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Real Analysis Notes by Manonmaniam Sundaranar University
This note explains the following topics: Basic topology, Series, Continuity and Differentiation, The Riemann–Steiltjes integral and Sequences and series of function, Uniform Convergence and differentiation.
Author(s): Manonmaniam Sundaranar University
139 Pages
A Story of Real Analysis How We Got From There To Here
This note covers the following topics: Numbers, Real (R) and Rational (Q), Calculus in the 17th and 18th Centuries, Power Series, Convergence of Sequences and Series, The Taylor Series, Continuity, Intermediate and Extreme Values, From Fourier Series back to the Real Numbers.
Author(s): Robert Rogers and Eugene Boman
144 Pages
Introduction to Real Analysis by Liviu I. Nicolaescu
This note covers the following topics: mathematical reasoning, The Real Number System, Special classes of real numbers, Limits of sequences, Limits of functions, Continuity, Differential calculus, Applications of differential calculus, Integral calculus, Complex numbers and some of their applications, The geometry and topology of Euclidean spaces, Continuity, Multi-variable differential calculus, Applications of multi-variable differential calculus, Multidimensional Riemann integration, Integration over submanifolds.
Author(s): Liviu I. Nicolaescu
696 Pages
This note is an activity-oriented companion to the study of real analysis. It is intended as a pedagogical companion for the beginner, an introduction to some of the main ideas in real analysis, a compendium of problems, are useful in learning the subject, and an annotated reading or reference list. Topics covered includes: Sets, Functions, Cardinality, Groups, Vector Spaces, And Algebras, Partially Ordered Sets, The Real Numbers, Sequences And Indexed Families, Categories, Ordered Vector Spaces, Topological Spaces, Continuity And Weak Topologies, Normed Linear Spaces, Differentiation, Complete Metric Spaces, Algebras And Lattices Of Continuous Functions.
Author(s): John M. Erdman
265 Pages
Real Analysis Notes by Prof. Sizwe Mabizela
This note explains the following topics: Logic and Methods of Proof, Sets and Functions , Real Numbers and their Properties, Limits and Continuity, Riemann Integration, Introduction to Metric Spaces.
Author(s): Prof. Sizwe Mabizela
120 Pages
This note covers the following topics: Topology Preliminaries, Elements of Functional Analysis, Measure Theory, Integration Theory, Product Spaces, Analysis On Locally Compact Spaces, Introduction to Harmonic Analysis.
Author(s): Gabriel Nagy
NA Pages
Real Analysis by Dr. Maria Cristina Pereyra
This text is evolved from authors lecture notes on the subject, and thus is very much oriented towards a pedagogical perspective; much of the key material is contained inside exercises, and in many cases author chosen to give a lengthy and tedious, but instructive, proof instead of a slick abstract proof. Topics covered includes: The natural numbers, Set theory, Integers and rationals, The real numbers, Limits of sequences, Series, Infinite sets, Continuous functions on R, Differentiation of functions, The Riemann integral, the decimal system and basics of mathematical logic.
Author(s): Dr. Maria Cristina Pereyra
171 Pages
Real Analysis Guru Jambheshwar University
This note covers the following topics: Sequences and Series of Functions, Uniform Convergence, Power series, Linear transformations, Functions of several variables, Jacobians and extreme value problems, The Riemann-Stieltjes integrals, Measure Theory.
Author(s): Guru Jambheshwar University of Science and Technology, Hisar
132 Pages
A Radical Approach to Real Analysis (2nd edition)
This note covers the following topics: Crises in Mathematics: Fourier's Series, Infinite Summations, Differentiability and Continuity, The Convergence of Infinite Series, Understanding Infinite Series, Return to Fourier Series and Explorations of the Infinite.
Author(s): Macalester College
NA Pages
This note explains the following topics: Set Theory and the Real Numbers, Lebesgue Measurable Sets, Measurable Functions, Integration, Differentiation and Integration, The Classical Banach Spaces, Baire Category, General Topology, Banach Spaces, Fourier Series, Harmonic Analysis on R and S and General Measure Theory.
Author(s): Curtis T McMullen
140 Pages
This note covers the following topics: Mathematical proof, Sets, Relations, Functions, Dynamical Systems, Functions, Cardinal Number, Ordered sets and completeness, Metric spaces, Vector lattices, Measurable functions, Fubini’s theorem and Probability.
Author(s): William G. Faris
150 Pages
Notes in Introductory Real Analysis
This note covers the following topics related to Real Analysis: Ordered Fields and the Real Number System, Integration, The Extended Real Line and its Topology.
Author(s): Ambar N. Sengupta
123 Pages
Real Analysis Advanced Calculus
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Author(s): NA
NA Pages
Theory of Functions of Real Variable
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Author(s): NA
NA Pages
Real Analysis/Advanced Calculus(Santos D pdf)
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Author(s): NA
NA Pages
General Topology and Real Analysis
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