much understanding will be had, and maybe...just maybe...mathematicians might find well paying real world jobs.
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Subjects:  1. Advanced    2. Functional Analysis    3. Functions Of Real Variables    4. Mathematical Analysis    5. Mathematics    6. Measure theory    7. Science/Mathematics    8. Mathematics / Advanced    9. Real analysis   

Reviews (84)

Simply the best ...
If you didn't use this classic in your first pass at elementary
Analysis 101
Principles of Mathematical Analysis by Walter Rudin can rightly be called "the Bible of classical analysis".I have seen it cited in more books than I can count.And after a full year of working through the book in graduate school, I can see why.As many other reviewers here have pointed out, this book requires more than a little of that magical quality called "mathematical maturity".Simply defined, "mathematical maturity" is the ability to read between the lines and fill in the gaps in a given mathematical text.
Pretty Good
I want to start by listing some of my complaints. First of all, I do not think it is entirely appropriate for a student's first exposure to analysis. The majority of students would be better off taking a an honors calculus or advanced calculus course first, so they can learn how to prove things about the continuity of specific functions or convergence of series before they start proving things and functions and series in general (a look at, say, Bartle's book over summer break would probably work just as well, but my point remains the same). Second of all, the exercises are, for the most part, extremely challenging. While this is not a bad thing by any means, the book would probably benefit by having a few extra, easier problems. Third, it could use some pictures, not that many, but they would certainly help illustrate some of the ideas. Fourth, a few of the proofs are very difficult to understand because they are perhaps too concise (for example, the Cauchy-Schwarz inequality in the first Chapter). Finally, $140 is prohibitively expensive.
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Subjects:  1. Advanced    2. Mathematical Analysis    3. Mathematics    4. Science/Mathematics    5. Calculus & mathematical analysis    6. Mathematics / Advanced   

Reviews (5)

An all time classic
From the masters of the finite element method, this may well be the best book ever written on the subject. In this book, the authors come across as the sages of ancient India preaching what they know is the best, guiding us, and setting a stage of research for the years to come. This is a monumental piece of work in the history of engineering.

The milestone in FE analysis
This book is really THE milestone, the only one I really enjoy. A page-turner, a must for all people into FE stuff.

Excellent book for starters in the field
This is the ideal book for beginners in finite elements, though the approach is slightly more theoretical. If you have a good background in linear algebra and are comfortable with matrices etc, you should have notrouble finishing this one. You can aim at the definitive work by ProfessorBathe after finishing this one. ... Read more

Subjects:  1. Engineering - Civil    2. Engineering - Mechanical    3. Mathematical Analysis    4. Science/Mathematics    5. Technology    6. Technology & Industrial Arts    7. Mathematics for scientists & engineers    8. Technology / Engineering / Mechanical   

Reviews (10)

Very useful book
This is a great book for those who want to learn quantitative finance, but don't have the benefit of being enrolled in a financial engineering program. It has the advantage of being self-contained and begins instruction from the ground up: you can "cold start" on the subject with this book. Just a basic knowledge of differential equations (non-stochastic) is required.
If you already know the field
If you already know almost everything it is a very good book. No error and the guy knows what he is doing. However, if you know everything, why do you want to buy this book?
This is a highly recommended work for any quant.
As I write this in June of 2005, quantitative finance has grown up. What was once a cross-over subfield of finance with a veneer of mathematics is now a field unto itself, and hence, in the past decade there have been an explosion of books which often replicate or restate what has been said before with little new to add. Also, there remains an unforgiving gap between introductory texts that are too superficial and specialists' mathematics books that are rigorous and difficult works beyond the commitment for mastery of the busy, intelligent, practical front-line quant. In addition, works that were once adequate are now simplistic and under serve their readers by lulling them into false confidence. Into this fray Dr. Mark S. Joshi's "The Concepts and Practice of Mathematical Finance" enters with a modern voice and delivers what previous texts have only promised and failed to. The work lives up to its title by presenting both concepts and practicalities, and makes other works that do neither well obsolete. Those familiar with my other reviews on quantitative finance texts know that I place a premium on clarity, and on this front Joshi deserves six stars, for he is a master of what William Strunk called "the plain style." I am always sensitive to the fact that many of the world's best quants come from nations where English is not the first language. Readers from China, France, Germany, Greece, Italy, Norway, Sweden, Russia and eastern Europe will enjoy Joshi's clarity and find his English easy to follow. It would be impossible to cover everything in quanfin in a single volume, however there is nothing horribly glossed over here and neither is there a single wasted word or equation.
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Subjects:  1. Derivative securities    2. Finance    3. Interest rates    4. Mathematical Analysis    5. Mathematical models    6. Mathematics    7. Options (Finance)    8. Prices    9. Probability & Statistics - General    10. Reference    11. Science/Mathematics    12. Mathematics / Applied    13. Probability & statistics   

Reviews (4)

Very good for struggling in Real Analysis
There is no problem solutions for Real Analysis texts available in U.S. since most of the teachers believe that Math students in grad level should be more creative. However, not all students in Real Analysis are potential mathmatician. If they lost in class and must study by theirselves, they may feel frustrated missing all the stuff contained in problems. The material in "Principles of Real Analysis" may not superior much than other famous text(like Royden, I think Royden is clear enough but too much mysterious things lie in problems.). But use it with this workbook, you will find much comfortable in self study. It helps a lot not only in my homework assignment, but also in my understanding.

A must have!!!
This book rocks! It covers practically all the major topics of an introductory course in graduate Real Analysis. Excellent solutions that aid in the understanding of the material. This book's worth is immeasurable, or should I say, non-measurable.

Must have one
Great guide, must have for anyone taking Real Analysis. ... Read more

Subjects:  1. Functions of real variables    2. Mathematical Analysis    3. Mathematics    4. Science/Mathematics    5. Calculus & mathematical analysis    6. Mathematics / General   

Reviews (69)

Calculus From a Practical Point of View
I like this book because I hate limits.From a strict mathematical point of view limits are standard for explaining calculus.But from a practical point of view (physicists, engineers, economists) the notion of the infinitesimal may be the most appropriate.It's worth noting that Thompson's degrees of smallness are an accurate reflection of the theory of nilpotent infinitesimals described in "A Primer of Infinitesimal Analysis".A combination of these two books might make for a great introduction to practical and alternative-theoretical calculus.

Don't be afraid of maths.
If all maths teachers explained maths as clearly and gently as Mr. Thompson, very few, especially the ladies would no longer say I can't do maths. We are desperatly short of mathmaticians in this country and this usually starts when at secondary school level.
The concepts of calculus as clear as possible
A topic as complicated as calculus can be approached in many different ways, each appealing to a different kind of audience at a different level of understanding.I began my second college career as a physics major and consequently had to take calculus.Despite a firm grasp of precalc algebra and trig, I didn't really grasp the concepts at an intuitive level, which is necessary for facing anything other than very obvious problems cooked up for the occasion.Calculus Made Simple offered me a window into the crucial concepts and let me enter the mindset needed for tackling calculus problems.I read the original version without the benefit of Martin Gardner's improvements (I am sure he did a spectacular job) so I am not sure about the new version, but the writing did seem a little dated at times.It didn't bother me, but I know for others who might already be turned off by having to learn calc, it could just be another detail that pushes them away.A more modern approach is How to Ace Calculus, which I also found useful.Be warned, though, for those about to take calculus for engineering and the physical sciences, these books deal with grounding you in the most basic nuts and bolts of the subject.The problems you encounter in, say, the Thomas's calc textbook become waaaay more complicated than what you get in these guides.Regardless, I give the book high marks and hope you find it helpful too. ... Read more

Subjects:  1. Calculus    2. Mathematics    3. Science/Mathematics    4. Calculus & mathematical analysis   

Reviews (2)

Professors Should Choose Another Book
This was my undergraduate textbook for Advanced Calculus I and II (as they were called at my school).I am returning to school to start my master's degree this next term and am going through the book to refresh my memory.
Another excellent Real Analysis Text
The style of this book is a bit like Robert Bartle's Introduction to Real Analysis. It is detailed and rigorous. It is an excellent book for those who want to learn Real Analysis. ... Read more

Subjects:  1. Advanced    2. Calculus    3. Functions of real variables    4. Mathematical analysis    5. Mathematics    6. Science/Mathematics    7. Mathematics / Advanced    8. Real analysis   

Reviews (18)

Great Supplement
This outline will work best for those looking for a concise supplement to their course text.The strength of this outline is in the solved problems.The weakness is in the explanation of concepts.As advertised, the book contains over 1100 fully worked problems.These problems are indeed fully worked and looking over them can be of tremendous value if you are struggling with solving particular problems in your class.If you are having a tough time with the concepts rather than the problems of calculus I would not recommend this book.The explanations are kept to a bare minimum and tough topics like delta-epsilon proofs and Reimann Integrals are not explained in detail.For instance, this book will not try to justify why you can set delta equal to epsilon to complete your limit proof, it just tells you to do it (which is exactly what you need to do to solve the problem).In other words, this book will help you solve the problems you need to solve in order to pass your exams, but it will not necessarily help you understand why those solutions work.So please do not buy this thinking it will have fuller conceptual explanations.Its strength is in its fully solved problems.

Everything you need
This book will show you everything there is in calculus.It is not organized perfect, but the information is great.I am taking Cal 1, 2, and 3 so I use the book a lot.It has been a great buy, and I recomend it.

Great Resource
This book is a great resource for those out there who want to enhance their knowledge of calculus and supplement the instruction of a professor. It can also be used to a limited extent as a replacement. This book is invaluable to me, as I suffer from sub-standard education conditions and the schaums method breaks things down easily and clearly. ... Read more

Subjects:  1. Calculus    2. Education    3. Mathematical Analysis    4. Mathematics    5. Outlines, syllabi, etc    6. Problems, exercises, etc    7. Science/Mathematics    8. Study Guides    9. Calculus & mathematical analysis    10. Mathematics / Calculus   

Reviews (1)

Disappointing at best
The book was a major disappointment. I am glad that I did not purchase it for my class, but instead borrowed it. The ordering of topics and emphasis choices never seemed to make sense to me. The layout throughout most of the text is like one long, run-on sentence. The underlying structure of numerical analysis never developed and I was left swimming in meaningless details while the basics were short-changed by an over abundance ofspecialized algorithms. Perhaps the text's curriculum could be saved by a capable professor, but alas my professor was just as scatter-brained as the text. More pictures would also have been helpful. A replacement text I recommend, which covers the first, matrix theory portion of this book, is David S. Watkins' Fundamentals of Matrix Computations. ... Read more

Subjects:  1. Mathematical Analysis    2. Mathematics    3. Numerical analysis    4. Probability & Statistics - General    5. Science/Mathematics    6. Calculus & mathematical analysis    7. Mathematics / General   

Reviews (5)

Not for the uninitiated
I bought this book hoping to learn about matrix analyis. I did not. Thisbook is simply a reference manual with plenty of theorems, axioms etc. withlittle explanation. They give it to you rough and row. NOT A SINGLE SOLVEDEXAMPLE, and not evensolutions for the exercises given in the book areprovided. If you intend to learn about matrix analysis, as I did, let notthe 5 stars review mislead you. Don't make the same mistake, this book isnot for you.

An encyclopedic reference for matrix analysis and linear alg
Horn and Johnson's MATRIX ANALYSIS is simply a masterpiece. You can findeach and every result in matrix analysis along with it's proof in thisbook. Look at their companion volume "Topics in Matrix Analysis"too. Some of these results cannot be found elsewhere.

Excellent book.... for the initiated
Horn and Johnson has written an excellent reference book onsomewhat-advanced linear algebra (from the point of view of an engineer).There's a lot of treasures in this book, but this book is NOT for beginninglinear algebra. Rather, it is written as a handy reference to review andlearn certain topics in linear algebra.Read more

Subjects:  1. Algebra - Linear    2. Linear Algebra    3. Mathematical Analysis    4. Mathematics    5. Matrices    6. Science/Mathematics    7. Mathematics / Algebra / General   

Editorial Review

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

Reviews (7)

hidden methods?
Perhaps the most interesting part of this book is missing. For a comprehensive listing of integrals, there is no better book than this. Remarkably easy to find a desired integral, if the book covers it at all.
CD-ROM version may not work for you.
The paper version is a real touchstone for the practice of all manner of applied mathematics.The CD-ROM version belongs in the discount bin.Here is why:
This software is unusable on mac's and unix systems.
I bought this software hoping that it would help me to find required mathematical formulas faster. At home on my powermac (OSX.1, OS9.2) I only see messed up windows. Furthermore, the formulas are unreadable, using an archaic font. Trying to save the day, I went to my linux machine at work reading "Your operating system, Linux 2.2.19-7.0.1, is not supported by this software. It appears that the software is only suitable for some SUN and SGI machines. It only appears to run properly on a windows machine. From an editor, who I remember, is one of the few persons finding errors in Knuth's TeX system, I expected much better. ... Read more

Subjects:  1. Calculus    2. General    3. Mathematics    4. Mathematics (Specific Aspects)    5. Reference    6. Science/Mathematics    7. Tables    8. Integral equations    9. Mathematics / General   

Reviews (19)

Horrible
Reading this book is like riding on the back of a Bull. This book is horribly terrible. It is not an Introduction to Real Analysis as the author assumes the reader has familiarity with most of the topics. There are very few Examples and the worst thing about reading this book for me is coming accross the statement like "We leave it to the reader to show that ..." or another one like "We leave it to the reader to write out the detail of the proof". How can the author(s) say that and yet call the book an "Introduction" when in the real sense they take you half way and leave you there? I regret buying this book. Just looking at the cover makes my bllod pressure rise. There are few explanations, few examples and many excercises. This book is Horrible for a bigginer in Analysis. I wish I never bought this book and I will never ever buy any other book written by the same author(s).

Kohei Sato's review is absolutely correct
Reading the signs while driving on an interstate through a large city only helps if you know where you are going, what highway & exit numbers to look for. Reading this book is like being lost in a big city. It was written for people who already understand real analysis. So, if you're one of the many who begin this book with no previous experience in analysis, and you get a professor that teaches straight from the text, be prepared - you will need at least one tutor. Hopefully, the authors will consider writing a book for undergrad students, with more examples and longer homework solutions. Some of the exercises are so far removed from the text, it makes you wonder if the authors truly believed that students would be able to complete these problems. I made straight A grades through college algebra & trig, as well all three levels of calculus, yet I cannot understand anything in this book after the first chapter. If you want to learn real analysis for the first time, do not waste money on this book.

Good intro to real analysis.
This is a good book from which the neophyte can learn the ropes of mathematical analysis.It is clear, lean, to-the-point, and gives the reader a taste of what doing mathematics is like, viz, theorems and proofs.Most importantly, it does a good job of introducing the epsilon-delta method of proof to the reader, who most likely has up to this point learned mathematics as merely a collection of calculational techniques.
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Subjects:  1. Calculus    2. Functions Of Real Variables    3. Mathematical Analysis    4. Mathematics    5. Science/Mathematics    6. Mathematics / General    7. Mathematics for scientists & engineers    8. Real analysis   

Reviews (1)

Statistics text for people who understand statistics
Kuehl covers a lot of statistical designs, and provides great examples and practice problems.However, the book is not "user friendly" even for student who have had several semesters coursework in regressionanalysis.Also, the author tends to change his notation from chapter tochapter without telling the reader, thus creating great confusion.Forexample "r" or "k" could signify replicate.Somesections are poorly organized. ... Read more

Subjects:  1. Experiments    2. General    3. Mathematical Analysis    4. Numerical Analysis    5. Probability & Statistics - General    6. Research    7. Research & Methodology    8. Science    9. Science/Mathematics    10. Scientific Methodology And Research    11. Statistical methods    12. Statistics    13. Mathematics / Statistics    14. Mathematics for scientists & engineers   

Reviews (15)

A Pleasure to Read
First of let me state that I own the 2nd edition of this book, and that I am a doctoral student in computational physics.
Revolutionize the way calculus is taught
This is the textbook used for the math 223/224 Theoretical Calculus and Linear Algebra sequence in Cornell University. The book is designed for prospective math students. Although the book mainly follows a rigorous development of the theories of multi-dimensional calculus, the mathematical machinery used in developing the theories is immensely broad, especially in linear algebra. The book covers most of the standard topics in a first semester linear algebra course and touches on many other areas of mathematics such as, real and complex analysis, set theory, differential geometry, integration theory, measure theory, numerical analysis, probability theory, topology, etc. The highlight of the book is its introduction of differential forms to generalize the fundamental theorems of vector calculus. The author is not the first one who follows this path. There are many other books written before this one that have similar approach, such as Calculus On Manifolds by Spivak, which was written 40 years ago and was too old to suit modern students.
Confusing book
Math and Physics major
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Subjects:  1. Algebra - Linear    2. Algebras, Linear    3. Calculus    4. Linear Algebra    5. Mathematics    6. Science/Mathematics    7. Differential equations    8. Mathematics / Calculus    9. Vector & tensor analysis   

Reviews (2)

The best introduction to probability and measure
The book very nicely develops the basics of measure theory from a probability perspective (e.g. includes Caratheodory extension theorem, Lebesgue-Stieltjes measures, weak convergence and Kolmogorov extension theorem). It then gives a brief introduction to functional analysis and proceeds to probability theory, martingales and concludes with brownian motion and stochastic integration.
Exceptionally Clear
I first used this text in the earlier version, which comprises the first half of the book, in a one-year course in Hilbert Spaces and Lebesgue Measure theory when in the first year of grad school.The material is presented in a clearly written manner and the exposition is some of the clearest mathematical writing I've seen in a subject which is replete with textbooks.Read more

Subjects:  1. Mathematical Analysis    2. Mathematics    3. Measure Theory    4. Probabilities    5. Probability & Statistics - General    6. Science/Mathematics    7. Set Theory    8. Mathematics / General    9. Probability & statistics   

Reviews (6)

Improves on the classic
As a previous reviewer has noted, Walter Rudin's Principles of Mathematical Analysis is the standard textbook for a rigorous analysis course. Rudin's book is very good because of the level of rigour and abstraction, the bredth of material covered, the way it forces the reader to fill in the blanks, and because of the challenging exercises throughout. In my opinion, Pugh has managed to improve on the classic in every aspect.