Introduction to Real Analysis by Liviu I. Nicolaescu
Introduction to Real Analysis by Liviu I. Nicolaescu
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.
This note explains the following topics: Basic topology, Series,
Continuity and Differentiation, The Riemann–Steiltjes integral and Sequences and
series of function, Uniform Convergence and differentiation.
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.
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 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.
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 note explains the following
topics: Real Numbers, Sequences, Series, The Topology of R, Limits of Functions,
Differentiation, Integration, Sequences of Functions and Fourier Series.
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: 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.