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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.
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Different calculus textbooks will go in and out of fashion as professors try to overcome the poor preparation of their students, but Courant's book will endure as long as there are students who really want to understand thoroughly what they are doing.
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shares in Bobby's experiences and grow to love him.
Bobby is able to learn more about himself when he is
learning about another culture. The Korean backdrop,
peace corps experience, and military culture ring as
entirely authentic. Again, Wiley is incredibly funny
while also being entirely serious, a paradox which
renders this novel as an important work of art.
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SMAD offers a wealth of good information, but it's far too wordy and prone to personal ruminations on the parts of the contributors. It could profitably be shortened by at least 200 pages.
In addition, Chapter 9 (on payloads) needs significant re-work, especially on the discussion of optical payloads. The chapter somehow manages to be both too detailed, and too top-level, for the reader to actually use it. Those who can fill in the technical gaps will not need SMAD, and those who cannot, cannot use SMAD. The proper approach would be to offer a qualitative assessment of how payloads affect satellite design. Leave the deep-down technical details for other texts.
Finally, there are sections which can only be described as advertisements for Wertz's company. The discussions of autonomous orbit determination and autonomous orbit control are vastly biased, and do not cover the full range of considerations that have to go into selecting an approach for either activity.
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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!