Mathematical Foundations · Differential Calculus

Differential Calculus · Mathematical Optimization and Variational Methods

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Chart from the original guide

Overview

Topics covered

  • Introduction
  • Differential Calculus: Mathematical Optimization
  • Historical perspective and analytical foundations
  • Topological Fundamentals: Existence of Extremes
  • General theory in one-dimensional spaces ( )
  • Second and Higher Order Conditions

Related concepts

Main connections

  • Calculus & differentiation
  • Linear algebra & matrices
  • Supervised machine learning
  • Variance & standard deviation
  • Mathematical optimization & gradients
  • Conditional probability & independence

Compatible notation

Mathematical sample in LaTeX

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

f(𝐱*)≤f(𝐱)≤f(𝐱*),∀𝐱∈K.
View LaTeX sourcef(\mathbf{x}_*) \le f(\mathbf{x}) \le f(\mathbf{x}^*), \qquad \forall \mathbf{x} \in K.