# The Finite Difference Method

## First-Order Forward Difference Approximations

Differential equations are great, many first year college math majors have absolutely no idea about the fun that will ensue. Nevertheless, as an (financial) engineer myself, I am biased toward approximation. In this article I will demonstrate the finite difference method as an effective way to approximate differential equations.

This article will be broken up into the following sections so browse freely…

**Analytical Solution to First Order Linear Differential Equations****Finite Difference Approximation (First Order Forward Difference)****Python Implementation and Visualization****Shameless Plug for****Quant Guild****Resources and Courses**

## Analytical Solution to First Order Linear Differential Equations

Yes I know, I don’t want to solve this analytically either. Whenever we see an equation of the following form

we have a first order linear differential equation. *P* and *Q *are arbitrary functions of *x*.

Here is a first order linear differential equation.

It almost looks exactly like the general form — that’s cause it is.