This second edition of a very popular two-volume work presents a thorough first course in
analysis leading from real numbers to such advanced topics as differential forms on manifolds
asymptotic methods Fourier Laplace and Legendre transforms elliptic functions and
distributions. Especially notable in this course are the clearly expressed orientation toward
the natural sciences and the informal exploration of the essence and the roots of the basic
concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive
exercises problems and fresh applications to areas seldom touched on in textbooks on real
analysis. The main difference between the second and first editions is the addition of a series
of appendices to each volume. There are six of them in the first volume and five in the second.
The subjects of these appendices are diverse. They are meant to be useful to both students (in
mathematics and physics) and teachers who may be motivated by different goals. Some of the
appendices are surveys both prospective and retrospective. The final survey establishes
important conceptual connections between analysis and other parts of mathematics. The first
volume constitutes a complete course in one-variable calculus along with the multivariable
differential calculus elucidated in an up-to-date clear manner with a pleasant geometric and
natural sciences flavor.
