Product Description
Classic text leads from elementary calculus into more theoretic problems. Precise approach with definitions, theorems, proofs, examples and exercises. Topics include partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Numerous graded exercises with selected answers. 1961 edition.
... Read more

Customer Reviews (20)

it helped me prepare for advanced calculus
In 1963 I asked Lynn Loomis what I should bring to his course math 55 in abstract analysis (see Loomis and Sternberg) and he said I should know the theorem

that a continuous function on a closed bounded interval has a maximum.So I got a copy of Widder and read the proof. I recall it as clear and rigorous.

Thus I presume the rest of the book is similar.It fulfilled my need for rigorous background for abstract advanced calculus so I recommend it.

By the way,most of the critical comments here about it being old fashioned or criticizing the notation seem to me like the sort of remarks made by novices who

do not understand what they read and confuse terminology with content.

(I got B+/A- in Loomis' course in 1963/64 and have been a professional mathematician for the past 40 years.)

Great reference book
Prices in today's technical book market have gone ... well ... crazy. Dover deserves no end of praise for offering well made books of classics at a reasonable price. David V. Widder's, "Advanced Calculus" is such a book.
Even setting aside price, this is still a very, very good book ... maybe just a tad behind Apostol's "Mathematical Analysis," but still one of the best. Good featuresare: a) it covers much territory ... covering all the must topics of advanced calculus, and then some (i.e., gamma function); b) the proofs are sound, but do not enmesh the student in minutiae; c) the author has good intuition regarding what are the sticking points of a new concept, and takes care to cover these clearly.
Of course, as always, there are slight weaknesses. The main one is that in certain places the book seems "quaint" ... understandable, as it was first written some sixty years ago. I can't resist giving just one example: to solve a certain exercise, the student is urged to use a slide-rule! ... just getting one might cost more than the book! To its credit, the book employs a type of vector notation ... but the notation is lightly dated. There are diagrams; they are passable, but not great. (Come to think of it, Dover is not famous for great diagrams.)
At one point the writer almost seems to tip over into the "forbidden world of infinities and infinitesimals." I find this a plus rather than a minus.(This is my main criticism of Apostol: he not only shies away from infinitesimals, but gives the impression they are the "phlogiston" of mathematics.)

Great Price
The book is a reprint of an earlier version and had a great price.Couldn't believe it was priced so low.

Antiquated
This is a second edition of a book that came out in 1947 and it's obvious from the style that the style of the mathematics is very old fashioned here.
Students who are used to functions with domains and ranges, cartesian products and all that might hate this book. Those who have had little exposure to the more abstract view such as metric and topological spaces might well love it.
I personnally could not stand it and would relegate it to a museum piece.
Let me give examples of what I mean:
f(x) the function. Anyone who's modern will hate this: it's just f the function, and mentioning the variables can be useful if you have a formula, but what if you don't?
Dependent and independent variables: that's a nineteenth century style.
Defining a vector as a directed line segment is in my view outrageous, and what's this doing in chapter 2?
The discussion of the Heine Borel theorem would gain by being stated in more abstract terms than just real intervals.
I recommend you look at the Wikipedia article on this to see how this is done in today's abstract (and far more powerful) style.
You could also look at Rudin's books on analysis for a totally different approach.
However if you are willing to swallow this antiquated view of things it's a useful book, but not one I would recommend if you want to pursue higher mathematics.

Great book
I bought this book when I decided to go for graduate studies in mathematics. I was away from college for 3 years and wanted to refresh some of the advanced calc material. You could not ask for any better book. The generic Calculus book I used in college was too basic and this provided a nice bridge and a solid description of the "advanced" calculus. Although the order of the chapters are a little weird, it gets the job done without any lousy explanations. One thing to note is that "brdiging" book. So not so advanced but provides a nice transition if you want to look at some advanced calc books. This neverthless is a great addition ... Read more

Product Description
Praise for the First Edition

"An enticing approach to the subject. . . . Students contemplating a career in statistics will acquire a valuable understanding of the underlying structure of statistical theory. . . statisticians should consider purchasing it as an additional reference on advanced calculus."
–Journal of the American Statistical Association

"This book is indeed a pleasure to read. It is simple to understand what the author is attempting to accomplish, and to follow him as he proceeds. . . . I would highly recommend the book for one’s personal collection or suggest your librarian purchase a copy."
–Journal of the Operational Research Society

Knowledge of advanced calculus has become imperative to the understanding of the recent advances in statistical methodology. The First Edition of Advanced Calculus with Applications in Statistics has served as a reliable resource for both practicing statisticians and students alike. In light of the tremendous growth of the field of statistics since the book’s publication, André Khuri has reexamined his popular work and substantially expanded it to provide the most up-to-date and comprehensive coverage of the subject.

Retaining the original’s much-appreciated application-oriented approach, Advanced Calculus with Applications in Statistics, Second Edition supplies a rigorous introduction to the central themes of advanced calculus suitable for both statisticians and mathematicians alike. The Second Edition adds significant new material on:

• Basic topological concepts
• Orthogonal polynomials
• Fourier series
• Approximation of integrals
• Solutions to selected exercises

The volume’s user-friendly text is notable for its end-of-chapter applications, designed to be flexible enough for both statisticians and mathematicians. Its well thought-out solutions to exercises encourage independent study and reinforce mastery of the content. Any statistician, mathematician, or student wishing to master advanced calculus and its applications in statistics will find this new edition a welcome resource. ... Read more

Product Description
New publisher! Corrected version! Demonstrating analytical and numerical techniques for attacking problems in the application of mathematics, this well-organized, clearly written text presents the logical relationship and fundamental notations of analysis. Buck discusses analysis not solely as a tool, but as a subject in its own right. This skill-building volume familiarizes students with the language, concepts, and standard theorems of analysis, preparing them to read the mathematical literature on their own. The text revisits certain portions of elementary calculus and gives a systematic, modern approach to the differential and integral calculus of functions and transformations in several variables, including an introduction to the theory of differential forms. The material is structured to benefit those students whose interests lean toward either research in mathematics or its applications. ... Read more

Customer Reviews (8)

Intro Analysis
I used this text as an undergraduate 30 years ago. It amazes me that there has not been a valid rival published since Buck first appeared more than a half century ago. My students have thrived on it for many years now and I expect it to remain so into the future.

Thank you!
The book is in great condition and shipping was fast, however, the picture that's posted as the item I received is not the actual item. The book is, like I said, in perfect condition, and I'm able to use it. Thank you very much!

This Book is Weird
If you have had analysis with Rudin, this book is very weird - no metric spaces, no convergence theorems to speak of, no series - but it does have some very interesting stuff.Buck's explanation of things like open sets, the double integral, the Fundamental Theorem of Calculus are really interesting.If you have the spare change, buy this and really look at it - even better - check it out from the library.

From a physics student.
The book was excellent, starting with the basics of sets and topology and build quickly to the traditional subjects of calculus. I particularly enjoyed the way the author was able to draw attention to the key ideas that come up again and again, the mean value theorem for example. I have never seen a better view of the foundation of calculus, and this book is never leaving my shelf.

Great and accessible
This book provides a very readable and insightful account of the material that is usually covered in two semesters of advanced undergraduate courses usually called "Advanced Calculus" or "Real Analysis."Explanations are clear and concepts are well motivated.The problem sets are well-selected, and are do-able after reading the relevant chapters.This book is highly recommended for engineers or scientists wishing to gain a deeper understanding of mathematics, and for math majors preparing for graduate study in real analysis.It is a great book. ... Read more

Product Description
This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more

Product Description
Contains diagnostic tests to show areas of weakness, workedexamples with explanations of concepts, exercises with pre-tests and post-tests, and includes the answers to all exercises and test problems. ... Read more

Customer Reviews (3)

Perfect refresher to prepare for Calculus
I had taken Calculus in high school, but ten years later found myself having to take it again.I showed up for the first class as a confident 28 year-old, secure in the knowledge that my 'A' in high school would ensure another 'A' as an adult.What I failed to consider is the amount of intermediate Algebra and Trig that had escaped me over the years, so I left the first class feeling overwhelmed, defeated, and immediately dropped the course.Rather than signing up for Pre-Calculus instead, I spent the next two months working through every lesson and practice problem in this book.There aren't any lame cartoons to illustrate concepts, and the lessons aren't drawn out.Rather, each chapter quickly summarizes its lesson, provides a few clear examples, then gives the reader about 20 problems to work through at the end of each lesson.It's a welcome, bare-bones approach right down to the font (Courier).By the time Calculus was offered the next quarter, I was completely prepared.In fact, I got an 'A+' in the course, and this book *definitely* helped put me over the edge.

Excellent aid to the first-course calculus student!
I never learned certain mathematical prerequisites of calculus in high school.Going to college I found my self struggling in calculus I... until I studied this book.It contains all of the basics for the beginning calculus student (as far as the trigonometry and algebra one needs).I quickly read the text and worked out the problems because I was in desperate need of an understanding of those basic concepts.I was able to do relatively well in calculus I, thanks to studying this book.I highly recommend it to anyone in a similar situation as the one I was in.

Outstanding aide for serious student needing help!
This is an excellent text for any calculus student who has gaps in her/his algebraic preparation.The outstanding [and unusual] table of contents is a self-contained test and easily directs the user to parts of the book that will provide needed help.

Another particularly strong area of this little book are the sections on logarithmic and exponential functions. These pages contain a sound mix of graphs, explanations, and sample problems that can clarify gaps for any even semi-serious student.

This book will not spoon-feed the unprepared student, the student who never learned the necessary algebra and/or trigonometry that one needs for the calculus. However, it is an excellent resource for the student who has forgotten or never learned some topics. I have used the book as a reference since 1982 and very much appreciate it. ... Read more

Product Description
This fourth edition offers a comprehensive overview of advanced calculus in a highly readable format. The book offers substantial coverage of vector and matrices, vector analysis, and partial differential equations. Vectors are introduced at the outset and serve at many points to indicate geometric and physical significance of mathematical relations. Numerical methods are touched on at various points because of their practical value and the insights they give about theory. ... Read more

Customer Reviews (16)

Where it's good it's good. But I kept going back to Stewart.
The Kaplan book is direct, concise, and well-organized. In general, I liked it.

However, some of Kaplan's explanations were a bit TOO concise. In those cases, I found myself going back to Multivariable Calculus (Stewart's Calculus Series) -- i.e., the second half of Stewart's big calculus book, published separately so that you don't get a hernia from carrying it around. If you grasp a point quickly, Kaplan is better; if you need more help, Stewart is better.

One complaint: The Kaplan book is very cheaply bound. By the end of the semester, my copy was falling apart.

Excellent in depth treatment of multi-variable calculus
This text gives a much deeper treatment than what is found in the typical undergraduate textbook for Calc I, II, and III.I would recommend it especially for engineers and physicists who want a much deeper understanding of multivariable calculus without necessarily learning to prove everything, and I would recommend it for advanced math students who want to build some more intuition about calculus before trying to plow through a basic analysis text like Rudin's Principles of Mathematical Analysis.

It is Advanced Calculus.
First let me set the context of the review. I am not a math whiz kid. I have a very strong interest in mathematics I just don't have the facility that I have seen in others.
Now that being said I used this book as an upper level undergarduate course in Advanced Calculus. The book expects a lot of mathematical maturity and did not offer any real insights to me. As a consequence I did find myself having to constantly refer to other calculus texts to get an understanding of what Kaplan was explaining. As a resource for learning Advanced Calculus and gaining insight I find it useless, though it is quite useful as a reference.

great for engineering and non-theoretical science majors
I learned from this book during my sophomore year advanced calculus class. The best thing about this book -- answers to all the problems are included. What a novel idea -- answers! I can't speak for others, but I can still remember doing problem after problem from this book and knowing that I could always check my understanding, or lack understanding, of the material by checking my work against the answers.

As to why do I think this book is for engineers and non-theoretical science majors? Very simple, it does *not* cover real analysis as the books by Rudin, Shilov or Johnsonbaugh and Pfaffenberger (my favorite). These other books follow a very traditional approach -- axioms, lemmas, theorems, corollaries. Kaplan's book presents all the mathematics that an engineer, etc. will typically need and with a clear explanation. You won't find delta-epsilon proofs here, but you will find multi-variate calculus, vector differential and integral calculus, orthogonal functions and expansions (Fourier series), complex variables, and ODEs and PDEs. Everything is covered. The explanations are generally very good. There are examples, and of course, answers to the problems are included.

You can think of this book as a Schaum's Outline on Advanced Calculus, but with real explanations, not just statements. I'm not knocking Schaum's Outlines. I own several of them.

Excellent service!
Book was just as described. I am very satisfied. Fast service even I am in Mexico. ... Read more

Product Description
Confusing Textbooks? Missed Lectures? Tough Test Questions?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you:

• Practice problems with full explanations that reinforce knowledge
• Coverage of the most up-to-date developments in your course field
• In-depth review of practices and applications

Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!

Schaum's Outlines-Problem Solved. ... Read more

Customer Reviews (1)

Delivered as promised
Book was received in condition as described and in time suggested. No problems; very satsified. ... Read more

Product Description
The English edition does not differ essentially from the Polish one. Among the more important supplements I should mention 6.5 containing elementary information on the notation of mathematical logic. To this supple- ment I was inclined by the experience of many years. For many students (not for all, perhaps) the notation of definitions of certain notions by means of the logical symbols makes it easier to understand these notions (e.g. the notions of uniform continuity or uniform convergence). Besides that, this supplement is included in the book in such a manner that it can be omitted in reading the
whole book.... ... Read more

Customer Reviews (2)

Before you buy...
No idea how good the book is, but if you type kuratowski calculus into Google, you will find a link to archive.org where you can download it for free.

Excellent calculus text that rivals Spivak
This is a fantastic treatment of calculus written by a eminent Polish mathematician. The treatment of the material
rivals, if not surpasses, the well-known and respected treatment of Spivak.

Specifically,

(1) The book is rigorous but not overly so. It could easily be used to teach a course in honors calculus.
(2) The book is slim and compact so it is not as daunting as Spivak in terms ofphysical size/weight.
(3) The prose is tight and sharp due to a masterful translation from the original Polish into English
(4) The treatment of calculus starts with sequences which makes limits easier to understand. This book is also an excellent stepping
stone into the area of mathematical analysis and would help smooth the transition into a course based on Baby Rudin.


In summary, an excellent text that time forgot. I was lucky to stumble across a copy in a used bookstore some years ago.
If you can find a used copy of this gem, buy it and cherish it. ... Read more

Product Description
This monograph is unique in its treatment of the application of methods of nonstandard analysis to the theory of curves in the calculus of variations. It will be of particular value to researchers in the calculus of variations and optimal control theory. ... Read more

Product Description
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.

... Read more

Customer Reviews (1)

Gentlest Possible introduction to Lambda Calculus
Very easy to understand. Has the added bonus of solutions to all the questions. Unlike Hankins book you really can teach yourself Lambda Calculus with this. If you see a copy available grab it. ... Read more

Product Description
This text provides a clear concise introduction to the calculus of variations. The introduction chapter provides a general sense of the subject through a discussion of several classical and contemporary examples of the subject's use. In the second chapter the all-important Euler differential is dereived and the Lemma of Du Bois-Reymond is established. Other basic terminology is introduced and the underlying theory, which will later be extended smoothly to more complex problems, is developed. Chapters 3 through 6 are devoted to the crucial topics of necessary and sufficient conditions. The remainder of the text extends the concepts of the first half of hte book to problems involving variable boundaries, to parametic representations to the problems constrained by side conditions. ... Read more