Real Analysis Guru Jambheshwar University

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 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

Companion to Real Analysis

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

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

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

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

Introduction to Real Analysis I

This note explains the following topics: Real Numbers, Sequences, Series, The Topology of R, Limits of Functions, Differentiation, Integration, Sequences of Functions and Fourier Series.

Author(s): Lee Larson

NA Pages

Real Analysis Lecture Notes

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

Real Analysis Part I

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

A Little Real Analysis and Topology

This note covers the following topics: Intervals, Upper Bounds, Maximal Element, Least Upper Bound (supremum), Triangle Inequality, Cauchy-schwarz Inequality, Sequences and Limits, Functions and Point Set Topology.

Author(s): Arne Hallam

9 Pages

Real Analysis Advanced Calculus

Currently this section contains no detailed description for the page, will update this page soon.

Author(s): NA

NA Pages

Real Variables with Basic Metric Space Topology

This is a text in elementary real analysis. Topics covered includes: Upper and Lower Limits of Sequences of Real Numbers, Continuous Functions, Differentiation, Riemann-Stieltjes Integration, Unifom Convergence and Applications, Topological Results and Epilogue.

Author(s): Robert B. Ash

217 Pages

IRA Interactive Real Analysis(Wachsmuth B.G)

Currently this section contains no detailed description for the page, will update this page soon.

Author(s): NA

NA Pages

Real Analysis An Introduction(Wilde I.F)

Currently this section contains no detailed description for the page, will update this page soon.

Author(s): NA

NA Pages