Lev Semenovic Pontrjagin (1908) is one of the outstanding figures
in 20th century mathematics. In a long career he has made
fundamental con tributions to many branches of mathematics, both
pure and applied. He has received every honor that a grateful
government can bestow. Though in no way constrained to do so, he
has through the years taught mathematics courses at Moscow State
University. In the year 1975 he set himself the task of writing a
series of books on secondary school and beginning university
mathematics. In his own words, "I wished to set forth the
foundations of higher mathematics in a form that would have been
accessible to myself as a lad, but making use of all my experience
as a scientist and a teacher, ac cumulated over many years. " The
present volume is a translation of the first two out of four
moderately sized volumes on this theme planned by Pro fessor
Pontrjagin. The book begins at the beginning of modern mathematics,
analytic ge ometry in the plane and 3-dimensional space.
Refinements about limits and the nature of real numbers come only
later. Many concrete examples are given; these may take the place
of formal exercises, which the book does not provide. The book
continues with careful treatment of differentiation and
integration, of limits, of expansions of elementary functions in
power se ries."
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