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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > General
An authorised reissue of the long out of print classic textbook,
Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo
Sternberg both of Harvard University has been a revered but hard to
find textbook for the advanced calculus course for decades.This
book is based on an honors course in advanced calculus that the
authors gave in the 1960's. The foundational material, presented in
the unstarred sections of Chapters 1 through 11, was normally
covered, but different applications of this basic material were
stressed from year to year, and the book therefore contains more
material than was covered in any one year. It can accordingly be
used (with omissions) as a text for a year's course in advanced
calculus, or as a text for a three-semester introduction to
analysis.The prerequisites are a good grounding in the calculus of
one variable from a mathematically rigorous point of view, together
with some acquaintance with linear algebra. The reader should be
familiar with limit and continuity type arguments and have a
certain amount of mathematical sophistication. As possible
introductory texts, we mention Differential and Integral Calculus
by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure
Mathematics by G Hardy. The reader should also have some experience
with partial derivatives.In overall plan the book divides roughly
into a first half which develops the calculus (principally the
differential calculus) in the setting of normed vector spaces, and
a second half which deals with the calculus of differentiable
manifolds.
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