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Mathematical Foundations · Differential Equations

First-Order Ordinary Differential Equations · Rigor, Methods, and Applications

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Introduction Mathematical analysis and advanced calculus

Overview

Topics covered

  • Introduction
  • First Order Ordinary Differential Equations
  • Preliminaries and Fundamental Concepts
  • The Concept of Solution
  • Families of Curves and Singular Solutions
  • Theorem of Existence and Uniqueness (Picard-Lindelöf)

Related concepts

Main connections

  • Calculus & differentiation
  • Bayes' theorem & priors
  • Supervised machine learning

Compatible notation

Mathematical sample in LaTeX

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

F(x,y,dydx,d2ydx2,…,dnydxn)=0
View LaTeX sourceF\left(x, y, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\mathrm{d}^2 y}{\mathrm{d}x^2}, \dots, \frac{\mathrm{d}^n y}{\mathrm{d}x^n}\right) = 0