|
Showing 1 - 2 of
2 matches in All Departments
A typical source of mistakes that frequently lead to a wrong or
incomplete solution for the antiderivative of a given real function
of one real variable is a misuse of the technique of change of
variable. The increasing implementation of software in apparently
mechanic tasks such as the calculation of antiderivatives has not
improved the situation, yet those software packages issue generic
warnings such as "the answer's is not guaranteed to be continuous"
or "the solution might be only valid for parts of the function".
The practical meaning of those vague machine messages is clearly
envisaged in this book, which shows how to handle the technique of
change of variable in order to provide correct solutions. This book
is monographically focused on elementary antidifferentiation and
reasonably self-contained, yet it is written in a "hand-book"
style: it has plenty of examples and graphics in an increasing
level of difficulty; the most standard changes of variable are
studied and the hardest theoretic parts are included in a final
Appendix. Each practical chapter has a list of exercises and
solutions. This book is intended for instructors and university
students of Mathematics of first and second year.
Tauberian operators were introduced to investigate a problem in
summability theory from an abstract point of view. Since that
introduction, they have made a deep impact on the isomorphic theory
of Banach spaces. In fact, these operators have been useful in
several contexts of Banach space theory that have no apparent or
obvious connections. For instance, they appear in the famous
factorization of Davis, Figiel, Johnson and Pelczynski [49]
(henceforth the DFJP factorization), in the study of exact
sequences of Banach spaces [174], in the solution of certain
summability problems of tauberian type [63, 115], in the problem of
the equivalence between the Krein-Milman property and the
Radon-Nikodym property [151], in certain sequels of James'
characterization of reflexive Banach spaces [135], in the
construction of hereditarily indecomposable Banach spaces [13], in
the extension of the principle of local reflexivity to operators
[27], in the study of certain Calkin algebras associated with the
weakly compact operators [16], etc. Since the results concerning
tauberian operators appear scattered throughout the literature, in
this book we give a unified presentation of their properties and
their main applications in functional analysis. We also describe
some questions about tauberian operators that remain open. This
book has six chapters and an appendix. In Chapter 1 we show how the
concept of tauberian operator was introduced in the study of a
classical problem in summability theory - the characterization of
conservative matrices that sum no bounded divergent sequences - by
means of functional analysis techniques. One of those solutions is
due to Crawford [45], who considered the second conjugate of the
operator associated with one of those matrices.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
|
Email address subscribed successfully.
A activation email has been sent to you.
Please click the link in that email to activate your subscription.