Customer Reviews

Differential and Integral Calculus (2 Volume Set)

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I will not say, as is common in reviewers of books on calculus, that this is the best book of calculus that there is. Indeed, calculus is a subject with so many textbooks that it can be said that there is no best textbook, but that each person can find one that suits his/her needs.

Nonetheless, Courant's book is an old text, around 70 years old. It belongs to these classics of science that were influential and held its own as a source of common knowledge. Why?

I believe that the answer to this question is simple: Courant's book has the perfect balance between theory and applications. It does not use too much pedantry in its exposition, is full of examples (for the student to do and also some worked-out), ranging from simple to very difficult, and yet it proves everything that is important in a way that no mathematician can complain. Indeed, the authors leaves the most difficult demonstrations to appendixes that can be found in each chapter, so the reader that doesn't want to enter into the complications of the proofs can skip them. And the book is written in a conversational style, that much probably influenced the book that, in my humble opinion, is the best that can be found treating the subjects it treats (so I also have my favourite calculus text: Spivak's Calculus!).

There are two volumes, the first one dealing mainly with calculus of one variable and the second with multivariate and complex analysis. It contains the core of the mathematical theory useful for physicists and engineers and has this that is amazing: it develops the theory and always gives good physical examples. Indeed, a whole course of theoretical physics is contained in this book, almost hidden.

So, if someone is reading this review and is in doubt whether the book is good or not, I can say, with the experience of having read a long list of calculus texts, that the book is good and is worth-while. It is useful to the mathematician and to the engineer, to the philosopher and to the physicist, and serves extremely well both as a text book for class study, self-study and for reference. If you are worried that the treatment is dated, I can say that, although today the most common treatment of, say, multivariate calculus is through linear algebra, that leaves the subject much cleaner, Courant's work still is of value in that it explains everything in as simple way as possible, mantaining always ahead the objectives of each section. It is essentially a book of applications of analysis and if you read and work the examples, you will turn yourself into an expert both in theory and application and will be able to follow easily any work that has classical analysis as prerequisite.

Great classical book!

I agree whole heartedly with the other reviews here, and merely wish to second their opinions. I bought my copy in 1960 and would never part with it. I still have crystal clear images in my mind from courant's exposition of the 1-1 correspondence between points of the real line and infinite decimals, his comment that all absolute convergence tests result from comparing with a known convergent object - either the geometric series or an integral, and his preface emphasizing "the chief task" of one who would pursue the study of Science: acquiring a firm grasp of the application of general principles in particular cases.

I have studied and taught calculus, advanced calculus, real and complex analysis, Riemann surfaces, differential equations, and differential manifolds both real and complex, for over 40 years, but anyone who reads thoroughly these 2 volumes and masters them will know more calculus than I do.

I am a pure mathematician, and I believe these volumes are highly recommended not just to physicists and engineers, but to anyone who would master their subject. I also love the book of Spivak, but after teaching from them together one summer, and comparing proofs, I concluded that Spivak himself probably learned the subject from Courant.

This book was written by the main author of "What is Mathematics" and these two works are both masterpieces of advanced popularization in mathematical subjects.
Integral and differential calculus are explained in plain but accurate manner.
To be reccommended to those who want cleareness and deepness in the concepts of science.

There has been sufficient praise for the D^I Calculus of Courant and I would not add more to it. My comments: 1) The symbols are outdated 2) it's more verbose and descriptive than many other standard calculus textbooks. This is good in some sense because it helps the readers understand the concepts. Yet, it will not train you solve difficult problems and will not help you ace your tests and exams, be it GRE Subject test or your regular exams. But certainly you can benefit from reading it, no doubt! I used this book for self study and as my main reference. There is a book by Michael Comenetz 9810249047 that's written almost as a updated and concise version of Courant's books. Many points that Courant omits may be found in Comenetz' book. It has ample amount of problems (with solutions) of appropriate difficulty that help you reinforce what you read from Courant.