LEADER 04888nam 2200709 a 450 001 9911019659903321 005 20200520144314.0 010 $a9786613281142 010 $a9781283281140 010 $a1283281147 010 $a9781118096857 010 $a1118096851 010 $a9781118096864 010 $a111809686X 010 $a9781118096840 010 $a1118096843 035 $a(CKB)2550000000052915 035 $a(EBL)697633 035 $a(OCoLC)761321872 035 $a(SSID)ssj0000540647 035 $a(PQKBManifestationID)11925910 035 $a(PQKBTitleCode)TC0000540647 035 $a(PQKBWorkID)10586140 035 $a(PQKB)11126434 035 $a(MiAaPQ)EBC697633 035 $a(Perlego)1014043 035 $a(EXLCZ)992550000000052915 100 $a20110311d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aReal analysis $ea historical approach /$fSaul Stahl 205 $a2nd ed. 210 $aHoboken, N.J. $cWiley$d2011 215 $a1 online resource (316 p.) 225 1 $aPure and applied mathematics 300 $aDescription based upon print version of record. 311 08$a9780470878903 311 08$a0470878908 320 $aIncludes bibliographical references and index. 327 $aReal Analysis: A Historical Approach; Contents; Preface to the Second Edition; Acknowledgments; 1 Archimedes and the Parabola; 1.1 The Area of the Parabolic Segment; 1.2 The Geometry of the Parabola; 2 Fermat, Differentiation, and Integration; 2.1 Fermat's Calculus; 3 Newton's Calculus (Part 1); 3.1 The Fractional Binomial Theorem; 3.2 Areas and Infinite Series; 3.3 Newton's Proofs; 4 Newton's Calculus (Part 2); 4.1 The Solution of Differential Equations; 4.2 The Solution of Algebraic Equations; Chapter Appendix: Mathematica Implementations of Newton's Algorithm; 5 Euler 327 $a5.1 Trigonometric Series6 The Real Numbers; 6.1 An Informal Introduction; 6.2 Ordered Fields; 6.3 Completeness and Irrational Numbers; 6.4 The Euclidean Process; 6.5 Functions; 7 Sequences and Their Limits; 7.1 The Definitions; 7.2 Limit Theorems; 8 The Cauchy Property; 8.1 Limits of Monotone Sequences; 8.2 The Cauchy Property; 9 The Convergence of Infinite Series; 9.1 Stock Series; 9.2 Series of Positive Terms; 9.3 Series of Arbitrary Terms; 9.4 The Most Celebrated Problem; 10 Series of Functions; 10.1 Power Series; 10.2 Trigonometric Series; 11 Continuity; 11.1 An Informal Introduction 327 $a11.2 The Limit of a Function11.3 Continuity; 11.4 Properties of Continuous Functions; 12 Differentiability; 12.1 An Informal Introduction to Differentiation; 12.2 The Derivative; 12.3 The Consequences of Differentiability; 12.4 Integrability; 13 Uniform Convergence; 13.1 Uniform and Nonuniform, Convergence; 13.2 Consequences of Uniform Convergence; 14 The Vindication; 14.1 Trigonometric Series; 14.2 Power Series; 15 The Riemann Integral; 15.1 Continuity Revisited; 15.2 Lower and Upper Sums; 15.3 Integrability; Appendix A: Excerpts from ""Quadrature of the Parabola"" by Archimedes 327 $aAppendix B: On a Method for the Evaluation of Maxima and Minima by Pierre de FermatAppendix C: From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676) by Isaac Newton; Appendix D: From a Letter to Henry Oldenburg on the Binomial Series (October 24, 1676) by Isaac Newton; Appendix E: Excerpts from ""Of Analysis by Equations of an Infinite Number of Terms"" by Isaac Newton; Appendix F: Excerpts from ""Subsiduum Calculi Sinuum"" by Leonhard Euler; Solutions to Selected Exercises; Bibliography; Index 330 $a"Combining historical coverage with key introductory fundamentals, Real Analysis: A Historical Approach, Second Edition helps readers easily make the transition from concrete to abstract ideas when conducting analysis. Based on reviewer and user feedback, this edition features a new chapter on the Riemann integral including the subject of uniform continuity, as well as a discussion of epsilon-delta convergence and a section that details the modern preference for convergence of sequences over convergence of series. Both mathematics and secondary education majors will appreciate the focus on mathematicians who developed key concepts and the difficulties they faced"--$cProvided by publisher. 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aMathematical analysis 606 $aFunctions of real variables 615 0$aMathematical analysis. 615 0$aFunctions of real variables. 676 $a515/.8 686 $aMAT005000$2bisacsh 700 $aStahl$b Saul$0141807 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019659903321 996 $aReal analysis$94417500 997 $aUNINA