Book Description

Customer Reviews (4)

a good reference, but it could be organized better
I found this book very intimidating at first, since it is basically written backwards from how I feel it should be.The simple, elegant and relatively intuitive applications make the last chapter, the complex and lengthy definitions and theorems make up the first few chapters.

If the first few chapters were appendices and it focused more on the creation of special functions from the three fundamental ones and applications of semi-integrals and semi-derivatives to diffusion it would be more accessible.

Don't be afraid of skipping the first portion of this book, and only looking at the last few chapters (which only infrequently refer to the dense material of the first few chapters).After reading the last half of the book, you may be more motivated to try to understand some of the details and proofs behind these intriguing operators, found in the first part.

I also found their non-standard presentation of hypergeometric series insightful.

A classical book
The Fractional Calculus by Keith B. Oldham is a classic book on the topic. To my best knowledge, it was the first book devoted exclusively on fractional calcylus. It includes a useful tables of fractional derivatives. It also discuss in detail many of the original dmathematical derivations that in more recent books are simply ommited by citing the Oldham's book. Unfortunately, in some parts its notation is a little complicated and not intuitive. Any way, it is a mandatory reference in any worl on fractional calculus.

Excellent book!
This is a great book. The only prerequisite I would say is calc 2 (know your series and integration very well) and perhaps a little bit of ordinary differential equations.

Summary : An excellent introduction to the field.

This was the first textbook devoted entirely to Fractional Calculus, and remains perhaps the best introduction to the field.It is a graduate level text for mathematicians, engineers and scientists, written in a clear pedagogical style, with excellent references and bibliography.

A brief historical survey traces contributions as far back as Leibnitz.Basic results of the traditional integer-order differential and integral calculus are summarized, and properties of some special functions are examined, as a foundation for what follows.Later in the book, many advanced special functions are described in terms of the hypergeometric function.

The notions of differentiation and integration are unified as differintegration.Grünwald's definition is presented which extends differintegration to non-integer orders, applicable to functions which satisfy certain conditions.Other definitions used historically are shown to be equivalent to, or special cases of the Grünwald definition.General properties of differintegration are examined, such as linearity and homogeneity.Results corresponding to those of traditional calculus are derived, such as Leibnitz' rule.Significant differences from traditional calculus are also shown, such as the lack of a useful chain rule.

The preceding results are illustrated by example, using elementary algebraic, trigonometric, and logarithmic functions, and some special functions, such as hypergeometric, Bessel, and Heaviside.The semiderivative and semiintegral are accorded additional scrutiny, due to their importance in applications.Tables of formulae for semiderivative and semiintegral are provided for elementary functions and common special functions, as well as formulae valid for arbitrary functions.The LaPlace transform or tables of Riemann-Liouville transforms may be used to extend these tables.

Practical techniques are presented both for numerical differintegration, suitable for computer implementation, and analog differentegration by means of electrical circuits.Some extraordinary fractional differential equations and semidifferential equations are solved analytically.Techniques of the fractional calculus are applied to a number of well-known problems in traditional calculus, including Abel's equation and Bessel's equation.

The diffusion equation and its relatives are treated in a short chapter on practical applications of the fractional calculus.The usual formulations for planar and spherical geometries are examined, including incorporation of sources and sinks, and restriction to finite media.

However, the most recent innovations in fractional calculus are not described, such as generalization to complex order.Also, although algorithms for evaluation of differintegrals may be easily derived from the definitions through the book, a set of exemplary pseudocode fragments would be most welcome.These minor flaws are understandable, given the 1974 vintage of the book.A little more material could have been given on Heaviside's Operational Calculus and its relationship to the fractional calculus - it exists only in the references.Similarly, although the link to Weyl calculus is noted, it is not elaborated.Finally, a few examples from rheology would enrich the applications section.

COMPARISON : This book covers much the same area as Kenneth Miller and Bertram Ross in "An Introduction to the Fractional Calculus and Fractional Differential Equations", Wiley, 1993.

Whereas Oldham and Spanier base their treatise largely on the Grünwald definition, Miller and Ross prefer to use the equivalent Riemann-Liouville definition.Both books contain comparable historical surveys, but Oldham and Spannier provide a more extensive bibliography, and employ a better pedagogical style.Miller and Ross provide results in forms better suited to computer implementation, and rely more on matrix techniques.Also, Miller and Ross provide a chapter on Weyl Calculus, and their practical examples include one from hydrology, but omit diffusion problems.Other than this, the two books share most of their strengths and have only a few weaknesses ... Read more

Book Description

Students can gain a thorough understanding of differential and integral calculus with this powerful study tool. They'll also find the related analytic geometry much easier. The clear review of algebra and geometry in this edition will make calculus easier for students who wish to strengthen their knowledge in these areas. Updated to meet the emphasis in current courses, this new edition of a popular guide­­--more than 104,000 copies were bought of the prior edition--­­includes problems and examples using graphing calculators.

Customer Reviews (26)

Beginner's Calculus
This book is great for when you're beginning Calculus, but it doesn't give intense hard problems for it. Great study guide to review the basics but isn't the hardcore stuff.

Worth the investment
I bought this book to supplement my class textbook when I was having trouble in Calculus I. I chose this book over the many other supplements available because I knew I could carry forward into Calculus II and Multivariable Calculus.
As mentioned in many other reviews, this book provides plenty of practice problems, so if you're having an issue in one particular area in class or in the class's textbook, this is a good place to go to really thoroughly understand it. They provide a decent number of examples and solutions. Within each chapter are explanations of the lesson, followed by example problems with step-by-step solutions, and finally "Supplementary Problems" for you to solve on your own (though there are no answers in the back for you to check your work). It's also got some really good lists of trig formulas, geometric formulas, common integrals, and common derivitives.
The only thing I dislike about the book is that the explanations are rather poor compared to a textbook, but it's hardly surprising seeing as how this is an outline and that it covers topics from the beginning of Calc I all the way through differential equations of first and second order in under 600 pages.
I would totally recommend this book for the student looking to supplement a confusing textbook, or looking to brush up on concepts that have gotten a little rusty.

alright
This book does provide coverage of all major material in traditional calculus,however the manner in which the material is presented is similar to that of a condensed textbook which is niether entertaining nor completely clear. If you want a quick study guide then this is the book for you provided you understand most information you read in a textbook.All in all this book is alright ,but I would't depend solely on it.

I am VERY Happy with this Book - great 4 self-study
In order to take an advanced statistics course (since I have been out of college awhile) I have to take a calculus test. They gave me a sample of 60 questions from prior years and recomended a text that cost $180!!!

Well for 1/15 of the price of the expensive text, I can get about 55 out of 60 questions answered through this one. The ones that are not covered in this book pertain to complex integrations - I'll buy the Schaum's Advanced Calc text and get my answers and still have tons of money left over.

*** Another thing is that the first few chapters are an excellent review of pre-calc, something I did not think I would need but it turns out to be more useful than I thought. ****

The covering of some topics, like LaHopital's rule is better than most texts.

I have not encountered typos yet - when I have that that I did - once I plunge into it more - turns out he is right and I was mistaken.

****Having numberous worked out problems and problems with at least the solutions to check yourself is GREAT FOR SELF STUDY ****

kinda pointless, same examples you'll encounter in your book
not that great, if you have a good text, you'll notice that the examples are pretty much the same ... Read more

Book Description

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

Customer Reviews (2)

Good for quick review; you still need to do homework.
This book should help you in reviewing your notes that you took in class. As the title of the book suggests, this is a crash course for general calculus.

Figures and graphs in the book should help you understand many different problems and how their solutions are derived. You should expect to solve many of the problems in the book yourself, on paper, also. That is the only way to understand mathematics; by doing it yourself. This book should help you get started in the right direction because of the ample examples present in it.

Do not expect to get rid your other calculus books and use this as the sole text for reviewing Calculus. This book is meant to be a companion to your other calculus textbooks, not their replacement. As good as it may be, you still need detailed explaination of rules and theories about Calculus, which are not explained in this book.

Outstanding aid to Calculus!
I'm a graduating senior and i just bought this book to get myself ready for college this year! It's an amazing book and is easy to understand. ... Read more

Product Description
Calculus with applications to the management, social, behavioral, and biomedical sciences. ... Read more

Book Description

Variational analysis is a fruitful area in mathematics that, on one hand, deals with the study of optimization and equilibrium problems and, on the other hand, applies optimization, perturbation, and approximation ideas to the analysis of a broad range of problems that may not be of a variational nature.

Customer Reviews (1)

DEFFERENTIAL EQN'S
math methods in egineering, statics of rigid bodies ... Read more

Book Description
When it comes to understanding one of your most intimidating courses--calculus--even good students can be confused.Intended primarily for the non-engineering calculus student (though the more serious calculus student will also benefit), Calculus for the Utterly Confused is your ticket to success. Calculus concepts are explained and applied in such diverse fields as business, medicine, finance, economics, chemistry, sociology, physics, and health and environmental sciences. The message of Calculus for the Utterly Confused is simple: You donÕt have to be confused anymore. With the wealth of expert advice from the authors who have taught many, many confused students, youÕll discover a newer, fresher, clearer way to look at calculus.DonÕt wait another minute--get on the road to higher grades and greater confidence, and go from utterly confused to totally prepared in no time! ... Read more

Customer Reviews (5)

Good Idea-less than perfect execution
This little book is a terrific idea. However, it needed a careful editing before printing. The diagram on page 33 was not labeled. The answer on page 51 is wrong.The answer on page 55 contains an answer (t=533) that not only is wrong, but should have rung a bell with the authors when they got it. (The correct answer is 53.3, which can easily be verified.) This proves that using a hand calculator without thinking about what size the answer ought to be leads to embarassing errors. This actually is a very instructive example, but the conclusion that 27 years is the most appropriate time to harvest the forest has no supporting theory. At this frequency of errors, I expect to find more as I progress.

I'm sorry I wasted my money
Based on the description of this book, I thought I could gain a better grasp of the subject, only to discover that I was more confused than when I started.New concepts are thrown out with no explanation and examples are obscure at best.To make things worse, the silly cartoon-like attitude ofthe book is insulting to anyone who's looking for a serious solution totheir dilemma.The implication is that the material is as easy tounderstand as a child's book, but there is no help for those who don'timmediately grasp the concepts.After completing a Calculus class (andfeeling quite comfortable with the subject) I revisited the book andconfirmed that it is a terrible presentation for those who are in fact"Utterly Confused".I have sent it unceremoniously to the locallandfill.

A handy reference for calculus students.
This is one of the most easy to understand and clear calculus books that I have read in a long time. It concentrates on some of the most used/practical subjects that most college students will need for theirundergraduate studies. I have recommended this book to some of my friendsand the reason for me writing this review is because I would like to letother "confused" readers know about how much of a big help thisbook has been.

very helpful
I found the book very useful.I was terrified when I learned that I wouldhave to have calculus for my MBA program, but the book really helped mesucceed.I ended up with an A in the class, the first A I have everreceived in math.

The most confusing calculus book I have ever purchased
This book is confusing in two ways: First, it launches into complexconcepts, equations, problems and solutions without ever explaining theunderlying fundamentals; the authors assume that the reader is already incommand of many concepts and terms that would almost certainly escape aperson who is "Utterly Confused" by calculus.Second, althoughthe content of the book would be useful to a person who had successfullycompleted a formal education in calculus and was in need of a review, theauthors chose to bill this book as a quick and easy way to understand theintricacies of calculus for those who have failed to grasp the basicfundamentals.They do a great disservice to the readers whom they dupeinto buying this book by making false claims about its nature. ... Read more

Product Description

In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation.

As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.

Book Description
This powerful problem-solver gives you 3,000 problems in calculus, fully solved step-by-step! From Schaum’s, the originator of the solved-problem guide, and students’ favorite with over 30 million study guides sold—this timesaver helps you master every type of calculus problem that you will face in your homework and on your tests, from inequalities to differential equations. Work the problems yourself, then check the answers, or go directly to the answers you need with a complete index. Compatible with any classroom text, Schaum’s 3000 Solved Problems in Calculus is so complete it’s the perfect tool for graduate or professional exam review! ... Read more

Customer Reviews (19)

A good PRACTICE guide- not a way to first learn the topic....
I bought this book and several others to help my daughter with her AP calculus.Along those lines, this book is not very useful as the AP examiners have gone off and deviated from the traditional bread and butter calculus topics (volumes of revolution, techniques of integration, related rates, max/min/inflection points, etc.). They have fallen in love with calculating averages, the fundmaental theorem of calculus, and their calculators (see my other reviews).So if your buying this book for that purpose, it won't really help as this book covers only traditional techniques and topics without the need of a calculator.

HOWEVER, for a supplement to traditional class material, this is a great book.I agree with the prior reviewers that this is not a book that will teach you calculus from the start - you need to already know how to take a derivative and integrate, what is meant by a volume of revolution, related rate, and so forth.However, if you want EXCELLENT scores, practice is the key and this book gives you a lot of practice.After a while, you will realize that there are only so many variations on a particular topic that can be tested and they keep coming up over and over again (I orginally took calculus in the 1980's and ran across the same problems).

In summary, if you need to first learn the basics of the material, this book is not for you. If you already know the basics and want practice on the bread and butter topics, this is an excellent way to do so.I doubt that your instructor will give you problems not covered in some fashion in this book.

Be very careful!
If you want a reference book, this ain't it. Nor a textbook. You must understand the concepts before you even open the volume. It would then be a great help in applying your knowledge to real-world problems.

I say, "would" because the numerous typos and mistakes make it a dangerous tool to use. Some errors are obvious (if annoying), some will mislead and puzzle you and some, well... just pray.

I give it a three because it may still be useful. Just be careful how you use it!

Save your money
Every year a new class of desperate students buy into the Schaum no-help books.Save your money or try Michael Kelley.
Sincerely,Bert-Chapel Hill, North Carolina

Not Much Better Than a Solutions Manual
I purchased this for a Calculus II course because the book I had had some rather challenging problems. I bought it because I thought it was going to be exhaustive in its solutions. Unfortunately this was not the case. Some problems in calculus require less explanation that others. For this book however essentially all are given the same weight. Because of this you are left with a "how in the world did they come up with that?" type of feeling at the end of the problem. It is a good book however and the sheer number of problems solved is helpful when you have very specific things in your homework you need to see. Also there are general lessons on the topic before each chapter. This is a good resource but should be used in conjunction with other calculus books.

Forget this, if you want the best and most comprehensive TRY
THE KING OF ALL MATHEMATICAL PROBLEMS!!!!!!!!!

Problems in Mathematical Analysis (Hardcover)
by g. yankovsky (Translator), B. Demidovich (Author
Publisher: mir publisher; 4th Printing edition (1976)
ASIN: B000GTC2GA ... Read more