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.