id: 02315580
dt: b
an: 1997c.01842
au: Lang, S.
ti: Undergraduate analysis.
so: Springer, New York, NY (ISBN 0-387-94841-4). 657 p. (1997).
py: 1997
pu: Springer, New York, NY
la: EN
cc: I15
ut:
ci:
li:
ab: This is a logically self-contained introduction to analysis, suitable for
students who have had two years of calculus. The book centers around
those properties that have to do with uniform convergence and uniform
limits in the context of differentiation and integration. Topics
discussed include the classical tests for convergence of series,
Fourier series, polynomial approximation, the Poisson kernel, the
construction of harmonic functions on the disk, ordinary differential
equations, curve integrals, derivatives in vector spaces, multiple
integrals, and others. One of the authorâ€™s main concerns is to
achieve a balance between concrete examples and general theorems,
augmented by a variety of interesting exercises. Some new material has
been added in this second edition, for example: a new chapter on the
global version of integration of locally integrable vector fields; a
brief discussion of $L^1$-Cauchy sequences, introducing students to the
Lebesgue integral; more material on Dirac sequences and families,
including a section on the heat kernel; a more systematic discussion of
orders of magnitude; and a number of new exercises. (orig)
rv: