Mathematical Foundations · Differential Calculus

Rigorous Mathematical Analysis: Theory and Computation of Limits of Functions

Public introduction · full guide in Eikos

Introduction

What this guide covers

A comprehensive, rigorous and formal examination of the topology of the real line, the definition of Cauchy-Weierstrass, the systematic resolution of algebraic and transcendent indeterminacies, and its application in the characterization of continuity.

Overview

Topics covered

  • Introduction
  • Limit Theory of Real Functions
  • Intuitive Concept and Historical Genesis
  • Epistemological Evolution of the Limit
  • The Intuitive Idea of Approach
  • The Formal Definition Epsilon-Delta ( - )

Related concepts

Main connections

  • Calculus & differentiation
  • Supervised machine learning

Compatible notation

Mathematical sample in LaTeX

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

f(x)=x2−1x−1
View LaTeX sourcef(x) = \frac{x^2 - 1}{x - 1}