MARC Record from Library of Congress

LEADER: 03144cam a22002897a 4500
001 2011928556
003 DLC
005 20130518083125.0
008 110428s2011 nyua b 001 0 eng d
010 $a 2011928556
020 $a9780387721767 (hdbk. : acid-free paper)
020 $a0387721762 (hdbk. : acid-free paper)
020 $z9780387721774 (e-book)
020 $z0387721770 (e-book)
035 $a(OCoLC)ocn690089161
040 $aBTCTA$beng$cBTCTA$dYDXCP$dBWX$dMUU$dCDX$dCTN$dZWZ$dGYG$dTTU$dCWS$dNHA$dDLC
042 $alccopycat
050 00 $aQA241$b.B63 2011
100 1 $aBloch, Ethan D.,$d1956-
245 14 $aThe real numbers and real analysis /$cEthan D. Bloch.
260 $aNew York :$bSpringer,$cc2011.
300 $axxviii, 553 p. :$bill. ;$c24 cm.
504 $aIncludes bibliographical references (p. 539-543) and index.
505 00 $tConstruction of the real numbers: Introduction ; Entry 1: Axioms for the natural numbers ; Constructing the integers ; Entry 2: Axioms for the integers ; Constructing the rational numbers ; Dedekind cuts ; Constructing the real numbers ; Historical remarks --$tProperties of the real numbers: Introduction ; Entry 3: Axioms for the real numbers ; Algebraic properties of the real numbers ; Finding the natural numbers, the integers and the rational numbers in real numbers ; Induction and recursion in practice ; The least upper bound property and its consequences ; Uniqueness of the real numbers ; Decimal expansion of real numbers ; Historical remarks --$tLimits and continuity: Introduction ; Limits of functions ; Continuity ; Uniform continuity ; Two important theorems ; Historical remarks --$tDifferentiation: Introduction ; The derivative ; Computing derivatives ; The mean value theorem ; Increasing and decreasing functions, Part 1: Local and global extrema ; Increasing and decreasing functions, Part II: Further topics ; Historical remarks --$tIntegration: Introduction ; The Riemann integral ; Elementary properties of the Riemann integral ; Upper sums and lower sums ; Further properties of the Riemann integral ; Fundamental theorem of calculus ; Computing antiderivatives ; Lebesgue's theorem ; Area and arc length ; Historical remarks --$tLimits to infinity: Introduction ; Limits to infinity ; Computing limits to infinity ; Improper integrals ; Historical remarks -- Transcendental functions: Introduction ; Logarithmic and exponential functions ; Trigonometric functions ; More about [Pi] ; Historical remarks --$tSequences: Introduction ; Sequences ; Three important theorems ; Applications of sequences ; Historical remarks -- Series: Introduction ; Series ; Convergence tests ; Absolute convergence and conditional convergence ; Power series as functions ; Historical remarks --$tSequences and series of functions: Introduction ; Sequences of functions ; Series of functions ; Functions as power series ; A continuous but nowhere differentiable function ; Historical remarks.
650 0 $aNumbers, Real.
650 7 $aNombres réels.$2ram
776 08 $iElectronic version:$tReal numbers and real analysis.$dNew York : Springer, 2011$z9780387721774$w(OCoLC)725357389