Differential Equations Lecture 1

Convert bulk of handwritten notes from DE lecture one to markdown.

src/differential_equations_1.md

+---
+title: Differential Equations
+---
+
+# Differential equations
+
+A differential equation is any equation which involves both a function and some 
+derivative of that function. In this course we will be focusing on 
+*Ordinary Differential Equations*, meaning that our equations will involve 
+functions of one dependent variable and hence any derivatives will be full 
+derivatives. Equations which involve a function of several dependent variables
+and their partial derivatives are handled in courses on 
+*Partial Differential Equations*. 
+
+We consider functions $x(t)$ and define $\dot{x}(t)=\frac{dx}{dt}$, $x^{(n)}(t)=\frac{d^{n}x}{dt^{n}}$
+
+
+