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Introduction to Real Analysis by Theodore Kilgore
This note explains the following topics: Integers and Rational Numbers, Building the real numbers, Series, Topological concepts, Functions, limits, and continuity, Cardinality, Representations of the real numbers, The Derivative and the Riemann Integral, Vector and Function Spaces, Finite Taylor-Maclaurin expansions, Integrals on Rectangles.
Author(s): Theodore Kilgor
352 Pages 
Real Analysis Lecture Notes by Itay Neeman
This note covers the following topics: Construction of the Real Line, Uniqueness of R and Basic General Topology, Completeness and Sequential Compactness, Convergence of Sums, Path-Connectedness, Lipschitz Functions and Contractions, and Fixed Point Theorems, Uniformity, Normed Spaces and Sequences of Functions, Arzela-Ascoli, Differentiation and Associated Rules, Applications of Differentiation, The Riemann Integral, Limits of Integrals, Mean Value Theorem for Integrals, and Integral Inequalities, Inverse Function Theorem, Implicit Function Theorem and Lagrange Multipliers, Multivariable Integration and Vector Calculus
Author(s): Itay Neeman
99 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
Spaces An Introduction to Real Analysis
This note explains the following topics: Preliminaries: Proofs, Sets, and Functions, The Foundation of Calculus, Metric Spaces, Spaces of Continuous Functions, Modes of continuity, Applications to differential equations, Applications to power series.
Author(s): Tom L. Lindstrom
148 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
Basic Analysis Introduction to Real Analysis
This book is a one semester course in basic analysis.It should be possible to use the book for both a basic course for students who do not necessarily wish to go to graduate school but also as a more advanced one-semester course that also covers topics such as metric spaces. Topics covered includes: Real Numbers, Sequences and Series, Continuous Functions, The Derivative, The Riemann Integral, Sequences of Functions and Metric Spaces.
Author(s): Jiri Lebl
243 Pages
The subject of real analysis is concerned with studying the behavior and properties of functions, sequences, and sets on the real number line, which we denote as the mathematically familiar R. This note explains the following topics: Continuous Functions on Intervals, Bolzano’s Intermediate Value Theorem, Uniform Continuity, The Riemann Integrals, Fundamental Theorems Of Calculus, Pointwise and Uniform Convergence, Uniform Convergence and Continuity, Series Of Functions, Improper Integrals of First Kind, Beta and Gamma Functions.
Author(s): Nandakumar, University of Calicut
145 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
An Introduction to Real Analysis
These lecture notes are an introduction to undergraduate real analysis. They cover the real numbers and one-variable calculus.
Author(s): John K. Hunter
269 Pages
This is a lecture notes on Distributions (without locally convex spaces), very basic Functional Analysis, Lp spaces, Sobolev Spaces, Bounded Operators, Spectral theory for Compact Self adjoint Operators and the Fourier Transform.
Author(s): Sigurd Angenent
107 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
General Topology and Real Analysis
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Author(s): NA
NA Pages
IRA Interactive Real Analysis(Wachsmuth B.G)
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Author(s): NA
NA PagesAdvertisement
