Preview this item
Preview this item
Checking...

# Limits : a new approach to real analysis

Author: Alan F Beardon New York ; Berlin [u.a.] : Springer, 1997. Undergraduate texts in mathematics. Print book : EnglishView all editions and formats By unifying and simplifying all the various notions of limit, the author has successfully presented a novel approach to the subject matter, which has not previously appeared in book form. (not yet rated) 0 with reviews - Be the first.

## Find a copy in the library

Finding libraries that hold this item...

## Details

Genre/Form: Lehrbuch Internet resource Book, Internet Resource Alan F Beardon Find more information about: Alan F Beardon 0387982744 9780387982748 247482995 IX, 189 S : graph. Darst. I Foundations.- 1 Sets and Functions.- 1.1 Sets.- 1.2 Ordered pairs.- 1.3 Functions.- 2 Real and Complex Numbers.- 2.1 Algebraic properties of real numbers.- 2.2 Order.- 2.3 Upper and lower bounds.- 2.4 Complex numbers.- 2.5 Notation.- II Limits.- 3 Limits.- 3.1 Introduction.- 3.2 Directed sets.- 3.3 The definition of a limit.- 3.4 Examples of limits.- 3.5 Sums, products, and quotients of limits.- 3.6 Limits and inequalities.- 3.7 Functions tending to infinity.- 4 Bisection Arguments.- 4.1 Nested intervals.- 4.2 The Intermediate Value Therem.- 4.3 The Mean Value Inequality.- 4.4 The Cauchy Criterion.- 5 Infinite Series.- 5.1 Infinite series.- 5.2 Unordered sums.- 5.3 Absolute convergence and rearrangements.- 5.4 The Cauchy Product.- 5.5 Iterated sums.- 6 Periodic Functions.- 6.1 The exponential function.- 6.2 The trigonometric functions.- 6.3 Periodicity and ?.- 6.4 The argument of a complex number.- 6.5 The logarithm.- III Analysis.- 7 Sequences.- 7.1 Convergent sequences.- 7.2 Some important examples.- 7.3 Bounded sequences.- 7.4 The Fundamental Theorem of Algebra.- 7.5 Unbounded sequences.- 7.6 Upper and lower limits.- 8 Continuous Functions.- 8.1 Continuous functions.- 8.2 Functions continuous on an interval.- 8.3 Monotonic functions.- 8.4 Uniform continuity.- 8.5 Uniform convergence.- 9 Derivatives.- 9.1 The derivative.- 9.2 The Chain Rule.- 9.3 The Mean Value Theorem.- 9.4 Inverse functions.- 9.5 Power series.- 9.6 Taylor series.- 10 Integration.- 10.1 The integral.- 10.2 Upper and lower integrals.- 10.3 Integrable functions.- 10.4 Integration and differentiation.- 10.5 Improper integrals.- 10.6 Integration and differentiation of series.- 11 ?, ?, e, and n!.- 11.1 The number e.- 11.2 The number ?.- 11.3 Euler's constant ?.- 11.4 Stirling's formula for n!.- 11.5 A series and an integral for ?.- Appendix: Mathematical Induction.- References. Undergraduate texts in mathematics. Alan F. Beardon.

## Reviews

User-contributed reviews

Be the first.

## Similar Items

### Related Subjects:(5)

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

### Related Entities

<http://dbpedia.org/resource/New_York_City> # New York
a schema:Place ;
schema:name "New York" ;
.

a bgn:PublicationSeries ;
schema:hasPart <http://www.worldcat.org/oclc/247482995> ; # Limits : a new approach to real analysis
schema:name "Undergraduate texts in mathematics." ;
schema:name "Undergraduate texts in mathematics" ;
.

<http://experiment.worldcat.org/entity/work/data/807141988#Topic/mathematical_analysis> # Mathematical analysis
a schema:Intangible ;
schema:name "Mathematical analysis" ;
.

<http://id.worldcat.org/fast/1012068> # Mathematical analysis
a schema:Intangible ;
schema:name "Mathematical analysis" ;
.

<http://viaf.org/viaf/29597515> # Alan F. Beardon
a schema:Person ;
schema:familyName "Beardon" ;
schema:givenName "Alan F." ;
schema:name "Alan F. Beardon" ;
.

<http://worldcat.org/isbn/9780387982748>
a schema:ProductModel ;
schema:isbn "0387982744" ;
schema:isbn "9780387982748" ;
.

Content-negotiable representations