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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis
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Real Analysis - Series, Functions of Several Variables, and Applications (Paperback, Softcover reprint of the original 1st ed. 2017)
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Real Analysis - Series, Functions of Several Variables, and Applications (Paperback, Softcover reprint of the original 1st ed. 2017)
Series: Undergraduate Texts in Mathematics
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This book develops the theory of multivariable analysis, building
on the single variable foundations established in the companion
volume, Real Analysis: Foundations and Functions of One Variable.
Together, these volumes form the first English edition of the
popular Hungarian original, Valos Analizis I & II, based on
courses taught by the authors at Eoetvoes Lorand University,
Hungary, for more than 30 years. Numerous exercises are included
throughout, offering ample opportunities to master topics by
progressing from routine to difficult problems. Hints or solutions
to many of the more challenging exercises make this book ideal for
independent study, or further reading. Intended as a sequel to a
course in single variable analysis, this book builds upon and
expands these ideas into higher dimensions. The modular
organization makes this text adaptable for either a semester or
year-long introductory course. Topics include: differentiation and
integration of functions of several variables; infinite numerical
series; sequences and series of functions; and applications to
other areas of mathematics. Many historical notes are given and
there is an emphasis on conceptual understanding and context, be it
within mathematics itself or more broadly in applications, such as
physics. By developing the student's intuition throughout, many
definitions and results become motivated by insights from their
context.
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