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Whatever your calculus needs are, you’ll find plenty of them in this authoritative and definitive textbook on the topic. The authors have created a comprehensive, yet concise, introduction to calculus. The book is designed for those presenting themselves as either freshmen or sophomore college students who might be taking one or two courses in calculus. One of the hallmarks of this text is its clear and reasoned exposition, which will make it accessible to those who prefer a geometric point of view as well as those who like an algebraic approach. It seems like every semester we're asked to buy a new math book for one reason or another — "because we're moving up," "because we're moving down," "because we need more detailed coverage. In the past I've been inclined to listen to the sales pitch and buy what was being offered. I have since learned that, in my opinion, less is more when it comes to math texts. In a nutshell, a companion text should be of use to a teacher, not a burden. Using a good calculus book as a support makes it easier for the instructor to teach calculus and makes it possible for him or her to do so with fewer of his or her own notes. So which book is going to be most useful? The answer is one that will accommodate my style of teaching and your style of learning — not necessarily one that uses "my" approach or "your" approach, but "our" approach. And since I demand considerable flexibility in my curriculum, that means that I need to know what other topics will be covered along with calculus. I am extremely fond of the idea of a companion text that is clear, concrete, and focused on one single thing — calculus itself. The first companion text I ever used was the first edition of the book by Winifred Creamer, "Calculus." It was not very useful to me as a teacher because it was so focused on geometry. This text has long been out of print but can still be found used. Another book I used to frequent was "Calculus Refreshed" by Sherman Kayser. It was very well done and did an excellent job of teaching the material, but it was also oriented to algebraic and geometric calculus. I did not like this book for two reasons: first, it did not teach the main idea of calculus — that is, that we can reduce any set of equations to a single equation. I do not know if these are the only books that are out there, but they are two that I have used in the past. I would recommend another book with an emphasis on the idea of reducing problems to algebraic expressions through solving linear equations by substitution. This book is called "Calculus Made Easy." It is really aimed at students in high school or even in college in some cases. The authors, Silvanus Thompson and John Casey, have made calculus so easy that they have barely had to mention the derivative or the integral. These two texts are almost identical, except for the fact that "Calculus Made Easy" is geared toward students who are more interested in developing a geometric understanding of calculus. "Calculus Made Easy" is really an excellent textbook for high school senior or first-year college students. It does an excellent job of explaining what exactly differentiation is all about. It also contains good examples showing how integration is used to solve problems in geometry. What I like about both these books is that they make things very clear. eccc085e13
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