LEADER 03906nam 22006495 450 001 9910506382703321 005 20251204111431.0 010 $a9783030771393 010 $a3030771393 024 7 $a10.1007/978-3-030-77139-3 035 $a(CKB)5340000000068547 035 $a(MiAaPQ)EBC6792502 035 $a(Au-PeEL)EBL6792502 035 $a(OCoLC)1280604499 035 $a(PPN)25829681X 035 $a(BIP)81990544 035 $a(BIP)80071486 035 $a(DE-He213)978-3-030-77139-3 035 $a(EXLCZ)995340000000068547 100 $a20211025d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSharpening Mathematical Analysis Skills /$fby Alina Sīnt?m?rian, Ovidiu Furdui 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (543 pages) 225 1 $aProblem Books in Mathematics,$x2197-8506 311 08$a9783030771386 311 08$a3030771385 327 $aPreface -- Notations -- Sequences of Real Numbers -- Series of Real Numbers -- Power Series -- Derivatives and Applications -- Partial Derivatives and Applications -- Implicit Functions -- Challenges, Gems, and Mathematical Beauties -- An Artistry of Quadratic Series. Two New Proofs of Sandham-Yeung Series -- Solutions -- References -- Index. 330 $aThis book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research. The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory. Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions. Difficult problems have been structured in parts, helping the reader to find a solution. Challenges and open problems are scattered throughout the text, being an invitation to discover new original methodsfor proving known results and establishing new ones. The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers. In Part II, the reader will find solutions to the proposed exercises. Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren?t commonly seen in regular textbooks. . 410 0$aProblem Books in Mathematics,$x2197-8506 606 $aMathematical analysis 606 $aFunctions of real variables 606 $aSequences (Mathematics) 606 $aAnalysis 606 $aReal Functions 606 $aSequences, Series, Summability 615 0$aMathematical analysis. 615 0$aFunctions of real variables. 615 0$aSequences (Mathematics). 615 14$aAnalysis. 615 24$aReal Functions. 615 24$aSequences, Series, Summability. 676 $a515 700 $aSintamarian$b Alina$01072426 702 $aFurdui$b Ovidiu 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910506382703321 996 $aSharpening mathematical analysis skills$92900985 997 $aUNINA