Darlithoedd

Lecture 03

Summary.

  • Separable variables

  • Justification of the abuse of notation of considering \(\frac{\mathrm{d}y}{\mathrm{d}x}\) as a fraction

  • Examples

  • Homogeneous functions of degree \(n\)

  • Examples of such functions

Lecture 02

Summary.

  • Classification practice

  • Direct integration

  • General solutions and particular solutions

  • Observations from examples - an \(n\)th order ODE has at least \(n\) arbitrary constants in its general solution

  • Explicit and implicit solutions

  • Introduction to separable variables

Lecture 01

Summary.

  • How the module works

  • Why study differential equations?

  • Notation

  • What is a differential eqution?

  • Introducing classification: order, degree, and linearity