Abstract Algebra Algebra Algebraic Geometry Algebraic Topology Applied Mathematics Arithmetic Geometry Basic Algebra Basic Mathematics Calculus Category Theory Classical Analysis Combinatorics Commutative Algebra Complex Algebra Complex Analysis Differential Algebra Differential Analysis Differential Calculus Differential Equations Differential Geometry Differential Topology Discrete Mathematics Elliptic Curves Fourier Analysis Functional Analysis Fractals Fractional Calculus Geometric Algebra Geometry Geometric Topology Groups Theory Graph Theory Harmonic Analysis Higher Algebra History of Mathematics Homological Algebra Integral Calculus K-theory Lie Algebra Linear Algebra Mathematical Analysis Mathematical Series Modern Geometry Multivairable Calculus Number Theory Numerical Analysis Probability Theory Real Analysis Rings and Fileds Riemannian Geometry Theorems in Calculus Topology Trigonometry Set Theory Constants & Numerical Sequences
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
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
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
Introduction to Real Analysis (William F. Trench PDF 583P)
This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Topics covered includes: Real Numbers, Differential Calculus of Functions of One Variable, Integral Calculus of Functions of One Variable, Infinite Sequences and Series, Vector-Valued Functions of Several Variables, Integrals of Functions of Several Variables and Metric Spaces.
Author(s): William F. Trench
583 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
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
Currently this section contains no detailed description for the page, will update this page soon.
Author(s): NA
NA Pages
This note covers the following topics: Metrics and norms, Convergence , Open Sets and Closed Sets, Continuity , Completeness , Connectedness , Compactness , Integration , Definition and basic properties of integrals, Integrals depending on a parameter.
Author(s): Yu. Safarov
31 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
Theory of Functions of Real Variable
Currently this section contains no detailed description for the page, will update this page soon.
Author(s): NA
NA Pages
General Topology and Real Analysis
Currently this section contains no detailed description for the page, will update this page soon.
Author(s): NA
NA PagesAdvertisement
