Mathematical Foundations · Differential Equations

Differential Equations: PDEs and Diffusion Processes

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Mathematical Analysis · Differential Equations

Overview

Topics covered

  • Introduction
  • EDP and diffusion processes
  • Preliminaries: from EDOs to EDPs
  • Classification of second-order linear EDPs
  • The heat equation: physical deduction and conservation law
  • Analytical resolution techniques

Related concepts

Main connections

  • Calculus & differentiation
  • Mathematical expectation & moments
  • Linear algebra & matrices
  • Variance & standard deviation
  • Normal (Gaussian) distribution
  • Supervised machine learning

Compatible notation

Mathematical sample in LaTeX

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

Dαu(x)=∂|α|u(x)∂x1α1∂x2α2…∂xdαd
View LaTeX sourceD^\alpha u(x) = \frac{\pd^{|\alpha|} u(x)}{\pd x_1^{\alpha_1} \pd x_2^{\alpha_2} \dots \pd x_d^{\alpha_d}}