Mathematical Foundations · Differential Equations

Differential equations · Qualitative theory, nonlinear systems, and stability

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction General Theory of Dynamic Systems · Advanced Mathematical Analysis

Overview

Topics covered

  • Introduction
  • Differential Equations: Qualitative Theory, Nonlinear Systems and Stability
  • Historical perspective and qualitative motivation
  • Dynamic systems, flows and phase spaces
  • The Concept of Flow
  • Trajectories, Orbits and Limit Sets

Related concepts

Main connections

  • Calculus & differentiation
  • Linear algebra & matrices
  • Diagnostic test evaluation & ROC
  • Supervised machine learning
  • Bayes' theorem & priors

Compatible notation

Mathematical sample in LaTeX

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

x˙=dxdt=f(x),
View LaTeX source\dot{x} = \frac{\dd x}{\dd t} = f(x),