# Monte Carlo Methods: Assignment 06
*Assigned 2023-10-10, due 2023-10-24 on Gradescope*
## Written
None.
## Coding
Download this Jupyter notebook: [download here](differential-equations.ipynb). In this week's coding assignment, you will implement a few methods discussed in class for numerically integrating PDEs and SDEs. All instructions are contained within text cells in the notebook. When you're done implementing all the specified functions in the notebook, submit your completed notebook on Gradescope **with all output left visible in the notebook**.
The questions are described on [this page](differential-equations.html).
To help you, here are the expected outputs of the notebook.
### Part 1, (1) and (2)
Numerical integration of an ODE representing a response to a signal.
Numerical integration of an ODE representing projectile motion.
### Part 1, (3)
### Part 2, (4)
The equilibrium solution of the heat equation on a 2D domain given some input and boundary conditions, solved two different ways: using a finite-difference scheme to solve a PDE, and using Euler-Maruyama to solve a corresponding SDE.
