HarperCollins College Outline Introduction to Calculus

There is now a later, slightly updated, and renamed edition of this work, "Introduction to Calculus(Collins College Outlines)", with the author now identified as Joan Van Glabek (ISBN-10: 006088150X). There are a few changes and additions, but both editions are quite similar, so my reviews of both are closely matched. This is a relatively short, 250 page, book. Within that limited space, and in six chapters, it provides a review of basic pre-calculus topics followed by: Functions, Limits, and Continuity; Derivatives; Applications of Derivatives; Integrals; Applications of Integration, and an Index. Topics are presented quite concisely, e.g., 'Related Rates' is covered in about seven pages, and 'Approximating Area' in four. However, the text is quite well-written, and in this case the brevity is an advantage, allowing readers to quickly gain an understanding of the first semester calculus core. In text problems are provided for readers to work as each new topic is presented. These problems are provided with fully-worked solutions. The second edition includes a few additional problems compared to this edition. For example, in this book the Chapter on "Applications of Derivatives" ends with 19 practice exercises, the later edition ends with 22. These exercises were well-constructed to test understanding of key points. Although, for the end of chapter exercises, only answers not fully worked solutions are provided. The new edition is printed on better quality and brighter paper - the pages in my first edition are already browning. However, there is a serious problem with the second edition. The majority of the text in that edition was apparently retyped from this edition. Unfortunately, during the retyping, some errors not present in this edition were introduced in the second edition. For example, in the second edition's section on inequalities, a greater than or equal sign appears instead of the appropriate less than or equal sign. In another problem, solution points correct in this edition are inadvertently changed to incorrect values in the second edition, and a graph of the solution included in the first editon is missing in that edition, etc. As the title suggests, this is only an outline and not a detailed presentation of calculus topics. However, for its purpose, a quick and well-written presentation of the key topics in introductory calculus, this outline can be highly recommended, particularly for readers currently in a calculus class, or thus who have completed one in the past. In spite of some minor issues, this is an easy book to like. Considering the relatively minor changes and considerable number of errors introduced in the second edition, this first edition will likely prove a better value.

I'm no dummy, but I had a lot of trouble understanding Calculus (had to withdraw 2 times). The teachers couldn't or wouldn't explain, the class text was obscure, but this book explained the basics in a straightforward style leaving you to have to guess very little. Of all the *many* Calc books I tried, this was *easily* the best. Thanks, Ms. Dykes and Harper Collins for making Calculus comprehensible. (PS. I got an "A.")