Initial due date: Sunday, April 9 at 11:59pm ET Overview This miniproject introduces a version of Euler's Method as a numerical solution technique for systems. Prerequisites: You will need to be comfortable with using Euler's method for single differential equations. You'll also benefit from some familiarity with spreadsheets or Python in order to automate the calculations. Background This tutorial gives you the background you need for this assignment. Please read it and make sure you understand the concepts and the example: https://github.com/RobertTalbert/linalg-diffeq/blob/main/assignments/Euler's_Method_for_Systems.ipynb
3/22/2023Initial due date: Sunday, March 26 at 11:59pm ET Overview Eigenvalues of a matrix are incredibly useful and important for many applications. (Some of these applications are in Miniprojects 1-3.) But computing eigenvalues of a matrix, even of relatively small size, can be difficult or impossible to do exactly. So we need numerical approximation methods for most practical uses of eigenvalues. This miniproject will teach you one such method. Prerequisites: You'll need to know what an eigenvalue and eigenvector for a matrix are, and how to find these using SymPy. You'll also need to know how to multiply matrices and vectors. Background Complete the following warmup exercises first. These don't go in your writeup. They are just here to teach you some terminology you'll need in the main assignment.
3/3/2023Initial due date: Sunday, March 12 at 11:59pm ET Overview In this miniproject, you'll apply concepts from linear algebra to study discrete dynamical systems. These are related to the idea of Markov chains that was the subject of Miniproject 1 and are the linear algebra analogue of systems of differential equations which we will study later. Prerequisites: You'll need to know what an eigenvalue and eigenvector for a matrix are, and how to find these using SymPy. This miniproject also requires some knowledge of matrix-vector multiplication. Background Complete the following before beginning this miniproject. These are not part of your writeup, but you'll need the knowledge before you can understand the tasks in the assignment.
2/21/2023Initial due date: Sunday, February 26 at 11:59pm ET Overview In this miniproject, you'll explore the concept of matrix transformations and use matrix transformations in $\mathbb{R}^3$ to create a very simple computer animation --- and see how linear algebra is used to make more complex animations happen. Prerequisites: You'll need to know how to multiply a $3 \times 3$ matrix to a $3 \times 1$ vector using SymPy, as well as what some of our recent theorems about matrices and invertibility say. Also, you'll need to do a bit of background learning using the video mentioned below. Background Complete the following before beginning this miniproject. These are not part of your writeup, but you'll need the knowledge before you can understand the tasks in the assignment.
2/9/2023