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by Karo Maestro (Author), William Benjamin Fite (Author)
Old School Advanced Calculus is exactly what the title says it is: A full year course in advanced calculus the way it was offered at all American universities until the 1970's saw the sundering of the sequence into various "analysis for mathematicians" and "analysis for physical science students" courses. With the republication of this comprehensive, long-out-of-print text by Fite in a wonderfully inexpensive edition, the hope is to bring the advanced calculus course as it was taught for nearly half a century back into the consciousness of the 21st century mathematics and physical science students and educators. The main advantage of the original AC course, as exemplified by Fite, is a unified presentation of mathematical analysis comprised of virtually all the main topics of undergraduate analysis needed by both mathematics and physical science majors, covered using a uniform terminology and level of rigor. Even if each semester was taught by a different faculty member, they were both bound by more or less the same syllabus, which limited their ability to diverge from it drastically. When the subject selection, notation and rigor level is consistent throughout like it is with books like Fine's, then a balance that benefits all involved is achieved and maintained in the entire course. Pure mathematics students get exposed to important physical and geometric applications along with mathematical rigor. Physics and engineering students get exposed to pure mathematics and the abstract minimalist deductive skills it builds in them that will be invaluable when they begin research. Fite, in particular, does a terrific job of combining a careful "epsilon-delta' presentation of calculus of one and several variables with many applications to classical physics, differential equations and geometry. This book can be used for a number of different courses, either a standard classical advanced calculus course, an honors calculus course for strong freshman or independent reading by students or professors of analysis. Requiring only a year-long basic single variable calculus course as prerequisite, a course based on this book will give both the beginning mathematics major and serious physics or engineering major a thorough grounding in classical analysis and it's many applications in preparation for further research in either real variables or mathematical physics. A lengthy new preface has been added by Karo Maestro explaining the history of the advanced calculus course in America and where Fite's book was groundbreaking as one of the first standard such texts. He has also added a recommended reading section reviewing many of the other standard classical analysis texts for additional reading.
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