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Calculus for Engineers versus Calculus for Mathematicians Andrew Christie English 352 4/19/09 Table of Contents Abstract ......................................................................................................................................1 Introduction ................................................................................................................................1 Comparing Different Styl
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  Calculus for Engineers versus Calculus for Mathematicians Andrew Christie English 352 4/19/09    Table of Contents Abstract......................................................................................................................................1 Introduction................................................................................................................................1 Comparing Different Styles of Teaching the Same Theorem.......................................................2 How the Problems Differ............................................................................................................4 Conclusion..................................................................................................................................6 References..................................................................................................................................6 Annotated Bibliography..............................................................................................................7 .  1 Abstract I’m comparing two completely different calculus books. They cover the exact same material, they have roughly the same name, and would seem interchangeable to someone unfamiliar with either book. However, they are certainly different in both style and aim. My aim is to compare a few sections of the book in a very specific way, and then expand on that to show the general development of the book. In addition, I will show important difference such as; to whom each book would appeal, the aim of the book, and how the material is covered. Introduction The two books in my mind have different audiences in mind, and material inside is  presented accordingly. James Stewart’s book is for someone who wants to use the ideas of calculus and apply them elsewhere. Michael Spivak’s is for someone who wants to see the main ideas in calculus, and how those ideas were developed. I shall go into specifics on an important result in calculus, the so-called Intermediate Value Theorem. I will compare the treatment of it in each book, and the expectations of the reader by the author with regard to this theorem. Lastly, I shall look at how the problems intended to test the reader’s knowledge of ideas presented contrast.  2 Comparing Different Styles of Teaching the Same Theorem Figure 1 – Intermediate Value Theorem from James Stewart Figure 2 – Intermediate Value Theorem Example from James Stewart James Stewart gives you the definition of the theorem, allowing you to apply it as you see fit, but omits the proof of the theorem. An example is provided instead. This isn’t because this particular proof is difficult, most proofs in elementary calculus aren’t. Rather, the  book is geared more towards application of important concepts in calculus to problems in nature. James Stewart is likely thinking if he provides you with a tool, shows you under what conditions it can be used, and provides an example of its usefulness you will be able to apply this theorem. In essence, calculus is just the method used to solve problems for the audience of James Stewart.
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