LEADER 04087nam 2200577 450 001 9910824454303321 005 20230120014458.0 010 $a1-4831-5896-9 035 $a(CKB)3710000000199651 035 $a(EBL)1901273 035 $a(SSID)ssj0001266966 035 $a(PQKBManifestationID)12443092 035 $a(PQKBTitleCode)TC0001266966 035 $a(PQKBWorkID)11269418 035 $a(PQKB)11114622 035 $a(MiAaPQ)EBC1901273 035 $a(EXLCZ)993710000000199651 100 $a20150123h19731973 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 13$aAn introduction to real analysis /$fDerek G. Ball 205 $aFirst edition. 210 1$aOxford, England :$cPergamon Press,$d1973. 210 4$dİ1973 215 $a1 online resource (324 p.) 225 1 $aCommonwealth and International Library. Mathematical Topics 300 $aIncludes index. 311 $a1-322-55591-5 311 $a0-08-016936-8 327 $aFront Cover; An Introduction to Real Analysis; Copyright Page; Table of Contents; PREFACE; INTRODUCTION. THE PURPOSE OF REAL ANALYSIS; CHAPTER 1. SETS, RELATIONS, AND FUNCTIONS; 1.1. Sets; 1.2. Relations and Functions; CHAPTER 2. NUMBERS; 2.1. Natural numbers; 2.2. Integers; 2.3. Rationals; 2.4. Real Numbers; 2.5. Irrationals; 2.6. Appendix; CHAPTER 3. SEQUENCES; 3.1. Introduction; 3.2. Limits of sequences; 3.3. Elementary theorems about sequences; 3.4. Behaviour of monotonie sequences; 3.5. Sequences defined by recurrence relations; 3.6. More sequences and their limits 327 $a3.7. Upper and lower limitsCHAPTER 4. SERIES; 4.1. Introduction; 4.2. Convergence of a series; 4.3. More series, convergent and divergent; 4.4 The comparison test; 4.5. Decimal representation; 4.6. Absolute convergence; 4.7. Conditional convergence; 4.8. Rearrangement of series; 4.9. Multiplication of series; CHAPTER 5. FUNCTIONS OF A REAL VARIABLE; 5.1. Introduction; 5.2. Limits; 5.3. Properties of limits; 5.4. Continuity; 5.5. The place of pathological functions in real analysis; 5.6. The nature of discontinuities; 5.7. Properties of continuous functions; CHAPTER 6. THE DERIVATIVE 327 $a6.1. Derivatives and their evaluation6.2. Rolle's theorem and the nature of the derivative; 6.3. Mean value theorems; 6.4. Applications of derivatives; 6.5. Taylor series; CHAPTER 7. SOME IMPORTANT FUNCTIONS AND EXPANSIONS; 7.1. Power series; 7.2. The exponential function; 7.3. Trigonometric functions; 7.4. Logarithmic functions; 7.5. Infinite products; 7.6. The binomial theorem; CHAPTER 8. THE RIEMANN INTEGRAL; 8.1. Introduction; 8.2. The Riemann integral; 8.3. Integrability of monotonic functions; 8.4. Continuous functions and the Riemann integral 327 $a8.5. Further applications of the fundamental theorem8.6. Alternative approach to the logarithmic function; 8.7. Infinite and improper integrals; 8.8 Volumes of revolution; ANSWERS AND HINTS; INDEX 330 $aAn Introduction to Real Analysis presents the concepts of real analysis and highlights the problems which necessitate the introduction of these concepts. Topics range from sets, relations, and functions to numbers, sequences, series, derivatives, and the Riemann integral. This volume begins with an introduction to some of the problems which are met in the use of numbers for measuring, and which provide motivation for the creation of real analysis. Attention then turns to real numbers that are built up from natural numbers, with emphasis on integers, rationals, and irrationals. The chapters tha 410 0$aCommonwealth and international library.$pMathematical topics. 606 $aMathematical analysis 606 $aNumbers, Real 615 0$aMathematical analysis. 615 0$aNumbers, Real. 676 $a515 700 $aBall$b Derek$f1942-$01610763 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910824454303321 996 $aAn introduction to real analysis$93938648 997 $aUNINA