LEADER 03383nam 22006015 450 001 9910299980103321 005 20200707021925.0 010 $a1-4939-1926-1 024 7 $a10.1007/978-1-4939-1926-0 035 $a(CKB)3710000000269597 035 $a(SSID)ssj0001372706 035 $a(PQKBManifestationID)11787128 035 $a(PQKBTitleCode)TC0001372706 035 $a(PQKBWorkID)11304846 035 $a(PQKB)10498736 035 $a(DE-He213)978-1-4939-1926-0 035 $a(MiAaPQ)EBC6312722 035 $a(MiAaPQ)EBC5595334 035 $a(Au-PeEL)EBL5595334 035 $a(OCoLC)894569962 035 $a(PPN)182098796 035 $a(EXLCZ)993710000000269597 100 $a20141017d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMore Calculus of a Single Variable /$fby Peter R. Mercer 205 $a1st ed. 2014. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2014. 215 $a1 online resource (XVI, 411 p. 60 illus.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4939-1925-3 327 $aPreface -- 1 The Real Numbers -- 2 Famous Inequalities -- 3 Continuous Functions -- 4 Differentiable Functions -- 5 The Mean Value Theorem -- 6 The Exponential Function -- 7 Other Mean Value Theorems -- 8 Convex Functions and Taylor's Theorem -- 9 Integration of Continuous Functions -- 10 The Fundamental Theorem of Calculus -- 11 Techniques of Integration -- 12 Classic Examples -- 13 Simple Quadrature Rules -- 14 Error Terms -- A The Proof of Theorem 9.1 -- Index. 330 $aThis book goes beyond the basics of a first course in calculus to reveal the power and richness of the subject. Standard topics from calculus ? such as the real numbers, differentiation and integration, mean value theorems, the exponential function ? are reviewed and elucidated before digging into a deeper exploration of theory and applications, such as the AGM inequality, convexity, the art of integration, and explicit formulas for ?. Further topics and examples are introduced through a plethora of exercises that both challenge and delight the reader. While the reader is thereby exposed to the many threads of calculus, the coherence of the subject is preserved throughout by an emphasis on patterns of development, of proof and argumentation, and of generalization. More Calculus of a Single Variable is suitable as a text for a course in advanced calculus, as a supplementary text for courses in analysis, and for self-study by students, instructors, and, indeed, all connoisseurs of ingenious calculations. 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 14$aAnalysis. 676 $a510 700 $aMercer$b Peter R$4aut$4http://id.loc.gov/vocabulary/relators/aut$0722025 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299980103321 996 $aMore calculus of a single variable$91410128 997 $aUNINA