03373nam a22003975i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024003500137082001200172100003400184245012400218264004600342300002100388336002600409337002600435338003600461347002400497490005100521505039700572520161800969650001702587650003502604650001702639650001402656650003302670700003002703710003402733773002002767776003602787830005102823856010102874978-0-387-98098-0DE-He21320260521092023.0cr nn 008mamaa100301s2010    xxu|    s    |||| 0|eng d  a9780387980980  a997803879809807 a10.1007/978-0-387-98098-02doi04a5152231 aDavidson, Kenneth R.eauthor.10aReal Analysis and Applicationsh[electronic resource] :bTheory in Practice /cby Kenneth R. Davidson, Allan P. Donsig. 1aNew York, NY :bSpringer New York,c2010.  bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aUndergraduate Texts in Mathematics,x0172-60560 aAnalysis -- Review -- The Real Numbers -- Series -- Topology of -- Functions -- Differentiation and Integration -- Norms and Inner Products -- Limits of Functions -- Metric Spaces -- Applications -- Approximation by Polynomials -- Discrete Dynamical Systems -- Differential Equations -- Fourier Series and Physics -- Fourier Series and Approximation -- Wavelets -- Convexity and Optimization.  aThis new approach to real analysis stresses the use of the subject in applications, showing how the principles and theory of real analysis can be applied in various settings. Applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and physics, Fourier series and approximation, wavelets, and convexity and optimization. Each chapter has many useful exercises. The treatment of the basic theory covers the real numbers, functions, and calculus, while emphasizing the role of normed vector spaces, and particularly of Rn. The applied chapters are mostly independent, giving the reader a choice of topics. This book is appropriate for students with a prior knowledge of both calculus and linear algebra who want a careful development of both analysis and its use in applications. Review of the previous version of this book, Real Analysis with Real Applications: "A well balanced book! The first solid analysis course, with proofs, is central in the offerings of any math.-dept.; ---and yet, the new books that hit the market don't always hit the mark: the balance between theory and applications, ---between technical proofs and intuitive ideas, ---between classical and modern subjects, and between real life exercises vs. the ones that drill a new concept. The Davidson-Donsig book is outstanding, and it does hit the mark." Palle E. T. Jorgenson, Review from Amazon.com Kenneth R. Davidson is University Professor of Mathematics at the University of Waterloo. Allan P. Donsig is Associate Professor of Mathematics at the University of Nebraska-Lincoln. 0aMATHEMATICS. 0aGLOBAL ANALYSIS (MATHEMATICS).14aMATHEMATICS.24aANALYSIS.24aAPPLICATIONS OF MATHEMATICS.1 aDonsig, Allan P.eauthor.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387980973 0aUndergraduate Texts in Mathematics,x0172-605640uhttp://dx.doi.org/10.1007/978-0-387-98098-0zVer el texto completo en las instalaciones del CICY