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
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, Bolzanoís 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.
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.
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.
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.
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.