An Introduction to Analysis - Hardcover

MIKUSINSKI, PIOTR; MIKUSINSKI, JAN

Hardcover

ISBN 10: 9813202610 ISBN 13: 9789813202610

Verlag: WSPC, 2017

Inhaltsangabe

Páginas:318Géneros:12:PBK:Calculus&mathematicalanalysis12:PBKA:Calculus12:PBKJ:Differentialcalculus&equationsSinopsis: ,Thebookcontainsarigorousexpositionofcalculusofasinglerealvariable.Itcoversthestandardtopicsofanintroductoryanalysiscourse,namely,functions,continuity,differentiability,sequencesandseriesofnumbers,sequencesandseriesoffunctions,andintegration.AdirecttreatmentoftheLebesgueintegral,basedsolelyontheconceptofabsolutelyconvergentseries,ispresented,whichisauniquefeatureofatextbookatthislevel.Thestandardmaterialiscomplementedbytopicsusuallynotfoundincomparabletextbooks,forexample,elementaryfunctionsarerigorouslydefinedandtheirpropertiesarecarefullyderivedandanintroductiontoFourierseriesispresentedasanexampleofapplicationoftheLebesgueintegral.Thetextisforapost-calculuscourseforstudentsmajoringinmathematicsormathematicseducation.Itwillprovidestudentswithasolidbackgroundforfurtherstudiesinanalysis,deepentheirunderstandingofcalculus,andprovidesoundtraininginrigorousmathematicalproof._,

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Críticas:

What I liked most about this book is its style, which renders difficult notions easy to grasp by students who followed a calculus course. Yet it gives easy proofs and shows different sides of mathematical analysis. I strongly recommend it to every college library. --MAA Reviews

Reseña del editor:

The book contains a rigorous exposition of calculus of a single real variable. It covers the standard topics of an introductory analysis course, namely, functions, continuity, differentiability, sequences and series of numbers, sequences and series of functions, and integration. A direct treatment of the Lebesgue integral, based solely on the concept of absolutely convergent series, is presented, which is a unique feature of a textbook at this level. The standard material is complemented by topics usually not found in comparable textbooks, for example, elementary functions are rigorously defined and their properties are carefully derived and an introduction to Fourier series is presented as an example of application of the Lebesgue integral.The text is for a post-calculus course for students majoring in mathematics or mathematics education. It will provide students with a solid background for further studies in analysis, deepen their understanding of calculus, and provide sound training in rigorous mathematical proof.

Über diese Auflage

• Verlag: WSPC
• Erscheinungsdatum: 2017
• ISBN 10: 9813202610
• ISBN 13: 9789813202610
• Einband: Tapa dura
• Anzahl der Seiten: 318