Differential and Integral Calculus

by Richard Courant

Book Overview

"This is the perfect solid-as-they-come, timeless book on the calculus, and most likely it will never be surpassed in this domain." -Amazon ReviewThis book is intended for anyone who, having passed through an ordinary course of school mathematics, wishes to apply himself to the study of mathematics or its applications to science and engineering, no matter whether he is a student of a university or technical college, a teacher, or an engineer. Courant...

• Format: Hardcover
• Language: English
• ISBN: 0471178209
• ISBN13: 9780471178200
• Release Date: January 1937
• Publisher: John Wiley & Sons
• Length: 2 Pages
• Weight: 2.05 lbs.

Customer Reviews

great but not worth $135 to most people

This is one of the best calculus books ever written, But I bought my copy in 1960 for $6.95. Almost no one should pay over $160 for this book today. You are only encouraging greedy book resellers if you do. Buy a copy of Spivak's Calculus instead, or the followup book to this one by courant and fritz john.

Best calculus book, but not for beginners.

This is the best book on calculus that I have ever seen. However, it can never be used as a text for first year calculus students because they lack the mathematical sophistication to understand most of the material in this book. The book is not about the HOW TO, but instead it's about the WHY. There are lots of proofs and some interesting examples. This would be a good alternative book for Advanced Calculus. I read certain parts of this book when I have to teach a complicated topic to my calculus students (e.g. Fundamental Theorem of Calculus, Taylor Series) and then I streamline the material so that they can understand it. My main complaint is the absurd price! Try to find a cheaper used copy. It's outrageous that a book this important is so expensive.

Worth a look

This work has an honored place on my bookshelf. A colleague recommended it to me when I was in school and I bought a copy after looking at it in the school's library. It sits next to my copy of "The Feynman Lectures in Physics". These are works you go to for insight. I like Courant's mixture of physical examples with the mathematics. After encountering Courant's book for the first time, I remember wondering why the first volume wasn't used as the textbook for the typical year and a half of basic calculus. Then, as now, I can only conclude that teachers probably think it's not watered down enough for the students. Maybe it's a blessing in disguise to come across Courant after you've been taught calculus from an uninspiring "modern" text. Everyone's needs are different, so take all reviews with a grain of salt. As a working scientist/engineer, my primary use of the calculus is as a tool to get things done, so I'm typically more interested in learning the mechanics than getting a deep understanding like a mathematician would. Courant works for this, yet still allows one to dig in deeper when desired. It's still an awfully good book, even if it is 70 years old.

Classical German calculus

Courant knows the art of writing a good preface. He attacks "diffuseness" and "pedantry" and aims at "exhibiting the close connection between analysis and its applications" and "to give due credit to intuition as the source of mathematical truth". The book also has a tone that is unusual today: Courant speaks to us the way a dignified, open-hearted professor speaks to an intelligent student. No rambling pretensions; just to-the-point, good mathematics. This is the perfect solid-as-they-come, timeless book on the calculus, and most likely it will never be surpassed in this domain. One must be warned, however, that this is a very serious book and reader-friendliness has lower priority than technical coherence and brilliance of formal organisation. The likely reader will know calculus already and use Courant for masterful, concise exposition of standard topics as well as a wealth of topics that have been watered out of most current calculus curricula (e.g., evolutes, involutes, envelopes, curvature, geodesics, centres of mass, the gamma function, the catenary, the cycloid, the lemniscate, the brachistochrone problem, Kepler's laws, Maxwell's equations, the zeta function, etc.). Everybody knows that all the usual calculus books, "reform" or not, are pathetic. But what is even worse is that there are no good alternatives even if one is prepared to dig deep into the library shelves in hope of finding an author who has not sacrificed his intellectual dignity at the altar of royalties. Take for example Serge Lang's books "A First Course in Calculus" and "Short Calculus". Lang is of course the virtual definition of the mainstream of respectable mathematics. Nevertheless, these books are soaked with the common formalistic attitude. In fact, as if his books had not finished the job, Lang adds an appendix to both books called "Physics and Mathematics", which very explicitly drives a wedge between physics and intuition and mathematics. Courant is a good antidote to such modern nonsense.

What a wonderful book!

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 ofCourant'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.