/   Mathematics Books /

Real Analysis Books

Real Analysis Books

An Introduction to Real Analysis by Cesar O Angular

This note describes the following topics: preliminaries, The real numbers, Sequences, Limits of functions, Continuity, Differentiation, Riemann integration, Sequences of functions, Metric spaces, Multivariable differential calculus.

Author(s):

360Pages

Lecture Notes on Real Analysis by Xiaojing Ye

This note covers preliminaries, Measure and measurable sets, Measurable functions, Lebesgue integral, Signed measures and differentiations, Lp spaces and probability theory.

Author(s):

76Pages

Lecture Notes on Real Analysis by Nicolas Lerner

This note covers the following topics: Basic structures of topology and metrics, Basic tools of Functional Analysis, Theory of Distributions, Fourier Analysis, Analysis on Hilbert spaces.

Author(s):

170Pages

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):

696Pages

Companion to Real Analysis

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):

265Pages

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):

148Pages