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.
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 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.
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.
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 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
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: 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 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: 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.