Differential and Integral Calculus, Vol. One

I recommend this book to anyone that's taking the calculus sequence in college. At my school, proofs are not explored in-depth until intro to analysis which comes much later in a students college career if at all. I'm the type of learner that does poorly with rote memorization and better with rigorous explanation, so I felt like I needed to give myself an edge. That's where Courant's great book comes in. By supplementing in-class lectures with this book I have been able to keep my head above water, and felt like the material was coming to me much more naturally as the professor was presenting it. I find that reading a few pages of this book and then working his examples is the best strategy for consuming the knowledge contained within. I'm fairly certain I'll refer back to this specific tome for years to come. A final note: this book is not an easy read. If you're looking for a quick read and introduction to the subject of calculus without getting too deep into the nitty gritty details, I un-sarcastically recommend the calculus for dummies book instead.

This is a great reference book in calculus for mathematicians and engineers however it’s a very difficult book to comprehend for students of calculus I and Ii

wonderful, thanks!

for a better understanding of the subject-keep this book nearby. good binding but a bit pricey

I learned Calculus using this textbook at NYU.

As advertised, great book to add to math collection.

Great

This two-volume text, originally written in German while Courant was still at Gottingen, is very much better for a serious student than most introductory texts on analysis. Most introductory texts have a flavor of having been written by geniuses for idiots; in this book, Courant treats the student as being his peer in intellect and interest, lacking only knowledge. This makes it an excellent book even for somebody reasonably familiar with the calculus. Although it covers the material from a strictly classical viewpoint, the text and the examples provide enough thinking material to help the student understand the motivation that led to measure theory, Lebesgue-Stieltjes integration, and algebraic topology; the wellsprings of these in classical analysis are seldom explained in modern math courses. So I can recommend it to any senior planning to do graduate work in math, or to any first-year graduate student in math. And of course, it can be well used as a first calculus text for students who are prepared to think and put in effort on the subject. Courant himself, of course, was a great mathematician, although I don't personally consider him one of the greatest mathematicians of the 20th century; he was a better leader and inspirer of others than a creator of new mathematics. But among other things, he served as David Hilbert's personal assistant for two years, and this gave him superb judgment about what's important and what isn't. This shows throughout the book. It also helps that the translator into English was E. J. McShane. McShane is less well-known than he perhaps deserves to be, because he was a truly first-rate mathematical researcher (in analysis) himself. This, together with the fact that McShane spent a year or two at Gottingen while Courant was still leading the Mathematics Institute at Gottingen, and came to know Courant well, allowed McShane to translate Courant's text with great understanding of Courant's way of thinking. My own copy of this text, bought more than 50 years ago, is in tatters, because I still haul it out and re-read pieces of it to connect my thinking when I'm groping.

Richard Courant's two volume classic delves a little deeper than Hardy's textbook. It also reflects the German attitude to mathematics, placing geometry and physical applications in frame of pure mathematics.