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Review of Crowell: Calculus

Go to Calculus (2011, 181 pages, 2.2 MB pdf file. You can donwload the text as pdf or view the HTML version)

Calculus by Benjamin Crowell covers single variable calculus and, in chapter 9, iterated integrals. Throughout the text it contains many examples. At the end of each chapter are many problems, some of them with carefully explained solutions in Appendix B. Even if you have learned calculus from another text, I recommend that you try to solve the problems (but you may want to skip the problems where you have to prove something if you mostly want to learn how to apply calculus).

Section 2.2 discusses the hyperreal number system. It offers an alternate method of dealing with the infinitesimal quantities in calculus. If you are really interested in mathematics this may be quite interesting. If, however, you are just interested in using mathematics as a tool for engineering or science, you can skip this section and continue with section 2.3 where the product rule is explained. You can understand most parts of the book without knowing about hyperreal numbers. The same is true for appendix A, Detours, which covers formal definitions and proofs - it is only necessary if you want to understand the rigorous mathematical foundations of calculus.

Crowell has also written several excellent free physics books. They should not only be interesting for physics students, but for everybody who wants an easy to understand, but comprehensive introduction. One day I will write more about them, but for now here is just a very quick overview: Light and Matter is a very good introduction to physics if you do not know calculus. If you are already familiar with calculus, you can instead look at Simple Nature. If you are only interested in classical mechanics, take a look at Mechanics. The book Conceptual Physics is organized around the basic conservation laws of physics, but like the other books on a level that is very easy to understand, not the highly mathematical treatment that you would find in a book on theoretical physics. Finally, General Relativity is a book for the advanced reader who is really interested in this topic. General relativity is one of the fundamental pillars of modern physics, but be aware that it has almost no practical applications - so the book is really more for physics students than for engineering students.

All books are available in different formats (you can even view them online). I found it most convenient to download each as a single pdf file.

You may also be interested in some other recommendations for Introductions to Calculus.

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