02996nam 22006375 450 991029977440332120200705003445.03-319-13641-010.1007/978-3-319-13641-7(CKB)3710000000379575(SSID)ssj0001465514(PQKBManifestationID)11919366(PQKBTitleCode)TC0001465514(PQKBWorkID)11472153(PQKB)10977923(DE-He213)978-3-319-13641-7(MiAaPQ)EBC5610463(PPN)184888530(EXLCZ)99371000000037957520150321d2015 u| 0engurnn|008mamaatxtccrFrom Calculus to Analysis /by Steen Pedersen1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (XIX, 342 p. 48 illus., 14 illus. in color.) Bibliographic Level Mode of Issuance: Monograph3-319-13640-2 Part I -- Limits -- Introduction to Continuity -- Sets of Real Numbers -- Counting -- Continuity -- Derivatives and their Applications -- The Riemann Integral -- The Logarithm and the Exponential Function -- Part II -- Convergence of Sequences -- Series -- Trigonometric Functions and Applications -- Fourier Series -- Topology -- Appendices.This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers.  In addition to the standard results of advanced calculus, the book  contains several interesting applications of these results. The text is intended to form a bridge between calculus and analysis. It is based on the authors lecture notes used and revised nearly every year over the last decade. The book contains numerous illustrations and cross references throughout, as well as exercises with solutions at the end of each section.Integral equationsAlgebraMathematical analysisAnalysis (Mathematics)Integral Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12090Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Integral equations.Algebra.Mathematical analysis.Analysis (Mathematics).Integral Equations.Algebra.Analysis.512.9Pedersen Steenauthttp://id.loc.gov/vocabulary/relators/aut721072MiAaPQMiAaPQMiAaPQBOOK9910299774403321From calculus to analysis1522540UNINA