Shortcuts
Top of page (Alt+0)
Page content (Alt+9)
Page menu (Alt+8)
Your browser does not support javascript, some WebOpac functionallity will not be available.
.
Default
.
PageMenu
-
Main Menu
-
Simple Search
.
Advanced Search
.
Journal Search
.
Refine Search Results
.
Preferences
.
Search Menu
Simple Search
.
Advanced Search
.
New Items Search
.
Journal Search
.
Refine Search Results
.
Bottom Menu
Help
Italian
.
English
.
German
.
New Item Menu
New Items Search
.
New Items List
.
Links
SISSA Library
.
ICTP library
.
Italian National web catalog (SBN)
.
Trieste University web catalog
.
Udine University web catalog
.
© LIBERO v6.4.1sp220816
Page content
You are here
:
Catalogue Display
Catalogue Display
A Handbook of Real Variables: With Applications to Differential Equations and Fourier Analysis
.
Bookmark this Record
Catalogue Record 46513
.
.
Author info on Wikipedia
.
.
LibraryThing
.
.
Google Books
.
.
Amazon Books
.
Catalogue Information
Catalogue Record 46513
.
Reviews
Catalogue Record 46513
.
British Library
Resolver for RSN-46513
Google Scholar
Resolver for RSN-46513
WorldCat
Resolver for RSN-46513
Catalogo Nazionale SBN
Resolver for RSN-46513
GoogleBooks
Resolver for RSN-46513
ICTP Library
Resolver for RSN-46513
.
Share Link
Jump to link
Catalogue Information
Field name
Details
Dewey Class
515.8
Title
A Handbook of Real Variables ([EBook]) : With Applications to Differential Equations and Fourier Analysis / by Steven G. Krantz.
Author
Krantz, Steven George , 1951-
Other name(s)
SpringerLink (Online service)
Publication
Boston, MA : Birkhäuser , 2004.
Physical Details
XIII, 201 pages : online resource.
ISBN
9780817681289
Summary Note
The subject of real analysis dates to the mid-nineteenth century - the days of Riemann and Cauchy and Weierstrass. Real analysis grew up as a way to make the calculus rigorous. Today the two subjects are intertwined in most people's minds. Yet calculus is only the first step of a long journey, and real analysis is one of the first great triumphs along that road. In real analysis we learn the rigorous theories of sequences and series, and the profound new insights that these tools make possible. We learn of the completeness of the real number system, and how this property makes the real numbers the natural set of limit points for the rational numbers. We learn of compact sets and uniform convergence. The great classical examples, such as the Weierstrass nowhere-differentiable function and the Cantor set, are part of the bedrock of the subject. Of course complete and rigorous treatments of the derivative and the integral are essential parts of this process. The Weierstrass approximation theorem, the Riemann integral, the Cauchy property for sequences, and many other deep ideas round out the picture of a powerful set of tools.:
Contents note
Basics -- Sets -- Operations on Sets -- Functions -- Operations on Functions -- Number Systems -- Countable and Uncountable Sets -- Sequences -- to Sequences -- Limsup and Liminf -- Some Special Sequences -- Series -- to Series -- Elementary Convergence Tests -- Advanced Convergence Tests -- Some Particular Series -- Operations on Series -- The Topology of the Real Line -- Open and Closed Sets -- Other Distinguished Points -- Bounded Sets -- Compact Sets -- The Cantor Set -- Connected and Disconnected Sets -- Perfect Sets -- Limits and the Continuity of Functions -- Definitions and Basic Properties -- Continuous Functions -- Topological Properties and Continuity -- Classifying Discontinuities and Monotonicity -- The Derivative -- The Concept of Derivative -- The Mean Value Theorem and Applications -- Further Results on the Theory of Differentiation -- The Integral -- The Concept of Integral -- Properties of the Riemann Integral -- Further Results on the Riemann Integral -- Advanced Results on Integration Theory -- Sequences and Series of Functions -- Partial Sums and Pointwise Convergence -- More on Uniform Convergence -- Series of Functions -- The Weierstrass Approximation Theorem -- Some Special Functions -- Power Series -- More on Power Series: Convergence Issues -- The Exponential and Trigonometric Functions -- Logarithms and Powers of Real Numbers -- The Gamma Function and Stirling’s Formula -- An Introduction to Fourier Series -- Advanced Topics -- Metric Spaces -- Topology in a Metric Space -- The Baire Category Theorem -- The Ascoli-Arzela Theorem -- Differential Equations -- Picard’s Existence and Uniqueness Theorem -- The Method of Characteristics -- Power Series Methods -- Fourier Analytic Methods -- Glossary of Terms from Real Variable Theory -- List of Notation -- Guide to the Literature.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-0-8176-8128-9
Links to Related Works
Subject References:
Differential equation
.
Fourier Analysis
.
Functional Analysis
.
Functions of real variables
.
Ordinary differential equations
.
Real Functions
.
Authors:
Krantz, Steven George 1951-
.
Corporate Authors:
SpringerLink (Online service)
.
Classification:
515.8
.
.
ISBD Display
Catalogue Record 46513
.
Tag Display
Catalogue Record 46513
.
Related Works
Catalogue Record 46513
.
Marc XML
Catalogue Record 46513
.
Add Title to Basket
Catalogue Record 46513
.
Catalogue Information 46513
Beginning of record
.
Catalogue Information 46513
Top of page
.
Download Title
Catalogue Record 46513
Export
This Record
As
Labelled Format
Bibliographic Format
ISBD Format
MARC Format
MARC Binary Format
MARCXML Format
User-Defined Format:
Title
Author
Series
Publication Details
Subject
To
File
Email
Reviews
This item has not been rated.
Add a Review and/or Rating
46513
1
46513
-
2
46513
-
3
46513
-
4
46513
-
5
46513
-
Quick Search
Search for