This is part two of a two-volume book on real analysis and is intended
for senior undergraduate students of mathematics who have already been
exposed to calculus. The emphasis is on rigour and foundations of
analysis. Beginning with the construction of the number systems and
set theory, the book discusses the basics of analysis (limits, series,
continuity, differentiation, Riemann integration), through to power
series, several variable calculus and Fourier analysis, and then
finally the Lebesgue integral. These are almost entirely set in the
concrete setting of the real line and Euclidean spaces, although there
is some material on abstract metric and topological spaces. The book
also has appendices on mathematical logic and the decimal system. The
entire text (omitting some less central topics) can be taught in two
quarters of 25–30 lectures each. The course material is deeply
intertwined with the exercises, as it is intended that the student
actively learn the material (and practice thinking and writing
rigorously) by proving several of the key results in the theory.
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Produktdetaljer
ISBN
9789811018046
Publisert
2019
Utgave
3. utgave
Utgiver
Vendor
Springer
Språk
Product language
Engelsk
Format
Product format
Digital bok
Forfatter