LEADER 04444nam 22007213u 450 001 9911007078403321 005 20230802010913.0 010 $a9780486134680 010 $a0486134687 010 $a9781621986324 010 $a1621986322 035 $a(CKB)2550000001186511 035 $a(EBL)1894799 035 $a(SSID)ssj0001002736 035 $a(PQKBManifestationID)12489502 035 $a(PQKBTitleCode)TC0001002736 035 $a(PQKBWorkID)11016505 035 $a(PQKB)10452345 035 $a(MiAaPQ)EBC1894799 035 $a(Au-PeEL)EBL1894799 035 $a(CaONFJC)MIL565882 035 $a(OCoLC)868272603 035 $a(Perlego)110847 035 $a(EXLCZ)992550000001186511 100 $a20141222d2012|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to Analysis 205 $a1st ed. 210 $aNewburyport $cDover Publications$d2012 215 $a1 online resource (455 p.) 225 1 $aDover Books on Mathematics 300 $aDescription based upon print version of record. 311 08$a9780486650388 311 08$a0486650383 311 08$a9781306346313 311 08$a1306346312 327 $aCover; Title Page; Copyright Page; Preface; Contents; Chapter I. Notions from Set Theory; 1. Sets and elements. Subsets; 2. Operations on sets; 3. Functions; 4. Finite and infinite sets; Problems; Chapter II. The Real Number System; 1. The field properties; 2. Order; 3. The least upper bound property; 4. The existence of square roots; Problems; Chapter III. Metric Spaces; 1. Definition of metric space. Examples; 2. Open and closed sets; 3. Convergent sequences; 4. Completeness; 5. Compactness; 6. Connectedness; Problems; Chapter IV. Continuous Functions 327 $a 1. Definition of continuity. Examples 2. Continuity and limits; 3. The continuity of rational operations. Functions with values in En; 4. Continuous functions on a compact metric space; 5. Continuous functions on a connected metric space; 6. Sequences of functions; Problems; Chapter V. Differentiation; 1. The definition of derivative; 2. Rules of differentiation; 3. The mean value theorem; 4. Taylor's theorem; Problems; Chapter VI. Riemann Integration; 1. Definitions and examples; 2. Linearity and order properties of the integral; 3. Existence of the integral 327 $a 4. The fundamental theorem of calculus 5. The logarithmic and exponential functions; Problems; Chapter VII. Interchange of Limit Operations; 1. Integration and differentiation of sequences of functions; 2. Infinite series; 3. Power series; 4. The trigonometric functions; 5. Differentiation under the integral sign; Problems; Chapter VIII. The Method of Successive Approximations; 1. The fixed point theorem; 2. The simplest case of the implicit function theorem; 3. Existence and uniqueness theorems for ordinary differential equations; Problems 327 $aChapter IX. Partial Differentiation 1. Definitions and basic properties; 2. Higher derivatives; 3. The implicit function theorem; Problems; Chapter X. Multiple Integrals; 1. Riemann integration on a closed interval in En. Examples and basic properties; 2. Existence of the integral. Integration on arbitrary subsets of En. Volume; 3. Iterated integrals; 4. Change of variable; Problems; Suggestions for Further Reading; Index 330 $a
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. Rigorous and carefully presented, the text assumes a year of calculus and features problems at the end of each chapter. 1968 edition.
410 0$aDover Books on Mathematics 606 $aMathematical analysis 606 $aMathematical analysis 606 $aEngineering & Applied Sciences$2HILCC 606 $aApplied Mathematics$2HILCC 615 4$aMathematical analysis. 615 0$aMathematical analysis. 615 7$aEngineering & Applied Sciences 615 7$aApplied Mathematics 676 $a515 700 $aRosenlicht$b Maxwell$041614 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9911007078403321 996 $aIntroduction to analysis$91427464 997 $aUNINA