# The Finite Difference Method

## First-Order Forward Difference Approximations

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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.

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Graduate Engineering Student @ Columbia University Brazilian Jiu-Jitsu Competitor & Coach https://romanmichaelpaolucci.github.io