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Tom M. Apostol, "Calculus Volume 1 : One-Variable Calculus, with an Introduction to Linear Algebra"

The best Calculus book currently available

It's a shame that most high school and college students read whatever garbage they read nowadays to learn calculus. Fortunately, Apostol wrote his wonderful texts (you'll notice that this book hasn't had a new edition in about four decades, which means the author is under no pressure to artificially introduce new content to keep the sales up) for us to read.

This book is not only well-written, but has numerous quality exercises, and presents the material in a coherent and logical fashion. There is none of the typical clutter we see in many calculus texts nowadays, which makes the reading experience much simpler. Because Apostol writes so clearly, he can cover material significantly quicker than most other calculus texts. Even though many students are puzzled at the notion of understanding theoretical proofs and concepts, that understanding will often trivialize whatever homework problems and tests they will need to write in their classes.

It is true that this book is more abstract than other calculus texts, and the general consensus is that some knowledge of calculus would be helpful before tackling this book. However, a mathematically inclined student, given a good background in pre-calculus, should be capable of reading this entire book with little outside assistance. Of course, it wouldn't hurt to have a more experienced student or teacher available to answer any questions the reader may have.

Another advantage of this text is that, by adding linear algebra, Apostol can more cleanly integrate linear algebra with multivariable calculus (in volume two). In addition, he covers some topics in differential equations and probability, which are natural extensions of all the earlier material in the book.

The exposition is clear, the covered content is thorough, and the exercises are numerous and varied. If you want to learn calculus, this is the book (well, this and the second volume) to get.

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