This 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 is the clearly
expressed orientation toward the natural sciences and its 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 real analysis books. The
first volume constitutes a complete course on one-variable calculus along with
the multivariable differential calculus elucidated in an up-to-day, clear
manner, with a pleasant geometric flavor. TOC:Prefaces.- 1. Some General
Mathematical Concepts and Notation.- 2. The Real Numbers.- 3. Limits.- 4.
Continuous Functions.- 5. Differential Calculus.- 6. Integration.- 7. Functions
of Several Variables.- 8. Differential Calculus in Several Variables.- Some
Problems from the Midterm Examinations.- Examination Topics.- References.-
Subject Index.- Name Index.
