Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
|
Buy Now
Elementary Functional Analysis (Paperback)
Loot Price: R1,689
Discovery Miles 16 890
You Save: R521
(24%)
|
|
Elementary Functional Analysis (Paperback)
Series: De Gruyter Textbook
Expected to ship within 10 - 15 working days
|
Donate to Gift Of The Givers
Total price: R1,709
Discovery Miles: 17 090
|
While there is a plethora of excellent, but mostly "tell-it-all''
books on the subject, this one is intended to take a unique place
in what today seems to be a still wide open niche for an
introductory text on the basics of functional analysis to be taught
within the existing constraints of the standard, for the United
States, one-semester graduate curriculum (fifteen weeks with two
seventy-five-minute lectures per week). The book consists of seven
chapters and an appendix taking the reader from the fundamentals of
abstract spaces (metric, vector, normed vector, and inner product),
through the basics of linear operators and functionals, the three
fundamental principles (the Hahn-Banach Theorem, the Uniform
Boundedness Principle, the Open Mapping Theorem and its
equivalents: the Inverse Mapping and Closed Graph Theorems) with
their numerous profound implications and certain interesting
applications, to the elements of the duality and reflexivity
theory. Chapter 1 outlines some necessary preliminaries, while the
Appendix gives a concise discourse on the celebrated Axiom of
Choice, its equivalents (the Hausdorff Maximal Principle, Zorn's
Lemma, and Zermello's Well-Ordering Principle), and ordered sets.
Being designed as a text to be used in a classroom, the book
constantly calls for the student's actively mastering the knowledge
of the subject matter. It contains 112 Problems, which are
indispensable for understanding and moving forward. Many important
statements are given as problems, a lot of these are frequently
referred to and used in the main body. There are also 376 Exercises
throughout the text, including Chapter 1 and the Appendix, which
require of the student to prove or verify a statement or an
example, fill in necessary details in a proof, or provide an
intermediate step or a counterexample. They are also an inherent
part of the material. More difficult problems are marked with an
asterisk, many problem and exercises being supplied with
"existential'' hints. The book is generous on Examples and contains
numerous Remarks accompanying every definition and virtually each
statement to discuss certain subtleties, raise questions on whether
the converse assertions are true, whenever appropriate, or whether
the conditions are essential. The prerequisites are set
intentionally quite low, the students not being assumed to have
taken graduate courses in real or complex analysis and general
topology, to make the course accessible and attractive to a wider
audience of STEM (science, technology, engineering, and
mathematics) graduate students or advanced undergraduates with a
solid background in calculus and linear algebra. With proper
attention given to applications, plenty of examples, problems, and
exercises, this well-designed text is ideal for a one-semester
graduate course on the fundamentals of functional analysis for
students in mathematics, physics, computer science, and
engineering. Contents Preliminaries Metric Spaces Normed Vector and
Banach Spaces Inner Product and Hilbert Spaces Linear Operators and
Functionals Three Fundamental Principles of Linear Functional
Analysis Duality and Reflexivity The Axiom of Choice and
Equivalents
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
You might also like..
|