Differential Calculus: Mean Value Theorem and Function Analysis

Introduction

What this guide covers

An exhaustive and formal study of the local and global properties of real functions of a real variable. From the topological foundation of differentiability to the modeling of extremes, polynomial approximations and advanced numerical methods.

Overview

Topics covered

• Introduction
• Differential Calculus: Mean Value Theorems and Functional Analysis
• Continuity and Derivability
• The Structural Importance of Compactness
• Derivability in a Rigorous Analytical Sense
• Rolle's Theorem

Related concepts

Main connections

• Calculus & differentiation
• Mathematical optimization & gradients
• Supervised machine learning
• Bayes' theorem & priors

Compatible notation

Mathematical sample in LaTeX

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