LEADER 03851nam  22006015  450 
001 996418272703316
005 20200714192934.0
010   $a3-030-46321-4
024 7 $a10.1007/978-3-030-46321-2
035   $a(CKB)4100000011343395
035   $a(DE-He213)978-3-030-46321-2
035   $a(MiAaPQ)EBC6264005
035   $a(PPN)258059559
035   $a(EXLCZ)994100000011343395
100   $a20200714d2020      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aFundamental Mathematical Analysis$b[electronic resource] /$fby Robert Magnus
205   $a1st ed. 2020.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020.
215   $a1 online resource (XX, 433 p. 35 illus., 11 illus. in color.) 
225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085
300   $aIncludes index.
311   $a3-030-46320-6 
327   $a1 Introduction -- 2 Real Numbers -- 3 Sequences and Series -- 4 Functions and Continuity -- 5 Derivatives and Differentiation -- 6 Integrals and Integration -- 7 The Elementary Transcendental Functions -- 8 The Techniques of Integration -- 9 Complex Numbers -- 10 Complex Sequences and Series -- 11 Function Sequences and Function Series -- 12 Improper Integrals -- Index.
330   $aThis textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout. Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of ?, Bernoulli numbers, and the Gamma function. Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.
410  0$aSpringer Undergraduate Mathematics Series,$x1615-2085
606   $aFunctions of real variables
606   $aSequences (Mathematics)
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171
606   $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
615  0$aFunctions of real variables.
615  0$aSequences (Mathematics).
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615 14$aReal Functions.
615 24$aSequences, Series, Summability.
615 24$aAnalysis.
676   $a515
700   $aMagnus$b Robert$4aut$4http://id.loc.gov/vocabulary/relators/aut$01012544
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996418272703316
996   $aFundamental Mathematical Analysis$92351474
997   $aUNISA