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008			070612s2008 njua b 001 0 eng
010			_a 2007024690
015			_aGBA787064 _2bnb
016	7		_a014200662 _2Uk
020			_a9788126542376
035			_a(OCoLC)ocn144770075
040			_aDLC _cDLC _dBAKER _dBTCTA _dYDXCP _dUKM _dC#P _dIXA _dGZT _dNOR _dDLC
050	0	0	_aQA300 _b.S376 2008
082	0	0	_a515 _222 _bSCH-M
100	1		_aSchroder, Bernd S. W.
245	1	0	_aMathematical analysis : _ba concise introduction _cBernd S.W. Schroder.
260			_aHoboken, N.J. : _bWiley, _cc2008.
300			_axv, 562 p. : _bill. ; _c25 cm.
504			_aIncludes bibliographical references (p. 551-552) and index.
505	0	0	_tTable of contents -- _tPreface -- _gpt. 1. _tAnalysis of functions of a single real variable -- _g1. _tThe real numbers -- _g1.1. _tField axioms -- _g1.2. _tOrder axioms -- _g1.3. _tLowest upper and greatest lower bounds -- _g1.4. _tNatural numbers, integers, and rational numbers -- _g1.5. _tRecursion, induction, summations, and products -- _g2. _tSequences of real numbers -- _g2.1. _tLimits -- _g2.2. _tLimit laws -- _g2.3. _tCauchy sequences -- _g2.4. _tBounded sequences -- _g2.5. _tInfinite limits -- _g3. _tContinuous functions -- _g3.1. _tLimits of functions -- _g3.2. _tLimit laws -- _g3.3. _tOne-sided limits and infinite limits -- _g3.4. _tContinuity -- _g3.5. _tProperties of continuous functions -- _g3.6. _tLimits at infinity -- _g4. _tDifferentiable functions -- _g4.1. _tDifferentiability -- _g4.2. _tDifferentiation rules -- _g4.3. _tRolle's theorem and the mean value theorem -- _g5. _tThe Riemann integral 1 -- _g5.1. _tRiemann sums and the integral -- _g5.2. _tUniform continuity and integrability of continuous functions -- _g5.3. _tThe fundamental theorem of calculus -- _g5.4. _tThe Darboux integral --
505	0	0	_g6. _tSeries of real numbers 1 -- _g6.1. _tSeries as a vehicle to define infinite sums -- _g6.2. _tAbsolute convergence and unconditional convergence -- _g7. _tSome set theory -- _g7.1. _tThe algebra of sets -- _g7.2. _tCountable sets -- _g7.3. _tUncountable sets -- _g8. _tThe Riemann integral 2 -- _g8.1. _tOuter Lebesgue measure -- _g8.2. _tLebesgue's criterion for Riemann integrability -- _g8.3. _tMore integral theorems -- _g8.4. _tImproper Riemann integrals -- _g9. _tThe Lebesgue integral -- _g9.1. _tOuter Lebesgue measure -- _g9.2. _tLebesgue measurable sets -- _g9.2. _tLebesgue measurable functions -- _g9.3. _tLebesgue integration -- _g9.4. _tLebesgue integrals versus Riemann integrals-- _g10. _tSeries of real numbers 2 -- _g10.1. _tLimits superior and inferior -- _g10.2. _tThe root test and the ratio test -- _g10.3. _tPower series -- _g11. _tSequences of functions -- _g11.1. _tNotions of convergence -- _g11.2. _tUniform convergence -- _g12. _tTranscendental functions -- _g12.1. _tThe exponential function -- _g12.2. _tSine and cosine -- _g12.3. _tL'Hôpital's rule -- _g13. _tNumerical methods -- _g13.1. _tApproximation with Taylor polynomials -- _g13.2. _tNewton's method -- _g13.3. _tNumerical integration --
505	0	0	_gpt. 2. _tAnalysis in abstract spaces -- _g14. _tIntegration on measure spaces -- _g14.1. _tMeasure spaces -- _g14.2. _tOuter measures -- _g14.3. _tMeasurable functions -- _g14.4. _tIntegration of measurable functions -- _g14.5. _tMonotone and dominated convergence -- _g14.6. _tConvergence in mean, in measure, and almost everywhere -- _g14.7. _tProduct [sigma]-algebras -- _g14.8. _tProduct measures and Fubini's theorem -- _g15. _tThe abstract venues for analysis -- _g15.1. _tAbstraction 1 : Vector spaces -- _g15.2. _tRepresentation of elements : bases and dimension -- _g15.3. _tIdentification of spaces : isomorphism -- _g15.4. _tAbstraction 2 : inner product spaces -- _g15.5. _tNicer representations : orthonormal sets -- _g15.6. _tAbstraction 3 : normed spaces -- _g15.7. _tAbstraction 4 : metric spaces -- _g15.8. _tL[superscript]p spaces -- _g15.9. _tAnother number field : complex numbers -- _g16. _tThe topology of metric spaces -- _g16.1. _tConvergence of sequences -- _g16.2. _tCompleteness -- _g16.3. _tContinuous functions -- _g16.4. _tOpen and closed sets -- _g16.5. _tCompactness -- _g16.6. _tThe normed topology of R[superscript]d -- _g16.7. _tDense subspaces -- _g16.8. _tConnectedness -- _g16.9. _tLocally compact spaces --
505	0	0	_g17. _tDifferentiation in normed spaces -- _g17.1. _tContinuous linear functions -- _g17.2. _tMatrix representation of linear functions -- _g17.3. _tDifferentiability -- _g17.4. _tThe mean value theorem -- _g17.5. _tHow partial derivatives fit in -- _g17.6. _tMultilinear functions (tensors) -- _g17.7. _tHigher derivatives -- _g17.8. _tThe implicit function theorem -- _g18. _tMeasure, topology and differentiation -- _g18.1. _tLebesgue measurable sets in R[superscript]d -- _g18.2. _tC[infinity] and approximation of integrable functions -- _g18.3. _tTensor algebra and determinants -- _g18.4. _tMultidimensional substitution -- _g19. _tManifolds and integral theorems -- _g19.1. _tManifolds -- _g19.2. _tTangent spaces and differentiable functions -- _g19.3. _tDifferential forms, integrals over the unit cube -- _g19.4. _tk-forms and integrals over k-chains -- _g19.5. _tIntegration on manifolds -- _gg 19.6. _tStokes' theorem -- _g20. _tHilbert spaces -- _g20.1. _tOrthonormal bases -- _g20.2. _tFourier series -- _g20.3. _tThe Riesz representation theorem --
505	0	0	_gpt. 3. _tApplied analysis -- _g21. _tPhysics background -- _g21.1. _tHarmonic oscillators -- _g21.2. _tHeat and diffusion -- _g21.3. _tSeparation of variables, Fourier series, and ordinary differential equations -- _g21.4. _tMaxwell's equations -- _g21.5. _tThe Navier Stokes equation for the conservation of mass -- _g22. _tOrdinary differential equations -- _g22.1. _tBanach space valued differential equations -- _g22.2. _tAn existence and uniqueness theorem -- _g22.3. _tLinear differential equations -- _g23. _tThe finite element method -- _g23.1. _tRitz-Galerkin approximation -- _g23.2. _tWeakly differentiable functions -- _g23.3. _tSobolev spaces -- _g23.4. _tElliptic differential operators -- _g23.5. _tFinite elements -- _tConclusions and outlook -- _tAppendices -- _gA. _tLogic -- _gA.1. _tStatements -- _gA.2. _tNegations -- _gB. _tSet theory -- _gB.1. _tThe Zermelo-Fraenkel axioms -- _gB.2. _tRelations and functions -- _gC. _tNatural numbers, integers, and rational numbers -- _gC.1. _tThe natural numbers -- _gC.2. _tThe integers -- _gC.3. _tThe rational numbers -- _tBibliography -- _tIndex.
650		0	_aMathematical analysis.
856	4	1	_3Table of contents only _uhttp://www.loc.gov/catdir/toc/ecip0720/2007024690.html
856	4	2	_3Publisher description _uhttp://www.loc.gov/catdir/enhancements/fy0741/2007024690-d.html
856	4	2	_3Contributor biographical information _uhttp://www.loc.gov/catdir/enhancements/fy0806/2007024690-b.html
906			_a7 _bcbc _corignew _d1 _eecip _f20 _gy-gencatlg
942			_2ddc _cBK
999			_c9732 _d9732