Mathematical Analysis · Sequences and Series of Functions · Introduction

Introduction

What this guide covers

The transition from the study of numerical sequences to that of sequences and series of functions constitutes one of the most important qualitative leaps in mathematical analysis. This development analyzes the logical and topological foundations of functional convergence, elucidating when it is possible to exchange the limit operations of integration, differentiation and infinite addition.

Overview

Topics covered

Introduction
Sequences and series of functions
Preliminaries and pointwise convergence
Uniform convergence
The rule of the supreme
Uniform convergence criteria

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

\forall x \in A, \ \forall \epsilon > 0, \ \exists N(\epsilon, x) \in \N \ \text{As such} \ \forall n \ge N(\epsilon, x) \implies |f_n(x) - f(x)| < \epsilon

View LaTeX source

\forall x \in A, \ \forall \epsilon > 0, \ \exists N(\epsilon, x) \in \N \ \text{As such} \ \forall n \ge N(\epsilon, x) \implies |f_n(x) - f(x)| < \epsilon