![]() So, from one point of view, Part Two of Friedman's text would seem irrelevant. ![]() In fact no course in our program, and I suspect in most programs, would have students study the fundamentals of multivariate calculus in such detail. Our multivariate calculus course, while trying to emphasize understanding and rigor, does not leave room for the complete development of the subject found in Friedman's Part Two. Where Friedman differs significantly from the many of the newer introductory analysis texts is in Part Two, which covers the rigorous fundamentals of multivariate calculus from limits and continuity to Stokes' theorem. In most cases he chooses the concept that does best in providing an understandable proof. Friedman uses the traditional definition of continuity at a point then develops the equivalence to the sequential definition. He uses both concepts - in some cases providing two different proofs for one theorem. Ross relies almost completely on the sequential definition for developing most needed results with clear and simple proofs, though this does leave the student wondering how this connects to what he learned back in Calculus class. I prefer texts by Abbott and Ross which are more reasonably priced, seem more rigorous to me and, like Friedman, are more traditional.īoth Ross and Friedman recognize the pedagogical superiority of the sequential definition of continuity of a function at a point. ![]() Though some texts we use, those by Lay and Gaughan, are seen to be more readable by the students. Unfortunately most of the textbooks we use are not nearly as affordable. I am a mathematics professor at a small Liberal Arts college and regularly teach "Advanced Calculus" using textbooks similar in content to Part One of Friedman's book (limits, continuity, differentiation, integration, sequences and series). I take Friedman as an example of this school - a good example. Many people say that the study and teaching of analysis was so influenced by Rudin's Principles of Mathematical Analysis (1953) that we are still teaching the same topics in the same way today. The lack of change in nearly 40 years is not an indication of stagnation rather it is an indicator of a mature subject that has been nearly completely investigated and is well thought out pedagogically. Now, almost 20 more years later, the same material is covered and even the same notation is commonly used. I learned about analysis about 20 years later. I was born in 1969, probably around the time this book was planned and written. ![]() Two things struck me immediately concerning this textbook: How affordable it is and how little things have changed since 1971. This is a Dover Edition reprint, published in 2007, of a book first published in 1971 by Holt, Rinehart and Winston. ![]()
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