Chrysti added it Dec 15, Selected pages Title Page. Bob rated it it was ok May 22, Logan marked it as to-read Oct 10, Mark added it Aver 20, This rigorous two-part treatment advances from functions of one variable to those of several variables. No trivia or quizzes yet. Refresh and try again. To ask other readers questions about Advanced Calculusplease sign up. Account Options Sign in.
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Two things struck me immediately concerning this textbook: How affordable it is and how little things have changed since I was born in , probably around the time this book was planned and written. I learned about analysis about 20 years later.
Now, almost 20 more years later, the same material is covered and even the same notation is commonly used. This is not a bad thing.
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.
I take Friedman as an example of this school — a good example. Both Ross and Friedman recognize the pedagogical superiority of the sequential definition of continuity of a function at a point. Friedman uses the traditional definition of continuity at a point then develops the equivalence to the sequential definition.
In most cases he chooses the concept that does best in providing an understandable proof. 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. From my point of view, Part Two is excellent! The keener of my students would read some of Part Two for themselves and might even ask to do a reading course on the topic.
Each author has his or her own voice that can only be found through a careful reading or, better yet, careful use as a textbook. The table of contents is not available.