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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.