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In particular two books on the interesting history of mathematical analysis are listed. 2. Observe that. II X [a



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Mathematical analysis. 2. Functions of real variables. I. Title. II. Series: Pure and applied mathematics (John Wiley &. Sons: Unnumbered). QA300.F67 1999. 515 



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Jul 20 2020 Welcome to the first day of Real Analysis II



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mathematical theory and examples of its effective use in the solution of real problems of natural science. The textbook exposes classical analysis as it is ...



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integration for functions of a single real variable; Part II treats abstract spaces-topological spaces metric spaces



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MATH 36100: Real Analysis II Lecture Notes - Lewis University

Real Analysis is the formalizationof everything we learned in Calculus This enables you to make use of the examples andintuition from your calculus courses which may help you with your proofs Throughout thecourse we will be formally proving and exploring the inner workings of the Real NumberLine (hence the nameReal Analysis)



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2 Set Theory and the Real Numbers The foundations of real analysis are given by set theory and the notion of cardinality in set theory as well as the axiom of choice occur frequently in analysis Thus we begin with a rapid review of this theory For more details see e g [Hal] We then discuss the real numbers from both the axiomatic



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Goals The purpose of this course is three-fold: (1) to provide an introduction to the basic de?nitions and theo- rems of calculus and real analysis (2) to provide an introduction to writing and discovering proofs of mathematical theorems These proofs will go beyond the mechanical proofs found in your Discrete Mathematics course



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R = R+ [f0grepresents the set of non-negative real numbers R2 = R R is the set of ordered pairs of real numbers - also called the Cartesian plane In this book it is mostly used in reference to functions that map R to R:In subsequent study of real analysis Rn - ordered n-tuples of real numbers - take more central roles

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What are the major theorems of real analysis?

    Read and repeat proofs of the important theorems of Real Analysis: The Nested Interval Theorem The Bolzano-Weierstrass Theorem The Intermediate Value Theorem The Mean Value Theorem The Fundamental Theorem of Calculus Develop a library of the examples of functions, sequences and sets to help explainthe fundamental concepts of analysis.
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