Undergraduate analysis. 2nd ed. (English) Zbl 0962.46001

Lang, Serge

Undergraduate Texts in Mathematics. New York, NY: Springer. xv, 642 p. (1996).

The changes of this second edition compared to the first (1983; Zbl 0509.46037) are described by the publisher as follows: 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.
The first edition in turn is the successor of “Analysis I” (1968; Zbl 0159.34033).

MSC:

46-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
46G05	Derivatives of functions in infinite-dimensional spaces
26-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
26Bxx	Functions of several variables
26Axx	Functions of one variable

Keywords:

integration; differentiation; Fourier series; Fourier integral; differential equations; differential forms; inverse mapping theorem; Stokes’ formula; global version of integration of locally integrable vector fields; \(L^1\)-Cauchy sequences; Dirac sequences; heat kernel; orders of magnitude

Citations:

Zbl 0509.46037; Zbl 0159.34033